Jeremy J. PiggottpersName, Colin R. TownsendpersName, Christoph D. MatthaeipersName (2015date). “Reconceptualizing synergism and antagonism among multiple stressors.” Ecology and Evolutiontitle·venue.
Object of study — TWO WORDS AND THE ARITHMETIC BEHIND THEM - 'synergismterm' and 'antagonismterm' as used for multiple-stressor interactions in ecology, where the same interaction can be both depending on which stressorterm you take as the reference
Research question — how to classify an interaction between two stressorsterm when their individual effects run in opposite directions, and the existing terms give opposite answers depending on the point of view
Contribution — a directional classification with five classes (+/- synergistic, +/- antagonistic, additive) built on an additive-effects model, a new class called MITIGATING SYNERGISMterm for reversed-and-enhanced effects, and a reclassification of Crain et al.'s 170-study dataset under it
phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | a pair of terms in universal use in a field with no committee to standardise them, whose meaning depends on the sign convention of the response variable — “Despite common use of “synergism” in the scientific literature, a consensus on its operational definition when classifying interactive effects is still lacking (Berenbaum 1989 ; Folt et al. 1999 ; Chou 2010 ; Dunne 2010 ; Vanhoudt et al. 2012 ). In the ecological multiple stressor context, the term most commonly relates to an additive effects model. Thus, synergism is used to define a cumulative effect of multiple stressors that are greater than the additive sum of effects produced by the stressors acting in isolation; this contrasts with the term “antagonism,” used to define a cumulative effect that is less than additive” | |
| claim-type | critique — “As an emerging field in ecology, there are increasing numbers of multiple stressor studies reporting synergisms and antagonisms that are based on imprecise descriptions or simply the judgment of the authors (Dunne 2010 ). These inconsistencies are aggravated by recent reviews and meta-analyses that define and measure these interactions differently and, therefore, are not comparative studies of any exact phenomenon” | |
| method — evidence | — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” | |
| object of study — evidence | — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” | |
| research question — evidence | — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” | |
| contribution — evidence | — “A potentially controversial aspect of the system is the inclusion of a further new class, which we call “mitigating synergism.” In this class, two stressors operating in the same direction create a cumulative effect completely opposite to what would have been predicted; that is, two positives make a negative (−S in “Double positive” row of Table 1 ) or two negatives make a positive (+S in “Double negative” row). Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressor effects in absolute terms.” | |
| mechanism | THE SAME 170 STUDIES, TWO DEFINITIONS, DIFFERENT ANSWERS: `this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% ANTAGONISM, 31% SYNERGISM, AND 26% ADDITIVE, versus Crain et al. (2008) 38% ANTAGONISM, 36% SYNERGISM, AND 26% additive based on an identical dataset.` Not two cohorts, not two instruments, not two decades - THE SAME DATA RECLASSIFIED. The cleanest demonstration in this corpus that a definition changes the number — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” | mechanisms[0] |
| mechanism | AND THE RECLASSIFICATION IS ITEMISED: `Of the 49 OPPOSING interactions classified by Crain et al., we reclassified three antagonisms as positive synergisms ... and eleven synergisms as positive antagonisms ... Thus, Crain et al.'s conceptualization of synergism and antagonism for interactions involving stressors with opposing individual effects UNDERREPRESENTED POSITIVE SYNERGISMS (because they were not possible) but OVERREPRESENTED NEGATIVE SYNERGISMS.` A class that could not be counted because the definition had no name for it — “Of the 49 opposing interactions classified by Crain et al. ( 2008 ), we reclassified three antagonisms as positive synergisms (enhanced positive effect when negative stressor present) and eleven synergisms as positive antagonisms (less positive than predicted additively, but less negative than the negative stressor alone). Thus, Crain et al.'s ( 2008 ) conceptualization of synergism and antagonism for interactions involving stressors with opposing individual effects underrepresented positive synergisms (because they were not possible) but overrepresented negative synergisms.” | mechanisms[1] |
| mechanism | AND THE TERM IS PARADOXICAL BY CONSTRUCTION: `for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa.` The same interaction carries both labels at once, and which one you report is a choice of reference point rather than a finding — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” | mechanisms[2] |
| mechanism | AND THE VERDICT FLIPS WITH THE SIGN CONVENTION OF THE RESPONSE VARIABLE: `This interactive pattern of leaf decay could be presented either positively (as rate of leaf mass loss) or negatively (as leaf mass remaining). Depending on which perspective was assumed in the analysis, one could conclude synergism for leaf mass remaining or antagonism for rate of loss, yet the interaction is clearly synergistic.` One measurement, two ways of writing it down, two opposite classifications - and no experiment can settle it — “Take the example of a data set for decomposition of leaf matter where nutrient enrichment alone accelerates decay while sediment addition alone slows decay, but both stressors in combination cause a decay rate even greater than with nutrient enrichment alone. This interactive pattern of leaf decay could be presented either positively (as rate of leaf mass loss) or negatively (as leaf mass remaining). Depending on which perspective was assumed in the analysis, one could conclude synergism for leaf mass remaining or antagonism for rate of loss, yet the interaction is clearly synergistic” | mechanisms[3] |
| mechanism | AND TWO META-ANALYSES DISAGREE BY SEVENTEEN POINTS FOR THE SAME REASON: `Holmstrup et al. (2010) reported synergisms in OVER HALF of their studies, whereas Darling and Cote (2008) reported synergisms in ONLY A third, most likely reflecting the upward bias of Holmstrup et al.'S DEFINITION OF SYNERGY VERSUS DARLING AND COTE'S DOWNWARD BIAS.` And the general form: `recent reviews and meta-analyses that define and measure these interactions differently and, therefore, are not comparative studies of any exact phenomenon` — “Not surprisingly, Holmstrup et al. ( 2010 ) reported synergisms in over half of their studies, whereas Darling and Cote ( 2008 ) reported synergisms in only a third, most likely reflecting the upward bias of Holmstrup et al.'s ( 2010 ) definition of synergy versus Darling and Cote's ( 2008 ) downward bias (a weakness of an additive effects model when individual effects are large or numerous; Folt et al. 1999 ).” | mechanisms[4] |
| mechanism | AND THE SAME PHENOMENON HAS ANOTHER FIELD'S NAME: `In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization. Chou (2010) argues that this interaction type IS NOT A TRUE SYNERGISM because it is `ONE-SIDED` and the underlying modes of action are different.` A cross-field renaming AND a dispute about whether the case falls under the term at all, in two sentences — “In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization (Odum and Barrett 2005 ). Chou ( 2010 ) argues that this interaction type is not a true synergism because it is “one-sided” and the underlying modes of action are different. If this perspective was to be generally accepted, the term synergy would only apply when both stressors operate in the same direction.” | mechanisms[5] |
| mechanism | AND A THIRD FIELD HAS A THIRD NAME FOR THE NEW CLASS: `In EPIDEMIOLOGICAL RESEARCH, such SO-CALLED CROSSOVER INTERACTIONS are considered the most statistically robust class of interaction because they indicate that risk factors flip from being disease predisposing in one background to protective in another. There is, however, DEEP CONTROVERSY surrounding the expected prevalence of such interactions between epidemiologists.` Ecology's `mitigating synergism` is epidemiology's `crossover interaction`, and the two fields disagree about how often it happens — “Moreover, such strong interactions may have the most interesting ecological consequences because they suggest that when both stressors act together, they synergistically mitigate or inhibit their individual effects even more than under control conditions (i.e., effect reversal with enhancement). In epidemiological research, such so-called crossover interactions are considered the most statistically robust class of interaction because they indicate that risk factors flip from being disease predisposing in one background to protective in another (Kendler and Gardner 2010 ). There is, however, deep controversy surrounding the expected prevalence of such interactions between epidemiologists” | mechanisms[6] |
| mechanism | AND THE PHENOMENON WAS OBSERVED BEFORE IT WAS NAMED: `A recent review ... by Strain et al. (2014) utilized a directional interaction classification that documented examples of mitigating synergisms, although they did not use the term. However, their approach neglected to distinguish antagonism in situations where stressor effects were opposing.` The instances were in the literature with nothing to call them - which is what a missing term looks like from outside — “A recent review of the interacting roles of stressors driving the global loss of canopy-forming to mat-forming algae in marine ecosystems by Strain et al. ( 2014 ) utilized a directional interaction classification that documented examples of mitigating synergisms, although they did not use the term. However, their approach neglected to distinguish antagonism in situations where stressor effects were opposing.” | mechanisms[7] |
