Thomas J. Hossie
Dennis L. MurrayEditorial on the Research Topic
New perspectives and emerging directions in predator–prey functional response research: hommage to C.S. Holling (1930–2019)
1 Introduction
More than 60 years have passed since C. S. “Buzz” Holling (1930–2019) published his landmark papers describing the relationship between prey density and the predator’s per capita kill rate (i.e., the “functional response”) (Holling, 1959a; Holling, 1959b; Holling, 1961). Holling proposed three forms of the functional response, and provided mechanistic models for these relationships that were grounded in empirical support. Building these relationships into predator–prey models, which had previously assumed a linear functional response, radically changed predictions and potential outcomes for prey populations in ways that continue to yield new insights. Holling’s initial work spurred decades of basic and applied research into functional responses that spanned a variety of predator and prey species, study systems, and ecological constraints. The functional response provides an explicit connection between behavioral and population ecology and has now been cemented as a key integrating concept in ecology, conservation biology, wildlife management, and biological control. Today, increasingly complex functional response models continue to be developed, novel data are collected to parameterize these models (e.g., through the advent of bio-logging and continuous-time animal monitoring techniques), and the analytical methods used to fit or parameterize functional response models have become increasingly sophisticated. More than half a century after Holling’s contributions, functional response research remains a fruitful and active area of investigation.
Notwithstanding these advances, application of contemporary insights into the functional response can be hindered by lingering misconceptions, which we dispel below. Following this, we briefly showcase the impressive contributions to this Research Topic, and finally we end with suggestions for future investigation.
2 Lingering misconceptions related to the functional response
2.1 The observed functional response type is characteristic of the predator or predator–prey pair
This notion reflects a failure to appreciate the degree to which a predator’s feeding rate is influenced by a variety of ecological factors. A large body of empirical and theoretical work has illustrated that the functional response shape (e.g., hyperbolic vs. sigmoidal) and key parameter estimates (e.g., attack rate, handling time) can vary dramatically depending on environmental conditions including: temperature (e.g., Kratina et al.), presence of refugia (e.g., Hossie and Murray, 2010), alternate prey availability (e.g., Hossie et al., 2021), predator density (Abrams and Ginzburg, 2000), prey spatial arrangement (Hossie and Murray, 2016), prey or predator group size (e.g., Fryxell et al., 2007, Fryxell et al.), and even non-prey species diversity (Kratina et al., 2007). Abrams explains that many variables that influence feeding rates are not included in contemporary models, including ecological processes operating at other trophic levels. This also reflects the challenge of effectively transitioning predator–prey functional response theory or lab-based research to complex natural systems. As such, we should be mindful that empirically-derived functional responses represent a predator–prey relationship observed within a specific set of environmental conditions, and explicitly recognize the potential limitations to generalizing such functions more broadly.
2.2 Holling Type II is the most widespread form of functional response in nature
The hyperbolic prey-dependent (Type II) functional response remains the most commonly fitted model of predation, which can lead to the unwarranted assumption that this type of relationship adequately characterizes most predator–prey interactions. The apparent primacy of Type II arises, in part, as a result of: (1) alternate models not being adequately considered (e.g., sigmoidal or predator-dependent models), (2) data limitations related to statistical power or experimental design (e.g., insufficient sample size, inadequate prey density range or spacing), and/or (3) flawed methods for model fitting or comparing the fit of competing models. Kalinkat et al. review the reasons why Type III (i.e., sigmoidal) functional responses remain rare in the empirical literature, and a strong case for considering predator dependence as a basic minimal model is made by Tyutyunov and Titova and Ginzburg and Damuth. Importantly, Gobin et al. show that assuming a Type II functional response adequately describes all trophic interactions leads to misleading inferences about food web dynamics.
