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.

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.

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).

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.

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.

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.