| mechanism | AND A TERM IS REDEFINED TO REMOVE AN ASSUMPTION BURIED IN IT: `the term `STRESSOR` has frequently been used synonymously with `POLLUTION,` `POLLUTANTS,` OR `PRESSURES` on the assumption that the effects of a stressor imply `STRESS` and must therefore be exclusively detrimental. However, what is stressful or detrimental to one species in an ecosystem is likely to be beneficial to another ... Therefore, WE DEFINE A STRESSOR AS A VARIABLE THAT ... affects (whether negatively or positively)`. The word carried a sign, and the redefinition removes it — “In ecological research, the term “stressor” has frequently been used synonymously with “pollution,” “pollutants,” or “pressures” on the assumption that the effects of a stressor imply “stress” and must therefore be exclusively detrimental (Folt et al. 1999 ). However, what is stressful or detrimental to one species in an ecosystem is likely to be beneficial to another, either directly or via species interactions. Moreover, stressor responses may follow a subsidy-stress gradient, as observed, for example, for stream taxa in relation to dissolved nutrient concentration (Niyogi et al. 2007 ). Therefore, we define a stressor as a variable that, as a result of human activity, exceeds its range of normal variation and affects (whether negatively or positively) individual taxa, community composition, or ecosystem functioning relative to a reference condition” | mechanisms[8] |
| mechanism | AND ANOTHER GROUP SOLVED THE SAME PROBLEM BY INVENTING ITS OWN VOCABULARY: `Vanhoudt et al. (2012) applied THEIR OWN DEFINITIONS of synergism and antagonism based on `Concentration Addition` or `Independent Action` toxicological models. Due to the lack of support for either of these models, the authors then devised their own simplifying terminology to give an overview of their results as `POSITIVE INTERACTIONS` (describing additive, synergism, `superaddition,` `potentiation,` or `increased effects`), `NEGATIVE INTERACTIONS` (loosely, antagonism), or no interactions.` Five terms collapsed into one, because none of them could be measured — “Acknowledging these differences of interpretation, Vanhoudt et al. ( 2012 ) applied their own definitions of synergism and antagonism based on “Concentration Addition” or “Independent Action” toxicological models. Due to the lack of support for either of these models, the authors then devised their own simplifying terminology to give an overview of their results as “positive interactions” (describing additive, synergism, “superaddition,” “potentiation,” or “increased effects”), “negative interactions” (loosely, antagonism), or no interactions.” | mechanisms[9] |
| contradicts | Crain, Kroeker & Halpern (2008), Ecology Letters 11:1304 - specifically their assumption that with opposing individual effects synergy occurs only when the cumulative effect is more negative than the additive sum. Reclassifying THEIR OWN 170-study dataset under the directional scheme gives 43/31/26 against their 38/36/26 — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” | claim_relations[0] |
| extends | Strain et al. (2014), which documented examples of mitigating synergism without a term for them and did not distinguish antagonism where stressor effects oppose — “A recent review of the interacting roles of stressors driving the global loss of canopy-forming to mat-forming algae in marine ecosystems by Strain et al. ( 2014 ) utilized a directional interaction classification that documented examples of mitigating synergisms, although they did not use the term. However, their approach neglected to distinguish antagonism in situations where stressor effects were opposing.” | claim_relations[1] |
| sense | `synergism` (prevailing ecological sense) - `a cumulative effect of multiple stressors that are greater than the additive sum of effects produced by the stressors acting in isolation`, with `antagonism` for less than additive — “Despite common use of “synergism” in the scientific literature, a consensus on its operational definition when classifying interactive effects is still lacking (Berenbaum 1989 ; Folt et al. 1999 ; Chou 2010 ; Dunne 2010 ; Vanhoudt et al. 2012 ). In the ecological multiple stressor context, the term most commonly relates to an additive effects model. Thus, synergism is used to define a cumulative effect of multiple stressors that are greater than the additive sum of effects produced by the stressors acting in isolation; this contrasts with the term “antagonism,” used to define a cumulative effect that is less than additive” | senses[0] |
| sense | `synergism` (Crain et al. 2008, opposing stressors) - synergy `only occurs when the cumulative effect is more negative than the additive sum of the opposing individual effects` - which makes positive synergism unnameable and therefore uncountable — “Of the 49 opposing interactions classified by Crain et al. ( 2008 ), we reclassified three antagonisms as positive synergisms (enhanced positive effect when negative stressor present) and eleven synergisms as positive antagonisms (less positive than predicted additively, but less negative than the negative stressor alone). Thus, Crain et al.'s ( 2008 ) conceptualization of synergism and antagonism for interactions involving stressors with opposing individual effects underrepresented positive synergisms (because they were not possible) but overrepresented negative synergisms.” | senses[1] |
| sense | `potentiation` / `sensitization` (TOXICOLOGY) - the same one-sided interaction ecology would call synergism; Chou (2010) holds it is `not a true synergism` because the modes of action differ — “In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization (Odum and Barrett 2005 ). Chou ( 2010 ) argues that this interaction type is not a true synergism because it is “one-sided” and the underlying modes of action are different. If this perspective was to be generally accepted, the term synergy would only apply when both stressors operate in the same direction.” | senses[2] |
| sense | `crossover interaction` (EPIDEMIOLOGY) - the same effect-reversal ecology now calls `mitigating synergism`, and there it is `the most statistically robust class of interaction` — “Moreover, such strong interactions may have the most interesting ecological consequences because they suggest that when both stressors act together, they synergistically mitigate or inhibit their individual effects even more than under control conditions (i.e., effect reversal with enhancement). In epidemiological research, such so-called crossover interactions are considered the most statistically robust class of interaction because they indicate that risk factors flip from being disease predisposing in one background to protective in another (Kendler and Gardner 2010 ). There is, however, deep controversy surrounding the expected prevalence of such interactions between epidemiologists” | senses[3] |
| sense | `stressor` (this paper) - `a variable that, as a result of human activity, exceeds its range of normal variation and affects (whether negatively or positively) individual taxa, community composition, or ecosystem functioning relative to a reference condition` - against the prior usage as a synonym for pollution — “In ecological research, the term “stressor” has frequently been used synonymously with “pollution,” “pollutants,” or “pressures” on the assumption that the effects of a stressor imply “stress” and must therefore be exclusively detrimental (Folt et al. 1999 ). However, what is stressful or detrimental to one species in an ecosystem is likely to be beneficial to another, either directly or via species interactions. Moreover, stressor responses may follow a subsidy-stress gradient, as observed, for example, for stream taxa in relation to dissolved nutrient concentration (Niyogi et al. 2007 ). Therefore, we define a stressor as a variable that, as a result of human activity, exceeds its range of normal variation and affects (whether negatively or positively) individual taxa, community composition, or ecosystem functioning relative to a reference condition” | senses[4] |
| sense | `mitigating synergism` (new here) - `two stressors operating in the same direction create a cumulative effect completely opposite to what would have been predicted`: two positives make a negative, or two negatives make a positive — “A potentially controversial aspect of the system is the inclusion of a further new class, which we call “mitigating synergism.” In this class, two stressors operating in the same direction create a cumulative effect completely opposite to what would have been predicted; that is, two positives make a negative (−S in “Double positive” row of Table 1 ) or two negatives make a positive (+S in “Double negative” row). Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressor effects in absolute terms.” | senses[5] |
| control | applying the new directional classification to the SAME dataset Crain et al. (2008) used, rather than to a new one — held — “Of the 49 opposing interactions classified by Crain et al. ( 2008 ), we reclassified three antagonisms as positive synergisms (enhanced positive effect when negative stressor present) and eleven synergisms as positive antagonisms (less positive than predicted additively, but less negative than the negative stressor alone). Thus, Crain et al.'s ( 2008 ) conceptualization of synergism and antagonism for interactions involving stressors with opposing individual effects underrepresented positive synergisms (because they were not possible) but overrepresented negative synergisms.” — rules out a difference in prevalence caused by different studies rather than by different definitions — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” | controls[0] |
| control | an additive effects model as the null, chosen for consistency with the prevailing definition of synergy and with ANOVA — partial — “Acknowledging these differences of interpretation, Vanhoudt et al. ( 2012 ) applied their own definitions of synergism and antagonism based on “Concentration Addition” or “Independent Action” toxicological models. Due to the lack of support for either of these models, the authors then devised their own simplifying terminology to give an overview of their results as “positive interactions” (describing additive, synergism, “superaddition,” “potentiation,” or “increased effects”), “negative interactions” (loosely, antagonism), or no interactions.” — rules out a classification whose null model differs from the one the field's statistics already assume — “The approach is potentially adaptable for testing against a multiplicative model (i.e., log additive; Folt et al. 1999 ). However, in this case, we recommend following the advice of Folt et al. ( 1999 ) that nonadditive responses should not be called synergisms or antagonisms so as to avoid confusion with the additive model.” | controls[1] |