2.3 The primary mechanism for Type III (sigmoidal) functional responses is prey switching
Much attention has been given to the Type III (sigmoidal) functional response, because the density-dependent predation which occurs at low-intermediate prey densities can stabilize predator–prey dynamics (Taylor, 1984; Turchin, 2003). In general, prey switching is perhaps the mechanism most often cited to explain Type III functional responses, likely because of the compelling work by Murdoch (1969) and Murdoch et al. (1975). The presence of prey refuges and predator learning (i.e., formation of a search image) are also commonly cited mechanisms (but see Bruzzone et al., 2022). DeLong (2021) reviews key mechanisms known to generate a Type III functional response. Given that any factor which causes the attack rate to increase with prey density can lead to a region of density-dependent predation, and thus a Type III response (Hassell, 1978; Juliano, 2001), we encourage researchers to consider a variety of possible mechanisms (e.g., density-dependent changes in predator search effort or foraging mode). Mechanisms generating sigmoidal responses in predator-dependent systems seem particularly underdeveloped (but see Hossie and Murray, 2016).
2.4 Linear functional responses are unrealistic in systems outside of filter feeders
Incorporating a non-linear functional response (e.g., Type II) into predator–prey models was a key improvement to the original Lotka-Volterra predator–prey model, which implicitly assumed that predator kill rate could increase linearly with prey density, without limit. Despite confusing terminology in the literature, the “linear” functional response embedded within the Lotka-Volterra equations is different from what Holling depicted as a Type I functional response, where feeding rate increases linearly with prey density up to a threshold point where consumption rate sharply transitions to a constant consumption rate (Holling, 1959a; Jeschke et al., 2004). Jeschke et al. (2004) outline why we should expect Holling Type I (i.e., rectilinear) functional responses to be restricted to filter feeders (i.e., because such consumers must be able to search for and capture food while handling other food or have a negligible handling time, and must search at the maximum rate until their gut is filled). Indeed, Type I responses have been observed exclusively in filter feeders (Jeschke et al., 2004), however Beardsell et al. points out that a growing number of empiricists have observed “linear” functional responses where the predator’s per capita kill rate increases linearly across the full range of prey densities observed in nature (e.g., Novak, 2010; Chan et al., 2017). Behaviours like prey caching, surplus killing, and partial consumption of prey can explain why the feeding rate fails to saturate in some systems (Gobin et al.). Alternatively, prey density may simply never reach levels high enough to satiate the predator in some systems, as indicated by a recent analysis by Coblentz et al. (2022). Therefore, despite theoretical limits to prey consumption, ecologists should not discount linear functional responses as they may best describe the trophic interactions in some systems. Notwithstanding this, apparent linearity in a fitted functional response may also arise as a statistical artifact from insufficient predation rate data at high prey densities or because of high variability in estimated predation rates and the focus on model parsimony in contemporary model-fitting exercises.
2.5 Functional responses take one of three shapes (Type I, II, III)
While Holling’s three “types” of functional response have been a helpful starting point, there is no strong theoretical basis for this strict level of categorization. Although categorization has been useful to help distinguish systems with vs. without density-dependent predation, this “false trichotomy” constrains our consideration of the full range of possible functional response shapes that might occur in natural systems. Dome- or roller-coaster shaped functional responses, where the per capita kill rate at very high densities begins to decline (e.g., due to confusion or coordinated prey defense; Taylor, 1984; Jeschke and Tollrian, 2005), are examples of how me might fail to detect interesting or important variation in the feeding rate by constraining the functional response shape to Types I–III. The theta-sigmoidal model (Real, 1977; Turchin, 2003; Okuyama and Ruyle, 2011) provides one solution where the shape is governed by a dimensionless parameter (see also Kalinkat et al.). This approach allows the model to fit cases where predation rate increases with prey density more slowly than predicted by a linear relationship (Ruxton, 2005; Travis and Palmer, 2005; Okuyama, 2009), allowing a continuous gradient in shape from a Type II to a Type III, and beyond (i.e., hyperbolic → weakly sigmoidal → strongly sigmoidal). However, the potential disadvantage of this type of model is that it discourages objective hypothesis testing about the factors which induce density-dependent predation, and instead promotes a phenomenological approach that may be less grounded in a mechanistic understanding of predator–prey interactions. Given that small changes in the slope of the functional response, especially at low prey densities, can lead to dramatically different population dynamics (e.g., Fussmann and Blasius, 2005), accurate characterization of the functional response shape remains a priority.
