Letters
What are hydra effects? A response to Schro¨der et al. Peter A. Abrams Department of Ecology and Evolutionary Biology, 25 Harbord Street, University of Toronto, Toronto, ON M5S 3G5, Canada
The ‘hydra effect’ was originally defined by Abrams and Matsuda [1] as an increase in mean population size in response to greater mortality. Recently, Schro¨der, van Leeuwen, and Cameron (SVC) [2] argued that such increases might be common, but that they are predominantly a phenomenon [‘stage specific overcompensation’ (SSO)] in which only a subset of the population increases. SVC assert that SSO, as well as other phenomena involving population increases in response to mortality, are not hydra effects. They conclude ([2], see p. 622) that, unlike these other phenomena, hydra effects are ‘likely to be scarce and limited to particular life histories that lack individual differences (ontogenetic symmetry) and to certain environmental circumstances (logistic resource dynamics)’. This conclusion is based on an erroneous definition of hydra effect and an inadequate review of relevant evidence. Neither [1] nor the vast majority of users of ‘hydra effect’ have restricted that term to particular types of mortality, population structures, measures of population size, or classes of model. Nevertheless, the Glossary definition in [2] states: ‘Hydra effects occur when unstructured consumer populations exhibit cyclic dynamics. The basis for the hydra effect is an exponential increase in resource productivity when resources are depleted and when the consumer population is at the maximum of the consumer–resource cycle. The combination of logistic resource growth and saturating resource ingestion rate of the consumer are hence essential ingredients for hydra effects.’ In fact, none of these conditions is required for a hydra effect; the article that introduced the term [1] employed several models with three or four species, all of which could have hydra effects at a stable equilibrium. In a review of ‘hydra effects’, Abrams [3] showed that population homogeneity, dynamic instability, saturating consumer responses, and logistic growth are not required for hydra effects, nor are hydra effects restricted to consumer populations. There is a growing literature on hydra effects in single-species difference equation models (reviewed in [3]). Within consumer–resource models, stage-structured consumers [3], stage-structured resources [4], and stability generally [1,3,4] all allow hydra effects. Even in the example that SVC used to illustrate the role of cycles (their Box 1), cycles are not the crucial feature producing a positive response to mortality. If the equilibrium were stabilized by predator interference, hydra effects could still occur [1,5]. The key property for the hydra effect in that model is the reduction in the predators’ attack rate produced by the higher prey densities implied by greater predator mortality [3]. Corresponding author: Abrams, P.A. ([email protected]) Keywords: hydra effect; mortality; overcompensation; stability. 0169-5347/ ß 2015 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tree.2015.01.013
Logistic resources, normally defined as resources having linear density dependence, were not assumed in [1,3] or in most other works demonstrating hydra effects. Even under SVC’s definition of ‘logistic’ as any resource with an S-shaped growth curve, logistic growth is not required for a hydra effect. Mortality that causes a hydra effect can be due to predators and predators often reduce prey foraging, which can increase prey density. Such an increase can occur in systems with chemostat resources ([5], see p. 299; [6], see Appendix C). A hydra effect can also occur in a consumer species with chemostat resources and scramble competition [3]. Several mechanisms producing hydra effects are more likely with at least partially selfreproducing resources, but such resources are extremely common, contrary to SVC’s claim that ‘. . .it has been argued that semi-chemostat dynamics prevail in nature (Persson et al. 1998, [7])’. In fact, the only relevant statement in [7] (see p. 275) is a single sentence: ‘Semi-chemostat dynamics may be more realistic than the commonly used logistic growth dynamics when (1) the resource has a physical refuge or (2) the resource includes invulnerable. . .size classes which grow into a vulnerable size range.’ No references to field studies are given. Other analyses [4,8] have examined both of these scenarios and did not find that they generally produced chemostat resource dynamics. Saturating functional responses are not required for a hydra effect in predators; Allee effects in the prey’s growth can cause hydra effects with linear functional responses. Resources, as well as consumers, can increase in response to mortality [9]. A wide variety of three-or-more-species systems beyond those explored in [1,9] can exhibit hydra effects; see [10] for a food chain example. Yodzis [11] found negative responses to immigration (implying hydra effects) for 27% of the 223 species present in the 16 empirically based Lotka–Volterra models of food webs he examined. More examples exist. ‘Hydra effect’ was introduced to call attention to the counterintuitive possibility of increased population because of increased removal. If a population comprises several distinct classes, the fact that a particular class increases should be due to mortality on that class for it to qualify as a hydra effect [3]. Thus, some but not all cases of SSO are hydra effects, and the dividing line often depends on how population size is measured. However, a phenomenon SVC simply call ‘overcompensation’, which usually reflects scramble competition, is always a hydra effect and was considered in [3]. The experimental evidence reviewed by SVC included only 13 studies and 11 species (including four fish and three cladocerans). This is too small a sample for broad generalizations. SVC identify only one hydra effect and suggest it is questionable, although no reason is given. Trends in Ecology & Evolution, April 2015, Vol. 30, No. 4
179
Letters They note that, for approximately half of their studies, the original study’s authors, [3], or both claimed that the responses were hydra effects; this is because most used the correct definition. Schro¨der’s own empirical study in Table 2 exhibits a clear hydra effect in response to juvenile mortality. SVC largely ignore natural enemies as mortality factors. However, decreased foraging in response to increased predation risk readily generates hydra effects. It has been shown to be common and to often increase the prey’s food intake rate because of greater resource abundance (see references in [3]). Acknowledgments The author thanks the Natural Sciences and Engineering Research Council of Canada for support and M.H. Cortez, M.G. Burgess, and H.C. Giacomini for their input on this response.
References 1 Abrams, P.A. and Matsuda, H. (2005) The effect of adaptive change in the prey on the dynamics of an exploited predator population. Can. J. Fish. Aquat. Sci. 62, 758–766
Trends in Ecology & Evolution April 2015, Vol. 30, No. 4
2 Schro¨der, A. et al. (2014) When less is more: positive population-level effects of mortality. Trends. Ecol. Evol. 29, 614–624 3 Abrams, P.A. (2009) When does greater mortality increase population size? The long history and diverse mechanisms underlying the hydra effect. Ecol. Lett. 12, 462–474 4 Abrams, P.A. and Quince, C. (2005) The impact of mortality on predator population size and stability in systems with stage-structured prey. Theor. Popul. Biol. 68, 253–266 5 Abrams, P.A. (2002) Will declining population sizes warn us of impending extinctions? Am. Nat. 160, 293–305 6 Abrams, P.A. (2014) The evolutionary and behavioral modification of consumer responses to environmental change. J. Theor. Biol. 343, 162–173 7 Persson, L. et al. (1998) Ontogenetic scaling of foraging rates and the dynamics of a size-structured consumer–resource model. Theor. Popul. Biol. 54, 270–293 8 Abrams, P.A. and Walters, C.J. (1996) Invulnerable prey and the paradox of enrichment. Ecology 77, 1125–1133 9 Abrams, P.A. (2012) The eco-evolutionary responses of a generalist consumer to resource competition. Evolution 66, 3130–3143 10 Abrams, P.A. and Vos, M. (2003) Adaptation, density dependence, and the abundances of trophic levels. Evol. Ecol. Res. 5, 1113–1132 11 Yodzis, P. (1988) The indeterminacy of ecological interactions as perceived through perturbation experiments. Ecology 69, 508–515
Empirical support for different types of positive mortality effects. A reply to Abrams Arne Schro¨der1, Anieke van Leeuwen2, and Tom C. Cameron3 1
Department 4: Biology and Ecology of Fishes, Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Mu¨ggelseedamm 310, 12587 Berlin, Germany 2 Department of Ecology and Evolutionary Biology, Princeton University, 106A Guyot Hall, Princeton, NJ 08544, USA 3 School of Biological Sciences, University of Essex, Colchester, CO4 3SQ, UK