| control | reporting the directional class (+S, -S, +A, -A) alongside the direction-independent one — held — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” — rules out the loss of information that makes a positive synergism unnameable and therefore uncountable — “Of the 49 opposing interactions classified by Crain et al. ( 2008 ), we reclassified three antagonisms as positive synergisms (enhanced positive effect when negative stressor present) and eleven synergisms as positive antagonisms (less positive than predicted additively, but less negative than the negative stressor alone). Thus, Crain et al.'s ( 2008 ) conceptualization of synergism and antagonism for interactions involving stressors with opposing individual effects underrepresented positive synergisms (because they were not possible) but overrepresented negative synergisms.” | controls[2] |
| weight | Crain, Kroeker & Halpern (2008), Ecology Letters 11:1304 - specifically their assumption that with opposing individual effects synergy occurs only when the cumulative effect is more negative than the additive sum. Reclassifying THEIR OWN 170-study dataset under the directional scheme gives 43/31/26 against their 38/36/26 — 0.95 — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” | claim_relations[0] |
| weight | Strain et al. (2014), which documented examples of mitigating synergism without a term for them and did not distinguish antagonism where stressor effects oppose — 0.85 — “A recent review of the interacting roles of stressors driving the global loss of canopy-forming to mat-forming algae in marine ecosystems by Strain et al. ( 2014 ) utilized a directional interaction classification that documented examples of mitigating synergisms, although they did not use the term. However, their approach neglected to distinguish antagonism in situations where stressor effects were opposing.” | claim_relations[1] |
| audit | synergism —renamed-across-fields→ potentiation — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span reports toxicology's name 'potentiation' and Chou's argument that it is not true synergism; contested. — “In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization (Odum and Barrett 2005 ). Chou ( 2010 ) argues that this interaction type is not a true synergism because it is “one-sided” and the underlying modes of action are different. If this perspective was to be generally accepted, the term synergy would only apply when both stressors operate in the same direction.” | concept_edges[0] |
| note | synergism —renamed-across-fields→ potentiation — 'In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization. Chou (2010) argues that this interaction type IS NOT A TRUE SYNERGISM because it is ONE-SIDED and the underlying modes of action are different.' Weight 0.9: it is a renaming AND a contested one, in the same two sentences - toxicology does not merely use a different word, it denies the ecological word applies — “In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization (Odum and Barrett 2005 ). Chou ( 2010 ) argues that this interaction type is not a true synergism because it is “one-sided” and the underlying modes of action are different. If this perspective was to be generally accepted, the term synergy would only apply when both stressors operate in the same direction.” | concept_edges[0] |
| relation | synergism —renamed-across-fields→ potentiation — the one-sided interaction ecology calls SYNERGISM is called POTENTIATION or SENSITIZATION in toxicology - and one toxicologist denies it is synergism at all — “In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization (Odum and Barrett 2005 ). Chou ( 2010 ) argues that this interaction type is not a true synergism because it is “one-sided” and the underlying modes of action are different. If this perspective was to be generally accepted, the term synergy would only apply when both stressors operate in the same direction.” — “In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization (Odum and Barrett 2005 ). Chou ( 2010 ) argues that this interaction type is not a true synergism” | concept_edges[0] |
| weight | synergism —renamed-across-fields→ potentiation — 0.9 — “In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization (Odum and Barrett 2005 ). Chou ( 2010 ) argues that this interaction type is not a true synergism because it is “one-sided” and the underlying modes of action are different. If this perspective was to be generally accepted, the term synergy would only apply when both stressors operate in the same direction.” | concept_edges[0] |
| note | synergism —distinct-from→ antagonism — 'the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa.' The edge records a distinction the paper argues is not stably drawable - and the leaf-decay worked example shows the verdict flipping when the same data is written as mass remaining rather than rate of loss. distance 354 characters, the largest on any edge I have merged, and it is honest: the contrast is carried by the SENTENCE STRUCTURE ('what is X to one ... is Y to the other'), not by a cue sitting between the arguments. The nearest DIFFERENTIATION cue is the opening 'While'. Weight stays at 0.95 because the paper asserts the relation outright - the distance measures the CUE, not the claim — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” | concept_edges[1] |
| relation | synergism —distinct-from→ antagonism — the two labels are opposites that the SAME interaction carries simultaneously when the individual stressor effects oppose each other — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa.” | concept_edges[1] |
| weight | synergism —distinct-from→ antagonism — 0.95 — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” | concept_edges[1] |
| note | mitigating synergism —distinct-from→ antagonism — 'Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic ... would be misleading in our view because the magnitude of the interaction effect is greater than one would predict.' Weight 0.85: the paper itself calls the class 'potentially controversial' and states the opposing reading before rejecting it — “A potentially controversial aspect of the system is the inclusion of a further new class, which we call “mitigating synergism.” In this class, two stressors operating in the same direction create a cumulative effect completely opposite to what would have been predicted; that is, two positives make a negative (−S in “Double positive” row of Table 1 ) or two negatives make a positive (+S in “Double negative” row). Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressor effects in absolute terms.” | concept_edges[2] |
| relation | mitigating synergism —distinct-from→ antagonism — the new class looks like antagonism (effects reversed) but is classed as synergism because the interaction effect is GREATER THAN predicted — “A potentially controversial aspect of the system is the inclusion of a further new class, which we call “mitigating synergism.” In this class, two stressors operating in the same direction create a cumulative effect completely opposite to what would have been predicted; that is, two positives make a negative (−S in “Double positive” row of Table 1 ) or two negatives make a positive (+S in “Double negative” row). Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressor effects in absolute terms.” — “Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressor effects in absolute terms.” | concept_edges[2] |
| weight | mitigating synergism —distinct-from→ antagonism — 0.85 — “A potentially controversial aspect of the system is the inclusion of a further new class, which we call “mitigating synergism.” In this class, two stressors operating in the same direction create a cumulative effect completely opposite to what would have been predicted; that is, two positives make a negative (−S in “Double positive” row of Table 1 ) or two negatives make a positive (+S in “Double negative” row). Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressor effects in absolute terms.” | concept_edges[2] |
| outcome | control — held — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” — “Of the 49 opposing interactions classified by Crain et al. ( 2008 ), we reclassified three antagonisms as positive synergisms (enhanced positive effect when negative stressor present) and eleven synergisms as positive antagonisms (less positive than predicted additively, but less negative than the negative stressor alone). Thus, Crain et al.'s ( 2008 ) conceptualization of synergism and antagonism for interactions involving stressors with opposing individual effects underrepresented positive synergisms (because they were not possible) but overrepresented negative synergisms.” | controls[0] |
| outcome | control — partial — “The approach is potentially adaptable for testing against a multiplicative model (i.e., log additive; Folt et al. 1999 ). However, in this case, we recommend following the advice of Folt et al. ( 1999 ) that nonadditive responses should not be called synergisms or antagonisms so as to avoid confusion with the additive model.” — “Acknowledging these differences of interpretation, Vanhoudt et al. ( 2012 ) applied their own definitions of synergism and antagonism based on “Concentration Addition” or “Independent Action” toxicological models. Due to the lack of support for either of these models, the authors then devised their own simplifying terminology to give an overview of their results as “positive interactions” (describing additive, synergism, “superaddition,” “potentiation,” or “increased effects”), “negative interactions” (loosely, antagonism), or no interactions.” | controls[1] |
| outcome | control — held — “Of the 49 opposing interactions classified by Crain et al. ( 2008 ), we reclassified three antagonisms as positive synergisms (enhanced positive effect when negative stressor present) and eleven synergisms as positive antagonisms (less positive than predicted additively, but less negative than the negative stressor alone). Thus, Crain et al.'s ( 2008 ) conceptualization of synergism and antagonism for interactions involving stressors with opposing individual effects underrepresented positive synergisms (because they were not possible) but overrepresented negative synergisms.” — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” | controls[2] |