2.6 The ratio-dependent controversy is settled
Ecologists generally agree that the functional response of most (but not all) predators is influenced by predator density, and this has been supported by several reviews on the topic (e.g., Arditi and Akçakaya, 1990; DeLong and Vasseur, 2011; Novak and Stouffer, 2021). Ecologists also tend to agree that a variety of ecological processes, broadly termed “mutual interference”, can generate such effects. Functional response models which account for interference have existed since 1975, with new models developed since then (see list in Tyutyunov and Titova). The ratio dependence approach to incorporating predator-dependence in the functional response (Arditi and Ginzburg, 1989), has received both support and criticism. Ultimately, this led to a key publication where a primary proponent (Ginzburg) and critic (Abrams) worked together to identify areas of agreement and disagreement (Abrams and Ginzburg, 2000). More than two decades later, disagreement remains. The argument for ratio dependence has been developed further in at least two books (Ginzburg and Colyvan, 2004; Arditi and Ginzburg, 2012), and subsequently countered in a review by Abrams (2015). Two papers in this Research Topic continue to advocate for the ratio dependence approach (Tyutyunov and Titova, Ginzburg and Damuth), but many points in Abrams (2015) remain to be fully addressed. Thus, despite consensus that predator dependence is widespread and relevant to broader predator–prey population dynamics, the best way to include these effects in functional response models remains unresolved and ultimately may depend on the specific objectives of a given project.
3 Topics explored in this Research Topic
We are excited by level of active research in this field, and the many valuable contributions made to this Research Topic, specifically. Valuable contributions were made from researchers at all career stages, spanning 10 countries, and reflect a mixture of empirical papers, review articles, and perspective pieces, as well as work conducted in both the lab and field. Both Abrams and Krebs review the historical context related to the development of predator–prey theory, and point to unresolved problems in our current understanding which deserve further attention. Two articles argue for the broader adoption of ratio dependence (Tyutyunov and Titova, Ginzburg and Damuth). Giacomini warns that functional response-stability relationships are critically influenced by analogous “metabolic responses” of predators to prey density, and ignoring such effects may lead to underestimates in the strength of predator–prey interactions. DeAngelis et al. illustrate that temporal and spatial scale critically influence the form that a functional response takes, and Kratina et al. show that the potentially destabilizing effect of warming temperatures on predator prey systems is mediated by a complex interaction between temperature and body size on the functional response. The extent to which environmental changes more broadly affect predator–prey interactions, and how this impact differs across taxa (e.g., endotherms vs. ectotherms), remains an important area for further investigation. Fryxell et al. employ a group-dependent functional response approach to illustrate why Serengeti lions are forced to broaden their diets in order to persist, thereby revealing important community ecology and conservation policy implications of functional response research. Several papers outline experimental or statistical considerations that are critical for robust inference when determining the functional response (Griffen et al., Novak and Stouffer, Papanikolaou et al., Juliano et al.), and three papers explore non-traditional ways to estimate or parameterize functional response models (Beardsell et al., DeLong et al., Portalier et al.). Gobin et al. demonstrates that correctly diagnosing the functional response is critical to developing accurate food web models, and Kalinkat et al. explores why Type III models are not more commonly reported in the literature.
4 Topics not explored in this Research Topic
We sought to collate a mixture of empirical papers, review articles, and perspective pieces including contributions from theoreticians, laboratory empiricists, and field biologists, with the broader goal of promoting dialogue and sustained interest among field biologists, mathematical theoreticians and laboratory empiricists who share an interest in the functional response. We acknowledge, however, that this Research Topic does not cover all aspects of contemporary research on the functional response. For example, multispecies functional response models have been developed to better understand how generalist predators operate in multi-prey systems (e.g., Gentleman et al., 2003; Morozov and Petrovskii, 2013; Ryabov et al., 2015). While not explored here, multispecies functional response models are particularly well-suited to explore prey switching (e.g., van Leeuwen et al., 2013; Vallina et al., 2014; Baudrot et al., 2016). There has also been a growing effort to explore the impact of invasive species by employing a comparative functional response approach (e.g., Dick et al., 2013; Dick et al., 2014; Faria et al., 2023), but this Research Topic does not include contributions specific to this valuable new use. Likewise, the principles of predator functional responses are directly relevant to novel approaches in the biological control of pests, which is the subject of active research in applied entomology (Fernández-arhex and Corley, 2003; Cuthbert et al., 2018).
