Maximal feeding with active prey-switching: A kill-the-winner functional response and its effect on global diversity and biogeography

Abstract

Predators’ switching towards the most abundant prey is a mechanism that stabilizes population dynamics and helps overcome competitive exclusion of species in food webs. Current formulations of active prey-switching, however, display non-maximal feeding in which the predators’ total ingestion decays exponentially with the number prey species (i.e. the diet breadth) even though the total prey biomass stays constant. We analyse three previously published multi-species functional responses which have either active switching or maximal feeding, but not both. We identify the cause of this apparent incompatibility and describe a kill-the-winner formulation that combines active switching with maximal feeding. Active switching is shown to be a community response in which some predators become prey-selective and the formulations with maximal or non-maximal feeding are implicitly assuming different food web configurations. Global simulations using a marine ecosystem model with 64 phytoplankton species belonging to 4 major functional groups show that the species richness and biogeography of phytoplankton are very sensitive to the choice of the functional response for grazing. The phytoplankton biogeography reflects the balance between the competitive abilities for nutrient uptake and the degree of apparent competition which occurs indirectly between species that share a common predator species. The phytoplankton diversity significantly increases when active switching is combined with maximal feeding through predator-mediated coexistence.

Introduction

Active prey-switching is a predatory behavior that has been documented in natural ecosystems (Murdoch, 1969, Murdoch, 1975, Hughes and Croy, 1993, Kiørboe et al., 1996, Gismervik and Andersen, 1997, Elliott, 2006, Kempf et al., 2008, Kiørboe, 2008, Kalinkat et al., 2011) and is known to stabilize ecosystem dynamics (Murdoch and Oaten, 1975, Haydon, 1994, Armstrong, 1999, Morozov, 2010). Active switching differs from passive switching in that the predators’ switching is variable and based on relative prey density (i.e. frequency-dependent predation), rather than being fixed and based on constant prey preferences (see Gentleman et al. (2003) for a review). Thus, active switching represents a behavioral change of the predator (Gentleman et al., 2003), either in terms of feeding strategy (e.g. from passive suspension feeding to active ambush feeding) (Kiørboe et al., 1996, Gismervik and Andersen, 1997, Wirtz, 2012b) or learning how to increase the efficiency of capturing and handling certain prey types (Murdoch, 1973). Active switching makes the proportion of a given prey attacked to change from less than expected to more than expected as the relative abundance of that prey increases (Hassell, 2000).

From an ecosystem modeling perspective, active switching is an interesting property because it allows for a greater degree of species co-existence in competitive food webs (Vallina and Le Quéré, 2011, Prowe et al., 2012a, Prowe et al., 2012b). Multi-species ecosystem models can overcome the competitive exclusion principle (Hardin, 1960, Hutchinson, 1961, Armstrong and McGehee, 1980) by including some form of active switching (Adjou et al., 2012). In a broad sense, selective predation can be argued to fit within the “killing the winner” theory, which is sometimes invoked to explain the high diversity we observe in microbial communities (Thingstad and Lignell, 1997, Thingstad, 2000). The basic idea is that the most abundant bacteria types will be killed preferentially by host-selective viral lysis. Therefore, the coexistence of competing bacterial species is ensured by the presence of viruses that kill-the-winner, whereas the differences in substrate affinity between the coexisting bacterial species determine viral abundance (Thingstad, 2000). Active switching follows conceptually the same principle but for predator–prey selectivity.

However, current formulations of active prey-switching show anomalous dynamics, like antagonistic feeding and sub-optimal feeding in which predators are unable to maximize the ingestion of the total food available when it becomes divided among several prey (Tilman, 1982, Holt, 1983, Gentleman et al., 2003). In antagonistic feeding, if total food abundance is evenly distributed among many prey, it will give a smaller total ingestion than if the same total food is concentrated in one prey species (Tilman, 1982). In other words, for a given total food availability, the most even distribution of prey biomass will give the lowest total ingestion. Sub-optimal feeding occurs when an increase in the abundance of one prey can also result in a decrease of ingestion, despite that total food is actually increasing. Sub-optimal feeding is an extreme form of antagonistic feeding (Gentleman et al., 2003). When taken to the limit where each prey contributes to an infinitesimal fraction of the total prey abundance, these two modes of non-maximal feeding imply that the total ingestion by the predators will tend towards zero, even if the combined biomass of all their prey is high.

These formulation inconsistencies are conceptually problematic and have been used to warn against the use of active switching functional responses in ecosystem models (Gentleman et al., 2003). Here we argue that the problem does not lie with the use of active switching per-se but with the fact that current formulations are not completely satisfactory representations of switching behavior (Holt, 1983, Mitra and Flynn, 2006, Anderson et al., 2010). Total ingestion should ideally depend on the total food amount and its quality but not necessarily on the biomass distribution of the prey. In such a functional response all the prey would be perfectly substitutable for equal fixed preferences (Tilman, 1982) and feeding will always be maximal. The original Holling Type II functional response is probably the best known example (Holling, 1959, Gentleman et al., 2003). However, it does not allow for active prey-switching and therefore the competitive exclusion among the prey is very difficult to prevent and the ecosystem stability is drastically reduced (Gismervik and Andersen, 1997). Ward et al. (2012) suggests an equation for the switching between herbivory and carnivory. We use a similar approach for the switching between individual prey.

The first objective of this work is to identify the origin of the observed incompatibility between active switching and maximal ingestion in current formulations of predation on multiple prey (Gentleman et al., 2003). We evaluate three classical formulations of predation: two that exhibit switching but non-maximal ingestion (one sub-optimal, one antagonistic); and one that exhibits maximal ingestion but no-switching. We also describe a kill-the-winner (KTW) functional response that combines active switching with maximal ingestion (see Appendix A). Maximal and non-maximal ingestion are shown to arise from the implicit assumptions of the food web configuration inherent to each functional response (see Appendix B).

The second objective of this work is to evaluate how grazing functional responses affect the simulated global distributions of marine phytoplankton diversity and biogeography. The choice of the grazing response has already been shown to drastically change the simulated distributions of phytoplankton biogeography (Anderson et al., 2010) and diversity (Prowe et al., 2012a). However, these results were obtained from comparing “passive-switching with maximal feeding” formulations (i.e. Real’s) against “active-switching with non-maximal feeding” formulations (i.e. Fasham’s and Ryabchenko’s). Following a similar approach here we also evaluate the effect of the new KTW formulation that combines active-switching with maximal feeding. Thus we implemented the four functional responses under study (i.e. Fasham, Ryabchenko, Real, KTW) in a global marine ecosystem model with 64 phytoplankton species belonging to 4 functional groups which are differentiated by their dependence of growth on external nutrients. We show that active switching is a mechanism that allows higher levels of species co-existence, specially when combined with strong top-down control (i.e. maximal feeding). We use the term “species” in a very broad and general sense, simply denoting variability of the phytoplankton traits for nutrient uptake. An alternative term could be phytoplankton ecotypes (Dutkiewicz et al., 2009).