| limitation | THE FIELD REPORTS THESE TERMS WITHOUT DEFINING THEM: `there are increasing numbers of multiple stressor studies reporting synergisms and antagonisms that are based on imprecise descriptions or simply the judgment of the authors. These inconsistencies are aggravated by recent reviews and meta-analyses that define and measure these interactions differently and, therefore, are not comparative studies of any exact phenomenon.` The strongest sentence in this corpus about what a shared word without a shared definition does to a literature — “As an emerging field in ecology, there are increasing numbers of multiple stressor studies reporting synergisms and antagonisms that are based on imprecise descriptions or simply the judgment of the authors (Dunne 2010 ). These inconsistencies are aggravated by recent reviews and meta-analyses that define and measure these interactions differently and, therefore, are not comparative studies of any exact phenomenon” | limitations[0] |
| limitation | AND THE FIELD IS BIASED IN THE DIRECTION IT LOOKS: `This is particularly pertinent given the bias toward investigating and reporting adverse multiple stressor effects (i.e., double-negative interaction type) in ecology.` The class frequencies are conditioned on which interactions anybody bothered to study, and the paper says so in the sentence that reports them — “Our finding that the representation of interaction classes varied markedly by interaction type highlights the need to consider the direction of individual stressor effects when determining the occurrence of synergisms and antagonisms. This is particularly pertinent given the bias toward investigating and reporting adverse multiple stressor effects (i.e., double-negative interaction type) in ecology” | limitations[1] |
| limitation | AND THE NEW CLASS IS CONCEDED TO BE ARGUABLE: `Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view.` The objection is stated in the paper's own words before anyone else can make it — “A potentially controversial aspect of the system is the inclusion of a further new class, which we call “mitigating synergism.” In this class, two stressors operating in the same direction create a cumulative effect completely opposite to what would have been predicted; that is, two positives make a negative (−S in “Double positive” row of Table 1 ) or two negatives make a positive (+S in “Double negative” row). Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressor effects in absolute terms.” | limitations[2] |
| limitation | and a method imported from another field carries that field's assumptions: `isobolographic analysis ... seems of limited utility in many ecological contexts because it relies on establishing multiple levels of dose-concentration relationships ... and is further limited by implicitly assuming synergy only when effects are negative, reflecting its toxicological origins.` The instrument's home discipline is inside the instrument — “Alternative approaches for inferring synergism and antagonism utilizing isobolographic analysis exist in the fields of pharmacology, toxicology, and pathology (Nelson and Kursar 1999 ). While isobolographic analysis presents some key advantages over additive and multiplicative models (see Dunne 2010 ), it seems of limited utility in many ecological contexts because it relies on establishing multiple levels of dose–concentration relationships (a substantial ecological challenge in itself) and is further limited by implicitly assuming synergy only when effects are negative, reflecting its toxicological origins.” | limitations[3] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” | content_tags.findings[0] |
| finding | — “Of the 49 opposing interactions classified by Crain et al. ( 2008 ), we reclassified three antagonisms as positive synergisms (enhanced positive effect when negative stressor present) and eleven synergisms as positive antagonisms (less positive than predicted additively, but less negative than the negative stressor alone). Thus, Crain et al.'s ( 2008 ) conceptualization of synergism and antagonism for interactions involving stressors with opposing individual effects underrepresented positive synergisms (because they were not possible) but overrepresented negative synergisms.” | content_tags.findings[1] |
| finding | — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” | content_tags.findings[2] |
| finding | — “Take the example of a data set for decomposition of leaf matter where nutrient enrichment alone accelerates decay while sediment addition alone slows decay, but both stressors in combination cause a decay rate even greater than with nutrient enrichment alone. This interactive pattern of leaf decay could be presented either positively (as rate of leaf mass loss) or negatively (as leaf mass remaining). Depending on which perspective was assumed in the analysis, one could conclude synergism for leaf mass remaining or antagonism for rate of loss, yet the interaction is clearly synergistic” | content_tags.findings[3] |
| finding | — “Not surprisingly, Holmstrup et al. ( 2010 ) reported synergisms in over half of their studies, whereas Darling and Cote ( 2008 ) reported synergisms in only a third, most likely reflecting the upward bias of Holmstrup et al.'s ( 2010 ) definition of synergy versus Darling and Cote's ( 2008 ) downward bias (a weakness of an additive effects model when individual effects are large or numerous; Folt et al. 1999 ).” [ATTRIBUTED TO A CITED AUTHOR, NOT THIS PAPER] the paper’s own words: “Holmstrup et al. ( 2010 ) reported” | content_tags.findings[4] |
| finding | — “As an emerging field in ecology, there are increasing numbers of multiple stressor studies reporting synergisms and antagonisms that are based on imprecise descriptions or simply the judgment of the authors (Dunne 2010 ). These inconsistencies are aggravated by recent reviews and meta-analyses that define and measure these interactions differently and, therefore, are not comparative studies of any exact phenomenon” | content_tags.findings[5] |
| quantity | 43% antagonism, 31% synergism, 26% additive — — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” | content_tags.quantities[0] |
| quantity | 38% antagonism, 36% synergism, 26% additive — — “Together with our reclassification of four double-positive antagonisms as negative synergisms, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonism, 31% synergism, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonism, 36% synergism, and 26% additive based on an identical dataset.” | content_tags.quantities[1] |
| quantity | 3 antagonisms became positive synergisms; 11 synergisms became positive antagonisms, of 49 — — “Of the 49 opposing interactions classified by Crain et al. ( 2008 ), we reclassified three antagonisms as positive synergisms (enhanced positive effect when negative stressor present) and eleven synergisms as positive antagonisms (less positive than predicted additively, but less negative than the negative stressor alone). Thus, Crain et al.'s ( 2008 ) conceptualization of synergism and antagonism for interactions involving stressors with opposing individual effects underrepresented positive synergisms (because they were not possible) but overrepresented negative synergisms.” | content_tags.quantities[2] |
| quantity | over half (Holmstrup 2010) versus only a third (Darling and Cote 2008) — — “Not surprisingly, Holmstrup et al. ( 2010 ) reported synergisms in over half of their studies, whereas Darling and Cote ( 2008 ) reported synergisms in only a third, most likely reflecting the upward bias of Holmstrup et al.'s ( 2010 ) definition of synergy versus Darling and Cote's ( 2008 ) downward bias (a weakness of an additive effects model when individual effects are large or numerous; Folt et al. 1999 ).” [ATTRIBUTED TO A CITED AUTHOR, NOT THIS PAPER] the paper’s own words: “Holmstrup et al. ( 2010 ) reported” | content_tags.quantities[3] |
| variable | cumulative effect — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” | content_tags.variables[0] |
| definition | synergism — “Despite common use of “synergism” in the scientific literature, a consensus on its operational definition when classifying interactive effects is still lacking (Berenbaum 1989 ; Folt et al. 1999 ; Chou 2010 ; Dunne 2010 ; Vanhoudt et al. 2012 ). In the ecological multiple stressor context, the term most commonly relates to an additive effects model. Thus, synergism is used to define a cumulative effect of multiple stressors that are greater than the additive sum of effects produced by the stressors acting in isolation; this contrasts with the term “antagonism,” used to define a cumulative effect that is less than additive” | content_tags.definitions[0] |
| definition | stressor — “In ecological research, the term “stressor” has frequently been used synonymously with “pollution,” “pollutants,” or “pressures” on the assumption that the effects of a stressor imply “stress” and must therefore be exclusively detrimental (Folt et al. 1999 ). However, what is stressful or detrimental to one species in an ecosystem is likely to be beneficial to another, either directly or via species interactions. Moreover, stressor responses may follow a subsidy-stress gradient, as observed, for example, for stream taxa in relation to dissolved nutrient concentration (Niyogi et al. 2007 ). Therefore, we define a stressor as a variable that, as a result of human activity, exceeds its range of normal variation and affects (whether negatively or positively) individual taxa, community composition, or ecosystem functioning relative to a reference condition” | content_tags.definitions[1] |
| definition | mitigating synergism — “A potentially controversial aspect of the system is the inclusion of a further new class, which we call “mitigating synergism.” In this class, two stressors operating in the same direction create a cumulative effect completely opposite to what would have been predicted; that is, two positives make a negative (−S in “Double positive” row of Table 1 ) or two negatives make a positive (+S in “Double negative” row). Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressor effects in absolute terms.” | content_tags.definitions[2] |