5 Ongoing challenges & emerging directions
Our understanding of trophic interactions has expanded dramatically since Holling’s initial work. We end by identifying some questions we think are important and interesting areas for future investigation:
● How much variation is there among individual predators in their kill rate, and does it matter (i.e., are there personality effects on the functional response)?
● What are the effects of species other than the predator–prey pair on the functional response (e.g., alternate prey, competing predators, predators at higher trophic levels), and how should we account for them in our models?
● What are the relevant prey densities for functional response fitting, and how do we obtain the necessary data from field studies? Can we reliably estimate key functional response parameters without observational kill rate data (e.g., exclusively tracking prey mortality)?
● How well do phenomenological and mechanistic functional response models correspond to each other in the same system, and how variable are functional responses across space and time?
● How do we fit phenomenological models with sparce data, especially predation rate data that are scant in the low-intermediate prey density range where hyperbolic and sigmoidal functional responses are distinguished, or at high prey densities where predators theoretically reach saturation?
● What are the limitations of phenomenological models and best-fit approaches for functional response curve fitting? Do contemporary model selection exercises identify the most biologically-relevant model?
● What are the impacts of global environmental change (e.g., climate change, deforestation, invasive species, loss of apex predators, shrinking reserve sizes) on the functional response, and how might they impact our natural systems?
This Research Topic showcases the impact that Holling’s initial work on the consumer functional response continues to have. It is our hope that the work published in this Research Topic will inspire new research in this fundamental aspect of ecology.
Author contributions
TH and DM contributed to conception of this manuscript and its contents. TH wrote the first draft of the manuscript. Both authors contributed to manuscript revision, read, and approved the submitted version.
Acknowledgments
Throughout the preparation of this Research Topic, we have had several constructive conversations about predator–prey ecology with the authors who contributed papers. These conversations stimulated new ideas and reinforced or clarified our thinking on others. We thank all the contributing authors for their efforts, as well as the Frontiers in Ecology and Evolution editorial and support teams for their assistance throughout this process. We also thank A. B. Ryabov for constructive comments on this editorial.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
Abrams P. A. (2015). Why ratio dependence is (still) a bad model of predation. Biol. Rev. 90, 794–814. doi: 10.1111/brv.12134
Abrams P. A., Ginzburg L. R. (2000). The nature of predation: prey dependent, ratio dependent or neither? Trends Ecol. Evol. 15, 337–341. doi: 10.1016/S0169-5347(00)01908-X
Arditi R., Akçakaya H. R. (1990). Underestimation of mutual interference of predators. Oecologia 83, 358–361. doi: 10.1007/BF00317560
Arditi R., Ginzburg L. R. (1989). Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol. 139, 311–326. doi: 10.1016/S0022-5193(89)80211-5
Arditi R., Ginzburg L. R. (2012). How species interact: altering the standard view on trophic ecology (Oxford: Oxford University Press).