We thank Peter Abrams for his comments and thoughts [1] on our recent review of the empirical evidence for positive population-level effects of mortality, defined as an increase with increasing mortality in the numbers or biomass of a total population or of a specific life-history stage or size class within the population [2]. This evidence was compared with predictions of mathematical models. Empirically demonstrated positive mortality effects were predominately stage-specific, a pattern (stage-specific overcompensation [3]) most congruent with predictions by models that account for consumer stage-structure and ontogenetic development of individuals [3–5]. Increases in total density as predicted by unstructured models (hydra effects [6,7]) were rare in empirical studies (occurring in 1 of 15). We concluded that the type of positive mortality effects found in experiments corroborates the perspective of stage-structured population theory [3–5,8,9]. Abrams [1] claims that our ‘conclusion is based on an erroneous definition of hydra effect and an inadequate review of relevant evidence’. His arguments to support this claim are: (i) hydra effects occur under a far wider range of ecological scenarios than the ones we looked at, and (ii) stage-specific positive mortality effects often are Corresponding author: Schro¨der, A. ([email protected]) 0169-5347/ ß 2015 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tree.2015.02.004
180
hydra effects. By contrast, we argue that Abrams’ claim is based on a misunderstanding of the focus in our review. First, Abrams [1] argues that hydra effects in general do not require logistic resource growth dynamics and saturating functional responses, and are not tied to consumerresource cycles, in contrast to how we used the term for our purpose of comparing model predictions and experimental evidence. We agree and explicitly acknowledged that the connection between instability and hydra effects found in unstructured models breaks down in more complex ecological scenarios (Box 2 and p. 615 in [2]). Allee effects in resource populations, multiple interacting species, consumer interference, and reduced foraging activity based on altered morphological traits or behavior of individuals can all lead to hydra effects in stable unstructured consumer-resource systems [1,7]. Nevertheless, we maintain that hydra effects in unstructured one-consumer one-resource models with constant individual behavior or morphology are tightly linked to logistic resource growth and a type II functional response, in other words to systems displaying consumer-resource cycles. We restricted our review of models predicting positive mortality effects to those of only one consumer and one resource which do not incorporate such ecological scenarios. For example, in the models we considered, per capita foraging activity of individuals does not change with mortality pressure and consumer interference does not occur.
What are hydra effects? A response to Schro¨der et al. Peter A. Abrams Department of Ecology and Evolutionary Biology, 25 Harbord Street, University of Toronto, Toronto, ON M5S 3G5, Canada
The ‘hydra effect’ was originally defined by Abrams and Matsuda [1] as an increase in mean population size in response to greater mortality. Recently, Schro¨der, van Leeuwen, and Cameron (SVC) [2] argued that such increases might be common, but that they are predominantly a phenomenon [‘stage specific overcompensation’ (SSO)] in which only a subset of the population increases. SVC assert that SSO, as well as other phenomena involving population increases in response to mortality, are not hydra effects. They conclude ([2], see p. 622) that, unlike these other phenomena, hydra effects are ‘likely to be scarce and limited to particular life histories that lack individual differences (ontogenetic symmetry) and to certain environmental circumstances (logistic resource dynamics)’. This conclusion is based on an erroneous definition of hydra effect and an inadequate review of relevant evidence. Neither [1] nor the vast majority of users of ‘hydra effect’ have restricted that term to particular types of mortality, population structures, measures of population size, or classes of model. Nevertheless, the Glossary definition in [2] states: ‘Hydra effects occur when unstructured consumer populations exhibit cyclic dynamics. The basis for the hydra effect is an exponential increase in resource productivity when resources are depleted and when the consumer population is at the maximum of the consumer–resource cycle. The combination of logistic resource growth and saturating resource ingestion rate of the consumer are hence essential ingredients for hydra effects.’ In fact, none of these conditions is required for a hydra effect; the article that introduced the term [1] employed several models with three or four species, all of which could have hydra effects at a stable equilibrium. In a review of ‘hydra effects’, Abrams [3] showed that population homogeneity, dynamic instability, saturating consumer responses, and logistic growth are not required for hydra effects, nor are hydra effects restricted to consumer populations. There is a growing literature on hydra effects in single-species difference equation models (reviewed in [3]). Within consumer–resource models, stage-structured consumers [3], stage-structured resources [4], and stability generally [1,3,4] all allow hydra effects. Even in the example that SVC used to illustrate the role of cycles (their Box 1), cycles are not the crucial feature producing a positive response to mortality. If the equilibrium were stabilized by predator interference, hydra effects could still occur [1,5]. The key property for the hydra effect in that model is the reduction in the predators’ attack rate produced by the higher prey densities implied by greater predator mortality [3]. Corresponding author: Abrams, P.A. ([email protected]) Keywords: hydra effect; mortality; overcompensation; stability. 0169-5347/ ß 2015 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tree.2015.01.013
Logistic resources, normally defined as resources having linear density dependence, were not assumed in [1,3] or in most other works demonstrating hydra effects. Even under SVC’s definition of ‘logistic’ as any resource with an S-shaped growth curve, logistic growth is not required for a hydra effect. Mortality that causes a hydra effect can be due to predators and predators often reduce prey foraging, which can increase prey density. Such an increase can occur in systems with chemostat resources ([5], see p. 299; [6], see Appendix C). A hydra effect can also occur in a consumer species with chemostat resources and scramble competition [3]. Several mechanisms producing hydra effects are more likely with at least partially selfreproducing resources, but such resources are extremely common, contrary to SVC’s claim that ‘. . .it has been argued that semi-chemostat dynamics prevail in nature (Persson et al. 1998, [7])’. In fact, the only relevant statement in [7] (see p. 275) is a single sentence: ‘Semi-chemostat dynamics may be more realistic than the commonly used logistic growth dynamics when (1) the resource has a physical refuge or (2) the resource includes invulnerable. . .size classes which grow into a vulnerable size range.’ No references to field studies are given. Other analyses [4,8] have examined both of these scenarios and did not find that they generally produced chemostat resource dynamics. Saturating functional responses are not required for a hydra effect in predators; Allee effects in the prey’s growth can cause hydra effects with linear functional responses. Resources, as well as consumers, can increase in response to mortality [9]. A wide variety of three-or-more-species systems beyond those explored in [1,9] can exhibit hydra effects; see [10] for a food chain example. Yodzis [11] found negative responses to immigration (implying hydra effects) for 27% of the 223 species present in the 16 empirically based Lotka–Volterra models of food webs he examined. More examples exist. ‘Hydra effect’ was introduced to call attention to the counterintuitive possibility of increased population because of increased removal. If a population comprises several distinct classes, the fact that a particular class increases should be due to mortality on that class for it to qualify as a hydra effect [3]. Thus, some but not all cases of SSO are hydra effects, and the dividing line often depends on how population size is measured. However, a phenomenon SVC simply call ‘overcompensation’, which usually reflects scramble competition, is always a hydra effect and was considered in [3]. The experimental evidence reviewed by SVC included only 13 studies and 11 species (including four fish and three cladocerans). This is too small a sample for broad generalizations. SVC identify only one hydra effect and suggest it is questionable, although no reason is given. Trends in Ecology & Evolution, April 2015, Vol. 30, No. 4
179
Letters They note that, for approximately half of their studies, the original study’s authors, [3], or both claimed that the responses were hydra effects; this is because most used the correct definition. Schro¨der’s own empirical study in Table 2 exhibits a clear hydra effect in response to juvenile mortality. SVC largely ignore natural enemies as mortality factors. However, decreased foraging in response to increased predation risk readily generates hydra effects. It has been shown to be common and to often increase the prey’s food intake rate because of greater resource abundance (see references in [3]). Acknowledgments The author thanks the Natural Sciences and Engineering Research Council of Canada for support and M.H. Cortez, M.G. Burgess, and H.C. Giacomini for their input on this response.