| concept | synergism — not defined in this paper's own words; a cumulative effect greater than the additive sum - and, for opposing stressors, a label that depends on which stressor is the reference — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” | concepts[0] |
| concept | antagonism — not defined in this paper's own words; a cumulative effect less than the additive sum, and the label the same interaction carries from the other stressor's point of view — “While the identification of a synergism or antagonism is generally straightforward when both stressors operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergism seems paradoxical because what is synergistic to one stressor's effect direction is antagonistic to the other stressor's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effect relative to the individual stressor effects in absolute terms.” | concepts[1] |
| concept | potentiation — not defined in this paper's own words; toxicology's name for the one-sided interaction ecology calls synergism — “In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiation or sensitization (Odum and Barrett 2005 ). Chou ( 2010 ) argues that this interaction type is not a true synergism because it is “one-sided” and the underlying modes of action are different. If this perspective was to be generally accepted, the term synergy would only apply when both stressors operate in the same direction.” | concepts[2] |
| concept | mitigating synergism — not defined in this paper's own words; the new class: effects reversed AND enhanced - two positives making a negative, or two negatives a positive — “A potentially controversial aspect of the system is the inclusion of a further new class, which we call “mitigating synergism.” In this class, two stressors operating in the same direction create a cumulative effect completely opposite to what would have been predicted; that is, two positives make a negative (−S in “Double positive” row of Table 1 ) or two negatives make a positive (+S in “Double negative” row). Some might argue that such a pattern is the clearest example of antagonism because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressor effects in absolute terms.” | concepts[3] |
| concept | stressor — not defined in this paper's own words; redefined here to allow beneficial effects, against a usage that made 'stressor' a synonym for pollution — “In ecological research, the term “stressor” has frequently been used synonymously with “pollution,” “pollutants,” or “pressures” on the assumption that the effects of a stressor imply “stress” and must therefore be exclusively detrimental (Folt et al. 1999 ). However, what is stressful or detrimental to one species in an ecosystem is likely to be beneficial to another, either directly or via species interactions. Moreover, stressor responses may follow a subsidy-stress gradient, as observed, for example, for stream taxa in relation to dissolved nutrient concentration (Niyogi et al. 2007 ). Therefore, we define a stressor as a variable that, as a result of human activity, exceeds its range of normal variation and affects (whether negatively or positively) individual taxa, community composition, or ecosystem functioning relative to a reference condition” | concepts[4] |
| concept | additive effects model — not defined in this paper's own words; the null model the classification is built on, chosen for consistency with the prevailing definition and with ANOVA — “Despite common use of “synergism” in the scientific literature, a consensus on its operational definition when classifying interactive effects is still lacking (Berenbaum 1989 ; Folt et al. 1999 ; Chou 2010 ; Dunne 2010 ; Vanhoudt et al. 2012 ). In the ecological multiple stressor context, the term most commonly relates to an additive effects model. Thus, synergism is used to define a cumulative effect of multiple stressors that are greater than the additive sum of effects produced by the stressors acting in isolation; this contrasts with the term “antagonism,” used to define a cumulative effect that is less than additive” | concepts[5] |
| additive model | — “The approach is potentially adaptable for testing against a multiplicative model (i.e., log additive; Folt et al. 1999 ). However, in this case, we recommend following the advice of Folt et al. ( 1999 ) that nonadditive responses should not be called synergisms or antagonisms so as to avoid confusion with the additive model.” | content_tags.statistics[0] |
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Ecol Evol Ecol Evol 1740 ece ece3 Ecology and Evolution 2045-7758 Wiley PMC4395182 PMC4395182.1 4395182 4395182 25897392 10.1002/ece3.1465 1 Original Research Reconceptualizing synergismterm and antagonismterm among multiple stressorsterm PiggottpersName Jeremy J TownsendpersName Colin R MatthaeipersName Christoph D Department of Zoology, University of Otago P.O. Box 56, Dunedin, 9054, New Zealand Correspondence Jeremy J. PiggottpersName, Department of Zoology, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand., Tel: +64 3 4795855;, Fax: +64 3 4797584;, E-mail: jeremy.piggottpersName@otago.ac.nz Funding Information Funding was provided by New Zealand's Ministry of Business, Innovation and Employment contract C01X1005.
4 2015 11 3 2015 5 7 251772 1538 1547 02 2 2015 22 2 2015 01 04 2015 20 04 2015 08 07 2023 © 2015 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd. 2015 https://creativecommons.org/licenses/by/4.0/ This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. The potential for complex synergistic or antagonistic interactions between multiple stressorsterm presents one of the largest uncertainties when predicting ecological change but, despite common use of the terms in the scientific literature, a consensus on their operational definition is still lacking. The identification of synergismterm or antagonismterm is generally straightforward when stressorsterm operate in the same direction, but if individual stressorterm effects oppose each other, the definition of synergismterm is paradoxical because what is synergistic to one stressorterm's effect direction is antagonistic to the others. In their highly cited meta-analysis, Crain et al. ( Ecology Letters , 11, 2008: 1304) assumed in situations with opposing individual effects that synergy only occurs when the cumulative effectterm·var is more negative than the additive sum of the opposing individual effects. We argue against this and propose a new systematic classification based on an additive effects modelterm that combines the magnitude and response direction of the cumulative effectterm·var and the interaction effect. A new class of “mitigating synergismterm” is identified, where cumulative effectsterm·var are reversed and enhanced. We applied our directional classification to the dataset compiled by Crain et al. ( Ecology Letters, 11, 2008: 1304) to determine the prevalence of synergistic, antagonistic, and additive interactions. Compared to their original analysis, we report differences in the representation of interaction classes by interaction type and we document examples of mitigating synergismterm, highlighting the importance of incorporating individual stressorterm effect directions in the determination of synergismsterm and antagonismsterm. This is particularly pertinent given a general bias in ecology toward investigating and reporting adverse multiple stressorterm effects (double negative). We emphasize the need for reconsideration by the ecological community of the interpretation of synergismterm and antagonismterm in situations where individual stressorterm effects oppose each other or where cumulative effectsterm·var are reversed and enhanced.
Antagonismterm ecological surprise interaction stressorterm synergismterm pmc-status-qastatus 0 pmc-status-live yes pmc-status-embargo no pmc-status-released yes pmc-prop-open-access yes pmc-prop-olf no pmc-prop-manuscript no pmc-prop-legally-suppressed no pmc-prop-has-pdf yes pmc-prop-has-supplement yes pmc-prop-pdf-only no pmc-prop-suppress-copyright no pmc-prop-is-real-version no pmc-prop-is-scanned-article no pmc-prop-preprint no pmc-prop-in-epmc yes pmc-license-ref CC BY Introduction The potential for complex synergistic or antagonistic interactions between multiple stressorsterm presents one of the largest uncertainties when predicting ecological change (Sala et al. 2000 ; MEA 2005 ; Mothersill et al. 2007 ; Darling and Cote 2008 ). Despite common use of “synergismterm” in the scientific literature, a consensus on its operational definition when classifying interactive effects is still lacking (Berenbaum 1989 ; Folt et al. 1999 ; Chou 2010 ; Dunne 2010 ; Vanhoudt et al. 2012 ). In the ecological multiple stressorterm context, the term most commonly relates to an additive effects modelterm. Thus, synergismterm is used to define a cumulative effectterm·var of multiple stressorsterm that are greater than the additive sum of effects produced by the stressorsterm acting in isolation; this contrasts with the term “antagonismterm,” used to define a cumulative effectterm·var that is less than additive (Hay et al. 1994 ; Hay 1996 ; Folt et al. 1999 ).
In ecological research, the term “stressorterm” has frequently been used synonymously with “pollution,” “pollutants,” or “pressures” on the assumption that the effects of a stressorterm imply “stress” and must therefore be exclusively detrimental (Folt et al. 1999 ). However, what is stressful or detrimental to one species in an ecosystem is likely to be beneficial to another, either directly or via species interactions. Moreover, stressorterm responses may follow a subsidy-stress gradient, as observed, for example, for stream taxa in relation to dissolved nutrient concentration (Niyogi et al. 2007 ). Therefore, we define a stressorterm as a variable that, as a result of human activity, exceeds its range of normal variation and affects (whether negatively or positively) individual taxa, community composition, or ecosystem functioning relative to a reference condition (e.g., modified after Breitburg et al. 1999a ; Crain et al. 2008 ; TownsendpersName et al. 2008 ).