Baudrot V., Perasso A., Fritsch C., Giraudoux P., Raoul F. (2016). The adaptation of generalist predators’ diet in a multi-prey context: insights from new functional responses. Ecology 97, 1832–1841. doi: 10.1890/15-0427.1
Bruzzone O. A., Aguirre M. B., Hill J. G., Virla E. G., Logarzo G. (2022). Revisiting the influence of learning in predator functional response, how it can lead to shapes different from type III. Ecol. Evol. 12, e8593. doi: 10.1002/ece3.8593
Chan K. W., Boutin S., Hossie T. J., Krebs C. J., O’Donoghue M., Murray D. L. (2017). Improving the assessment of predator functional responses by considering alternate prey and predator interactions. Ecology 98, 1787–1796. doi: 10.1002/ecy.1828
Coblentz K. E., Novak M., DeLong. J. P. (2022). Predator feeding rates may often be unsaturated under typical prey densities. Ecol. Lett. 26, 302–312. doi: 10.1111/ele.14151
Cuthbert R. N., Dick J. T. A., Callaghan A., Dickey J. W. E. (2018). Biological control agent selection under environmental change using functional responses, abundances, and fecundities; the relative control potential metric. Biol. Control 121, 50–57. doi: 10.1016/j.biocontrol.2018.02.008
DeLong J. P. (2021). Predator ecology: evolutionary ecology of the functional response (Oxford: Oxford Academic). doi: 10.1093/oso/9780192895509.001.0001
DeLong J. P., Vasseur D. A. (2011). Mutual interference is common and mostly intermediate in magnitude. BMC Ecol. 11, 1. doi: 10.1186/1472-6785-11-1
Dick J. T., Alexander M. E., Jeschke J. M., Ricciardi A., MacIsaac H. J., Robinson T. B., et al. (2014). Advancing impact prediction and hypothesis testing in invasion ecology using a comparative functional response approach. Biol. Invasions 16, 735–753. doi: 10.1007/s10530-013-0550-8
Dick J. T., Gallagher K., Avlijas S., Clarke H. C., Lewis S. E., Leung S., et al. (2013). Ecological impacts of an invasive predator explained and predicted by comparative functional responses. Biol. Invasions 15, 837–846. doi: 10.1007/s10530-012-0332-8
Faria L., Cuthbert R. N., Dickey J. W. E., Jeschke J. M., Ricciardi A., Dick J. T. A., et al. (2023). The rise of the functional response in invasion science: a systematic review. NeoBiota 85, 43–79. doi: 10.3897/neobiota.85.98902
Fernández-arhex V., Corley J. C. (2003). The functional response of parasitoids and its implications for biological control. Biocontrol Sci. Tech. 13, 403–413. doi: 10.1080/0958315031000104523
Fryxell J. M., Mosser A., Sinclair A. R. E., Packer C. (2007). Group formation stabilizes predator? Prey dynamics Nature 449, 1041–1043. doi: 10.1038/nature06177
Fussmann G. F., Blasius B. (2005). Community response to enrichment is highly sensitive to model structure. Biol. Lett. 1, 9–12. doi: 10.1098/rsbl.2004.0246
Gentleman W., Leising A., Frost B., Strom S., Murray J. (2003). Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics. Deep Sea Res. Part II: Topical Stud. Oceanogr. 50, 2847–2875. doi: 10.1016/j.dsr2.2003.07.001
Ginzburg L., Colyvan M. (2004). Ecological orbits: how planets move and populations grow (New York, USA: Oxford University Press, New York).
Hassell M. P. (1978). The dynamics of arthropod predator-prey systems (Princeton, NJ: Princeton University Press).
Holling C. S. (1959a). The components of predation as revealed by a study of small mammal predation of the European pine sawfly. Can. Entomol. 91, 293–320. doi: 10.4039/Ent91293-5
Holling C. S. (1959b). Some characteristics of simple types of predation and parasitism. Can. Entomol. 91 (7), 385–398. doi: 10.4039/Ent91385-7
Holling C. S. (1961). Principles of insect predation. Annu. Rev. Entomol. 6, 163–182. doi: 10.1146/annurev.en.06.010161.001115
Hossie T. J., Chan K., Murray D. L. (2021). Increasing availability of palatable prey induces predator-dependence and increases predation on unpalatable prey. Sci. Repts. 11, 6763. doi: 10.1038/s41598-021-86080-x
Hossie T. J., Murray D. L. (2010). You can’t run but you can hide: refuge use in frog tadpoles elicits density-dependent predation by dragonfly larvae. Oecologia 163, 395–404. doi: 10.1007/s00442-010-1568-6
Hossie T. J., Murray D. L. (2016). Spatial arrangement of prey affects the shape of ratio-dependent functional response in strongly antagonistic predators. Ecology 97, 834–841. doi: 10.1890/15-1535.1
Jeschke J. M., Kopp M., Tollrian R. (2004). Consumer-food systems: why type I functional responses are exclusive to filter feeders. Biol. Rev. Camb. Philos. Soc 79, 337–349. doi: 10.1017/S1464793103006286
Jeschke J., Tollrian R. (2005). Effects of predator confusion on functional responses. Oikos 111, 547–555. doi: 10.1111/j.1600-0706.2005.14118.x
Juliano S. A. (2001). “Nonlinear curve fitting: predation and functional response curves,” in Design and analysis of ecological experiments. Eds. Scheiner S. M., Gurevitch J. (London: Chapman and Hall), 178–196.