References 1 Abrams, P.A. and Matsuda, H. (2005) The effect of adaptive change in the prey on the dynamics of an exploited predator population. Can. J. Fish. Aquat. Sci. 62, 758–766
Trends in Ecology & Evolution April 2015, Vol. 30, No. 4
2 Schro¨der, A. et al. (2014) When less is more: positive population-level effects of mortality. Trends. Ecol. Evol. 29, 614–624 3 Abrams, P.A. (2009) When does greater mortality increase population size? The long history and diverse mechanisms underlying the hydra effect. Ecol. Lett. 12, 462–474 4 Abrams, P.A. and Quince, C. (2005) The impact of mortality on predator population size and stability in systems with stage-structured prey. Theor. Popul. Biol. 68, 253–266 5 Abrams, P.A. (2002) Will declining population sizes warn us of impending extinctions? Am. Nat. 160, 293–305 6 Abrams, P.A. (2014) The evolutionary and behavioral modification of consumer responses to environmental change. J. Theor. Biol. 343, 162–173 7 Persson, L. et al. (1998) Ontogenetic scaling of foraging rates and the dynamics of a size-structured consumer–resource model. Theor. Popul. Biol. 54, 270–293 8 Abrams, P.A. and Walters, C.J. (1996) Invulnerable prey and the paradox of enrichment. Ecology 77, 1125–1133 9 Abrams, P.A. (2012) The eco-evolutionary responses of a generalist consumer to resource competition. Evolution 66, 3130–3143 10 Abrams, P.A. and Vos, M. (2003) Adaptation, density dependence, and the abundances of trophic levels. Evol. Ecol. Res. 5, 1113–1132 11 Yodzis, P. (1988) The indeterminacy of ecological interactions as perceived through perturbation experiments. Ecology 69, 508–515
Empirical support for different types of positive mortality effects. A reply to Abrams Arne Schro¨der1, Anieke van Leeuwen2, and Tom C. Cameron3 1
Department 4: Biology and Ecology of Fishes, Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Mu¨ggelseedamm 310, 12587 Berlin, Germany 2 Department of Ecology and Evolutionary Biology, Princeton University, 106A Guyot Hall, Princeton, NJ 08544, USA 3 School of Biological Sciences, University of Essex, Colchester, CO4 3SQ, UK
We thank Peter Abrams for his comments and thoughts [1] on our recent review of the empirical evidence for positive population-level effects of mortality, defined as an increase with increasing mortality in the numbers or biomass of a total population or of a specific life-history stage or size class within the population [2]. This evidence was compared with predictions of mathematical models. Empirically demonstrated positive mortality effects were predominately stage-specific, a pattern (stage-specific overcompensation [3]) most congruent with predictions by models that account for consumer stage-structure and ontogenetic development of individuals [3–5]. Increases in total density as predicted by unstructured models (hydra effects [6,7]) were rare in empirical studies (occurring in 1 of 15). We concluded that the type of positive mortality effects found in experiments corroborates the perspective of stage-structured population theory [3–5,8,9]. Abrams [1] claims that our ‘conclusion is based on an erroneous definition of hydra effect and an inadequate review of relevant evidence’. His arguments to support this claim are: (i) hydra effects occur under a far wider range of ecological scenarios than the ones we looked at, and (ii) stage-specific positive mortality effects often are Corresponding author: Schro¨der, A. ([email protected]) 0169-5347/ ß 2015 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tree.2015.02.004
180
hydra effects. By contrast, we argue that Abrams’ claim is based on a misunderstanding of the focus in our review. First, Abrams [1] argues that hydra effects in general do not require logistic resource growth dynamics and saturating functional responses, and are not tied to consumerresource cycles, in contrast to how we used the term for our purpose of comparing model predictions and experimental evidence. We agree and explicitly acknowledged that the connection between instability and hydra effects found in unstructured models breaks down in more complex ecological scenarios (Box 2 and p. 615 in [2]). Allee effects in resource populations, multiple interacting species, consumer interference, and reduced foraging activity based on altered morphological traits or behavior of individuals can all lead to hydra effects in stable unstructured consumer-resource systems [1,7]. Nevertheless, we maintain that hydra effects in unstructured one-consumer one-resource models with constant individual behavior or morphology are tightly linked to logistic resource growth and a type II functional response, in other words to systems displaying consumer-resource cycles. We restricted our review of models predicting positive mortality effects to those of only one consumer and one resource which do not incorporate such ecological scenarios. For example, in the models we considered, per capita foraging activity of individuals does not change with mortality pressure and consumer interference does not occur.