In their highly cited synthesis of 170 studies manipulating pairs of stressorsterm in marine and coastal ecosystems, Crain et al. ( 2008 ) conceptualized three broad categories of interaction type based on the directions of individual stressorterm effects: The two individual stressorsterm operate negatively (double negative), positively (double positive), or with opposing (one positive and one negative) individual effects relative to control conditions (Fig. 1 ). While the identification of a synergismterm or antagonismterm is generally straightforward when both stressorsterm operate in the same direction (i.e., double positive or double negative; Folt et al. 1999 ; Dunne 2010 ), for opposing individual effects, the definition of synergismterm seems paradoxical because what is synergistic to one stressorterm's effect direction is antagonistic to the other stressorterm's effect direction and vice versa. Note that from a purely mathematical perspective, this is not a paradox because synergy can be defined in either direction determined by a larger positive or negative cumulative effectterm·var relative to the individual stressorterm effects in absolute terms. Given the lack of consensus regarding these terms, Crain et al. ( 2008 ) assumed that in situations where two individual stressorsterm oppose each other, synergy only occurs when the cumulative effectterm·var is more negative than the additive sum of the opposing individual effects (see Fig. 1 ii). While this may be appropriate in situations where the effect direction is implicitly negative (e.g., decreased survival rate), such a definition is problematic from an ecological perspective because effect direction is entirely context dependent. Take the example of a data set for decomposition of leaf matter where nutrient enrichment alone accelerates decay while sediment addition alone slows decay, but both stressorsterm in combination cause a decay rate even greater than with nutrient enrichment alone. This interactive pattern of leaf decay could be presented either positively (as rate of leaf mass loss) or negatively (as leaf mass remaining). Depending on which perspective was assumed in the analysis, one could conclude synergismterm for leaf mass remaining or antagonismterm for rate of loss, yet the interaction is clearly synergistic (as measured by the magnitude of the cumulative effectterm·var).
Figure 1 Redrawn from Crain et al. ( 2008 ). Conceptual approach to interpreting interaction types from response data presented in factorial studies. Treatments in factorial studies include control (CT), with stressorterm A (A), with stressorterm B (B), and with both stressorsterm (A + B). Interaction types are classified as additive, synergistic, and antagonistic, depending on the A + B response compared to the additive sum (AD) of individual effects for stressorterm A (a), B (b) relative to the control (CT). The three plots show interaction types that have double-negative (i), opposing (ii), and double-positive (iii) individual stressorterm effects on the response variable of interest.
The assumption of synergy when the cumulative effectterm·var is more negative than the additive sum of the opposing individual effects raises a further conceptual issue, because this pattern does not necessarily mean the cumulative effectterm·var of the opposing stressorsterm is more negative than the single negative stressorterm acting alone (equivalent to the “comparative effects” model of Folt et al. 1999 ). This can be illustrated by the following theoretical example: a positive stressorterm individually has an effect of +1, a negative stressorterm individually has an effect of −1, and the additive cumulative effectterm·var of both stressorsterm combined is 0 (i.e., they counteract each other). In this situation, Crain et al. ( 2008 ) would invoke synergy for any cumulative effectterm·var more negative than 0. But if the cumulative effectterm·var is between −1 and 0, this outcome is intuitively antagonistic from the perspective of the negative stressorterm's individual effect (i.e., the cumulative effectterm·var of both stressorsterm is less negative than the single negative stressorterm acting alone).
In toxicology, in contrast to ecological usage, if one chemical is rendered more effective by the presence of another that has no effect or a different effect on its own, the interaction is called potentiationterm or sensitization (Odum and Barrett 2005 ). Chou ( 2010 ) argues that this interaction type is not a true synergismterm because it is “one-sided” and the underlying modes of action are different. If this perspective was to be generally accepted, the term synergy would only apply when both stressorsterm operate in the same direction.
To resolve the issues raised above (stressorterm effects may be detrimental or beneficial, difficulty in defining synergy when individual effects are opposing), we believe an alternative system is needed that systematically classifies synergismsterm in any directional context as measured by the magnitude of the cumulative effectterm·var compared to the individual stressorterm effects.
A new directional interaction classification for ecological data We propose a classification system based on an additive effects modelterm that combines the magnitude and response direction (+ or −) of the cumulative effectterm·var (effect of combined stressorsterm relative to control) and interaction effect (effect deviation from the additive modelterm·stat prediction) to determine synergismterm and antagonismterm relative to individual stressorterm effects in absolute terms (Fig. 2 ). Selection of an additive effects modelterm is consistent with the prevailing definition of synergy and the use of ANOVA as the statistical analysis of choice for response data presented in factorial studies (Quinn and Keough 2002 ; Dunne 2010 ). In this directional classification system, the meanings of the words synergismterm and antagonismterm respectively translate to “more-than” or “less-than” predicted additively in absolute terms (i.e., with the stated direction; PiggottpersName et al. 2015a , b ).
Figure 2 Our conceptual approach to interpreting interaction types from data presented in factorial studies determined from the magnitude and direction of the cumulative effectterm·var and interaction effect in absolute terms. Treatments in factorial studies include control (CT), with stressorterm A (A), with stressorterm B (B), and with both stressorsterm (A + B). Directional interaction classes are additive (AD), +synergistic (+S), −synergistic (−S), +antagonistic (+A) and -antagonistic (−A) that vary depending on A + B compared to the additive sum (AD) of individual effects for stressorterm A (a), B (b) relative to the control (CT). The three plots show interaction types that have double-negative (i), opposing (ii), and double-positive (iii) individual stressorsterm effects on the response variable of interest. (X) indicates that an interaction class is not applicable for the interaction type in question. Figure based on a reanalysis of the database of Crain et al. ( 2008 ).
An additive effect (i.e., no significant interaction in ANOVA) represents the sum of the individual effects that may arise from double-positive effects (e.g., +1 + 1 = 2 for an effect of one for each stressorterm), double-negative effects (−1 + −1 = −2), or opposing effects (−1 + 1 = 0).
An interaction that deviates from additive (i.e., a significant two-factor interaction term in ANOVA) and is less than the sum of the individual effects or less-than-or-equal-to any individual effect in the same direction is positive antagonistic (+A; less positive than predicted additively) when +1 + 1 = 0 < (+A) < 2 or −1 + 1 = −1 ≤ (+A) < 0, or negative antagonistic (−A; less negative than predicted additively) when −1 + −1 = −2 < (−A)<0 or −1 + 1 = 0 < (−A) ≤ 1.
A deviation from additive that is greater than the sum of individual effects and greater than any individual effect in the same direction or has an interaction effect that is greater than both in absolute terms is positive synergistic (+S; more positive than predicted additively) when +1 + 1 = (+S) > 2 or −1 + −1 = (+S) > 0 or −1 + 1 = (+S) > 1, or negative synergistic (−S; more negative than predicted additively) when +1 + 1 = (−S) < 0 or −1 + −1 = (−S) < −2 or −1 + 1 = (−S) < −1.
Table 1 presents directional classifications for all potential two-factor interaction types that may theoretically occur in addition to those stated above.
Table 1 Potential interaction types and directional classifications for two-variable response data in factorial studies. The direction of individual stressorterm effects (a) or (b) and interaction effect (a + b) are coded as positive (+), negative (−), or neutral (0). Double-sign symbols (++) or (––) indicate the direction of a cumulative effectterm·var (a + b) that is greater than the sum of individual effects and greater than any individual effect in the same direction or has an interaction effect that is greater than both in absolute terms. Directional interaction classes are additive (AD), +synergistic (+S), −synergistic (−S), +antagonistic (+A), and –antagonistic (−A) Interaction Type a b a + b Classification Double positive + + ++ +S + + + +S + + 0 AD + + − +A + + –– −S Double negative − − ++ +S − − + −A − − 0 AD − − − −S − − –– −S Opposing + − ++ +S + − + −A + − 0 AD + − − +A + − – −S Opposing − + ++ +S − + + −A − + 0 AD − + − +A − + –– −S Negative Neutral − 0 ++ +S − 0 + −A − 0 0 AD − 0 − −S − 0 –– −S Negative Neutral 0 − ++ +S 0 − + −A 0 − 0 AD 0 − − −S 0 − –– −S Positive Neutral + 0 ++ +S + 0 + +S + 0 0 AD + 0 − +A + 0 –– −S Positive Neutral 0 + ++ +S 0 + + +S 0 + 0 AD 0 + − +A 0 + –– −S Double Neutral 0 0 ++ +S 0 0 + +S 0 0 0 AD 0 0 − −S 0 0 –– −S Assessing the directional classification using Crain et al.'s dataset To assess the applicability of our directional classification approach to ecological inquiry, we applied it to the dataset compiled by Crain et al. ( 2008 ). Following their methodology, we inferred additive cumulative effectsterm·var where the 95% confidence intervals of the Hedge's d interaction effect overlapped zero (i.e., effect summation; Gurevitch et al. 2000 ). We then applied our directional classification to nonadditive interactions based on interaction type (Table 1 ). In situations where individual stressorterm effects opposed each other or where large interaction effects were present, we inferred synergismterm only in situations where the 95% confidence intervals of the cumulative effectterm·var Hedge's d did not overlap the Hedge's d effect values of the individual stressorsterm or the control (refer to Crain et al. 2008 for details).