Kratina P., Vos M., Anholt B. R. (2007). Species diversity modulates predation. Ecology 88, 1917–1923. doi: 10.1890/06-1507.1
Morozov A., Petrovskii S. (2013). Feeding on multiple sources: towards a universal parameterization of the functional response of a generalist predator allowing for switching. PloS One 8, e74586. doi: 10.1371/journal.pone.0074586
Murdoch W. W. (1969). Switching in general predators: experiments on predator specificity and stability of prey populations. Ecol. Monogr. 39, 335–354. doi: 10.2307/1942352
Murdoch W. W., Avery S., Smyth M. E. B. (1975). Switching in predatory fish. Ecology 56, 1094–1105. doi: 10.2307/1936149
Novak M. (2010). Estimating interaction strengths in nature: experimental support for an observational approach. Ecology 91, 2394–2405. doi: 10.1890/09-0275.1
Novak M., Stouffer D. B. (2021). Systematic bias in studies of consumer functional responses. Ecol. Lett. 24, 580–593. doi: 10.1111/ele.13660
Okuyama T. (2009). Local interactions between predators and prey call into question commonly used functional responses. Ecol. Model. 220, 1182–1188. doi: 10.1016/j.ecolmodel.2009.02.010
Okuyama T., Ruyle R. L. (2011). Solutions for functional response experiments. Acta Oecol. 37, 512–516. doi: 10.1016/j.actao.2011.07.002
Real L. A. (1977). The kinetics of the functional response. Am. Nat. 111, 289–300. doi: 10.1086/283161
Ruxton G. D. (2005). Increasing search rate over time may cause a slower than expected increase in prey encounter rate with increasing prey density. Biol. Lett. 1, 133–135. doi: 10.1098/rsbl.2004.0292
Ryabov A. B., Morozov A., Blasius B. (2015). Imperfect prey selectivity of predators promotes biodiversity and irregularity in food webs. Ecol. Lett. 18, 1262–1269. doi: 10.1111/ele.12521
Travis J. M. J., Palmer S. C. F. (2005). Spatial processes can determine the relationship between prey encounter rate and prey density. Biol. Lett. 1, 136–138. doi: 10.1098/rsbl.2004.0293
Turchin P. (2003). Complex population dynamics: a theoretical/empirical synthesis (Princeton, New Jersey, USA: Princeton University Press).
Vallina S. M., Ward B. A., Dutkiewicz S., Follows M. J. (2014). Maximal feeding with active prey-switching: a kill-the-winner functional response and its effect on global diversity and biogeography. Prog. Oceanogr. 120, 93–109. doi: 10.1016/j.pocean.2013.08.001
Keywords: consumer-resource dynamics, density-dependence, predation, predator-dependence, population ecology, predation rate, species interactions
Citation: Hossie TJ and Murray DL (2023) Editorial: New perspectives and emerging directions in predator–prey functional response research: Hommage to C.S. Holling (1930–2019). Front. Ecol. Evol. 11:1238953. doi: 10.3389/fevo.2023.1238953
Received: 12 June 2023; Accepted: 27 June 2023;
Published: 07 July 2023.
Edited and Reviewed by:
Alexei B. Ryabov, University of Oldenburg, GermanyCopyright © 2023 Hossie and Murray. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Thomas J. Hossie, thossie@trentu.ca