The 170 multiple stressorterm studies yielded examples of all six potential interaction types set out in Table 1 . Double-negative (41%) interactions were most frequent, while opposing (29%) and double-positive interactions (22%) were also common. Negative neutral (5%) interactions were less frequent, and positive neutral (2%) and double-neutral (1%) interactions were rare (Table 2 ; Fig. S1 ). Overall, interactions (regardless of direction) were most often antagonistic (43%), but also frequently synergistic (31%) or additive (26%) (Table 2 ). Applying a directional orientation to all nonadditive effects revealed that negative antagonismsterm (28%) and negative synergismsterm (24%) were the most common nonadditive interaction classes, whereas positive antagonismsterm (15%) were less frequent and positive synergismsterm (7%) least common. Frequencies of interaction classes varied markedly by interaction type. Double-negative interactions (70 instances) were less negative than predicted additively in more than half of all instances (negative antagonistic; 51%), more negative than predicted in about a quarter (negative synergistic; 26%), and as predicted in roughly a fifth of all instances (additive; 21%). In contrast, double-positive interactions (38 instances) were as predicted in over a third of all instances (additive; 37%) or less positive than predicted in just under a third (positive antagonistic; 29%), with roughly a quarter yielding positive synergistic cumulative effectsterm·var (24%) and in four instances becoming negative (negative synergistic; 11%). Opposing interactions (49 instances) were fairly evenly distributed between positive antagonistic (27%), additive (24%), negative antagonistic (22%), and negative synergistic (20%) cumulative effectsterm·var, with positive synergistic (6%) outcomes least frequent. Negative neutral interactions (nine instances) resulted in enhanced negative effects (negative synergistic; 67%) in two-thirds of instances but were unchanged in a third (additive; 33%). Positive neutral interactions (three instances) tended to be less positive with the addition of a neutral stressorterm (positive antagonistic; 67%) or became negative (negative synergistic; 33%). Lastly, the only double-neutral interaction in the dataset yielded a negative cumulative effectterm·var (negative synergistic; 100%).
Table 2 Frequencies and percentages of interaction classes by interaction type summarizing 170 studies manipulating two or more stressorsterm in marine and coastal systems reclassified from Crain et al. ( 2008 ). Directional interaction classes are additive (AD), +synergistic (+S), −synergistic (−S), +antagonistic (+A), and –antagonistic (−A). (X) indicates an interaction class is not applicable for the interaction type. Full details of each study/interaction are given in the Table S1 Interaction Type Classification Frequency % Double negative AD 15 21 (70 instances) −S 19 27 (41% of Total) +S 0 0 −A 36 51 +A X X Double positive AD 14 37 (38 instances) −S 4 11 (22% of Total) +S 9 24 −A X X +A 11 29 Opposing AD 12 24 (49 instances) −S 10 20 (29% of Total) +S 3 6 −A 11 22 +A 13 27 Negative neutral AD 3 33 (nine instances) −S 6 67 (5% of Total) +S 0 0 −A 0 0 +A X X Positive neutral AD 0 0 (three instances) −S 1 33 (2% of Total) +S 0 0 −A X X +A 2 67 Double neutral AD 0 0 (one instance) −S 1 100 (1% of Total) +S 0 0 −A X X +A X X Total AD 44 26 (170 instances) −S 41 24 (100%) +S 12 7 −A 47 28 +A 26 15 Total (w/o direction) Synergismterm 53 31 (170 instances) Antagonismterm 73 43 (100%) Additive 44 26 New classes of interaction – “positive synergismsterm” and “mitigating synergismsterm”
In contrast to Crain et al. ( 2008 ), our classification approach includes a new class of positive synergismterm in situations where effects are opposing (+S in “Opposing” rows of Table 1 ). Moreover, our system has the merit of providing additional information about the directional nature of each interaction. A potentially controversial aspect of the system is the inclusion of a further new class, which we call “mitigating synergismterm.” In this class, two stressorsterm operating in the same direction create a cumulative effectterm·var completely opposite to what would have been predicted; that is, two positives make a negative (−S in “Double positive” row of Table 1 ) or two negatives make a positive (+S in “Double negative” row). Some might argue that such a pattern is the clearest example of antagonismterm because individual effects are reversed. However, classifying this interaction as antagonistic (according to the currently prevalent definition of this term in the ecological literature) would be misleading in our view because the magnitude of the interaction effect is greater than one would predict based on the two single stressorterm effects in absolute terms. Moreover, such strong interactions may have the most interesting ecological consequences because they suggest that when both stressorsterm act together, they synergistically mitigate or inhibit their individual effects even more than under control conditions (i.e., effect reversal with enhancement). In epidemiological research, such so-called crossover interactions are considered the most statistically robust class of interaction because they indicate that risk factors flip from being disease predisposing in one background to protective in another (Kendler and Gardner 2010 ). There is, however, deep controversy surrounding the expected prevalence of such interactions between epidemiologists (Kendler and Gardner 2010 ).
A recent review of the interacting roles of stressorsterm driving the global loss of canopy-forming to mat-forming algae in marine ecosystems by Strain et al. ( 2014 ) utilized a directional interaction classification that documented examples of mitigating synergismsterm, although they did not use the term. However, their approach neglected to distinguish antagonismterm in situations where stressorterm effects were opposing.
Comparing the results of our classification with that of Crain et al When applying our directional classifications to the dataset compiled by Crain et al. ( 2008 ), we found examples of each potential interaction type and class, although class representation varied by interaction type. Of particular note were four instances of mitigating synergismterm that occurred in double-positive interactions (Breitburg et al. 1999b ; Przeslawski et al. 2005 ; Sargian et al. 2007 ; Swanson and Fox 2007 ), indicating that two positive stressorsterm can indeed produce a negative cumulative effectterm·var. Similarly, effect reversal and enhancement was observed in a positive neutral interaction (Pelletier et al. 2006 ), suggesting that agents that have no discernible effect individually may catalyze inhibitory or mitigating responses to other stressorterm effects. These examples involved the following stressorterm pairs: nutrient and toxin (Breitburg et al. 1999b ), CO 2 and UV (Swanson and Fox 2007 ), salinity and temperature (Przeslawski et al. 2005 ), and toxin and UV (Pelletier et al. 2006 ; Sargian et al. 2007 ). Toxin and UV also had no discernible individual effects in the only double-neutral interaction that resulted in a negative cumulative effectterm·var (i.e., negative synergismterm; Pelletier et al. 2006 ). Considering the numerous direct and indirect pathways along which these physicochemical stressorsterm may propagate through ecosystems, complex outcomes are perhaps not surprising. While we found no evidence in the dataset compiled by Crain et al. ( 2008 ) of two negative stressorsterm producing a positive cumulative effectterm·var (the second type of mitigating synergismterm defined above), such outcomes are not unheard of. For example, Christensen et al. ( 2006 ) observed a positive synergistic interaction for consumer biomass between raised temperature, drought-induced UVB exposure and acidity in temperate lakes, despite each stressorterm individually exerting negative effects. Our classification approach, with its identification of such instances, is a first step toward elucidating the mechanisms behind such complex patterns and inferring generality of effects.
Of the 49 opposing interactions classified by Crain et al. ( 2008 ), we reclassified three antagonismsterm as positive synergismsterm (enhanced positive effect when negative stressorterm present) and eleven synergismsterm as positive antagonismsterm (less positive than predicted additively, but less negative than the negative stressorterm alone). Thus, Crain et al.'s ( 2008 ) conceptualization of synergismterm and antagonismterm for interactions involving stressorsterm with opposing individual effects underrepresented positive synergismsterm (because they were not possible) but overrepresented negative synergismsterm. Together with our reclassification of four double-positive antagonismsterm as negative synergismsterm, this accounts for the discrepancy in the (direction-independent) prevalence of interaction classes between our overall findings of 43% antagonismterm, 31% synergismterm, and 26% additive, versus Crain et al. ( 2008 ) 38% antagonismterm, 36% synergismterm, and 26% additive based on an identical dataset. While this discrepancy is fairly modest at first glance, when coupled with the underlying conceptual issues outlined in our introduction, it highlights the need for a conceptual discussion in the ecological community regarding the interpretation of synergismterm and antagonismterm in situations where individual stressorterm effects oppose each other or where predicted cumulative effectsterm·var are reversed and enhanced.
Our finding that the representation of interaction classes varied markedly by interaction type highlights the need to consider the direction of individual stressorterm effects when determining the occurrence of synergismsterm and antagonismsterm. This is particularly pertinent given the bias toward investigating and reporting adverse multiple stressorterm effects (i.e., double-negative interaction type) in ecology (e.g., reviews by Darling and Cote 2008 ; Ban et al. 2014 ; Klaminder et al. 2014 ). Based on our findings, double-positive interactions conformed to an additive effects modelterm most frequently, but 63% of observed cases were nonadditive, and this proportion was larger for the other five interaction types. This further supports the notion that multiple stressorsterm may interact to generate “ecological surprises” (e.g., Paine et al. 1998 ) more often than simply producing additive effects (Crain et al. 2008 ; Darling and Cote 2008 ).
Contrasting concepts of synergismsterm and antagonismsterm and the need for a systematic approach As an emerging field in ecology, there are increasing numbers of multiple stressorterm studies reporting synergismsterm and antagonismsterm that are based on imprecise descriptions or simply the judgment of the authors (Dunne 2010 ). These inconsistencies are aggravated by recent reviews and meta-analyses that define and measure these interactions differently and, therefore, are not comparative studies of any exact phenomenon (Vanhoudt et al. 2012 ). For example, Holmstrup et al. ( 2010 ) defined synergismterm and antagonismterm as “a convenient way to indicate combinations of a set of stressorsterm that result in greater or lesser effects than expected from the single exposures” in their evaluation of 150 studies of stressorsterm including heat, cold, desiccation, oxygen depletion, pathogens, and immunomodulatory factors combined with a variety of environmental pollutants. In contrast, Darling and Cote ( 2008 ) applied an additive null model in their evaluation of 112 multiple stressorterm experiments on animal mortality in freshwater, marine, and terrestrial communities. Not surprisingly, Holmstrup et al. ( 2010 ) reported synergismsterm in over half of their studies, whereas Darling and Cote ( 2008 ) reported synergismsterm in only a third, most likely reflecting the upward bias of Holmstrup et al.'s ( 2010 ) definition of synergy versus Darling and Cote's ( 2008 ) downward bias (a weakness of an additive effects modelterm when individual effects are large or numerous; Folt et al. 1999 ). Acknowledging these differences of interpretation, Vanhoudt et al. ( 2012 ) applied their own definitions of synergismterm and antagonismterm based on “Concentration Addition” or “Independent Action” toxicological models. Due to the lack of support for either of these models, the authors then devised their own simplifying terminology to give an overview of their results as “positive interactions” (describing additive, synergismterm, “superaddition,” “potentiationterm,” or “increased effects”), “negative interactions” (loosely, antagonismterm), or no interactions. Interestingly, Vanhoudt et al. ( 2012 ) strongly opposed additive effect summation as an erroneous principle for determining synergismterm or antagonismterm despite this being the linear null model assumed in prevailing statistical techniques such as ANOVA and in our directional classification approach (Folt et al. 1999 ). Their explanation for this opposition is the fact that additive effect summation may result in cumulative effectterm·var estimates that exceed 100% (a particular problem when estimating standardized rate responses such as mortality where exceeding 100% is impossible). While multiplicative null models may correct for these “overestimates” (cumulative effectterm·var equals the product of individual stressorterm effects; Darling et al. 2010 ), the mechanistic and statistical basis for such approaches remains controversial (Greco et al. 1996 ; Kendler and Gardner 2010 ). Moreover, in a multiplicative model, one cannot know what the effect of any single stressorterm is on the cumulative effectterm·var without knowing the fractional contribution of all other stressorsterm in the model, even in the absence of the product terms (Kendler and Gardner 2010 ). Alternative approaches for inferring synergismterm and antagonismterm utilizing isobolographic analysis exist in the fields of pharmacology, toxicology, and pathology (Nelson and Kursar 1999 ). While isobolographic analysis presents some key advantages over additive and multiplicative models (see Dunne 2010 ), it seems of limited utility in many ecological contexts because it relies on establishing multiple levels of dose–concentration relationships (a substantial ecological challenge in itself) and is further limited by implicitly assuming synergy only when effects are negative, reflecting its toxicological origins. Consequently, if the aim of identifying synergismsterm or antagonismsterm among multiple stressorsterm is to determine whether ecological responses can be predicted from knowledge of single stressorterm effects, we encourage the use of an additive effects modelterm (Kendler and Gardner 2010 ).
Wider applicability of the classification system Distinguishing classes of potential interactions between multiple stressorsterm is important for elucidating stressorterm mechanisms and for separating effects based on severity (Folt et al. 1999 ). Irrespective of the experimental design, it is possible to reduce any multilevel or multivariable relationship to a set of two-variable relationships, but if higher-order interactions or highly influential covariates exist, it is possible that the effect direction can change from positive to negative (Nakagawa and Cuthill 2007 ). We have conceptualized a systematic approach for distinguishing such instances based on an additive effects modelterm. While our examples only demonstrate two stressorterm interactions, the approach may also be applied when more than two stressorsterm are operating, note that synergismsterm may be more likely to occur in such instances (Crain et al. 2008 ). The approach is potentially adaptable for testing against a multiplicative model (i.e., log additive; Folt et al. 1999 ). However, in this case, we recommend following the advice of Folt et al. ( 1999 ) that nonadditive responses should not be called synergismsterm or antagonismsterm so as to avoid confusion with the additive modelterm·stat.
A conceptually robust definition and systematic classification of synergismterm and antagonismterm is a prerequisite for improving our ability to predict and manage the interactive effects of multiple stressorsterm. We have illustrated how the typical direction-independent classification of these terms may prove problematic and have conceptualized a directionally oriented extension of the traditional framework. Although some researchers may view the presence of interaction classes and directional interaction types as unduly complicated, the incorporation of these categories overcomes the limitations of the traditional framework when confronted with the more complex outcomes that appear to be quite commonplace. Moreover, the complexity of the framework translates into more informative descriptions and straightforward interpretations of complex interactions, which would otherwise be difficult even to describe.
Management implications It is generally assumed that multiple stressorterm synergies represent a “worst-case” scenario for ecosystem management (Paine et al. 1998 ; Folt et al. 1999 ). Consequently, our finding that antagonismsterm are generally more common than synergismsterm might be perceived as a “better case” scenario for managers. However, this is a misguided assumption because any nonadditive interaction, regardless of whether it is synergistic or antagonistic, poses complex challenges to ecosystem managers. This is especially true in mitigation or restoration situations where multiple stressorsterm are already in operation and where impact and recovery trajectories are aligned (Scheffer et al. 2001 ). Here, it can be argued that antagonismsterm represent a particularly unfortunate scenario because efforts to reduce or eliminate a stressorterm may not yield proportional benefits unless a dominant stressorterm is driving the interaction (Halpern et al. 2008 ; Brown et al. 2013 ). On the other hand, synergismsterm can represent an optimistic scenario in certain situations (excluding mitigating synergismsterm), because efforts to reduce any particular stressorterm may yield larger overall benefits than otherwise expected (Crain et al. 2008 ). In contrast, mitigating synergismsterm suggest that the modes of action of single stressorterm effects are either eliminated when the stressorsterm are combined or they surpass a critical threshold, such that the mechanism of the cumulative effectterm·var is opposite to that of the single stressorterm effects. Finally, additive effects suggest that stressorsterm are operating independently of each other, so mitigation of any of the individual stressorsterm will yield predictable benefits (Darling and Cote 2008 ). An ongoing challenge is to determine which stressorsterm interact to generate nonadditive effects and to disentangle the mechanistic pathways by which multiple stressorsterm interact in ecosystems.
We thank Jeremy Frimer, Martin Krkosek, Richard Barker, and Shinichi Nakagawa for statistical advice. Funding was provided by New Zealand's Ministry of Business, Innovation and Employment contract C01X1005.
Conflict of Interest None declaerd.