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     * [10]Abstract
     * [11]Introduction
     * [12]Section snippets
     * [13]References (59)
     * [14]Cited by (12)

   [15]Elsevier

[16]Journal of Theoretical Biology

   [17]Volume 343, 21 February 2014, Pages 127-137
   [18]Journal of Theoretical Biology

Competition in di- and tri-trophic food web modules

   Author links open overlay panel (BUTTON) Vlastimil Krivan ^a ^b
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   [19]https://doi.org/10.1016/j.jtbi.2013.11.020[20]Get rights and content

Highlights

     * o Competition in many species in di- and tri-trophic food webs is studied.
     * o The top species have either fixed or adaptive preferences for their prey.
     * o It is shown that prey switching strongly promotes species coexistence.
     * o In food-web modules studied, prey switching leads to food-web dynamics that
       are similar to linear-food chains.

Abstract

   Competition in di- and tri-trophic food web modules with many competing species
   is studied. The food web modules considered are apparent competition between n
   species sharing a single predator and a diamond-like food web with a single
   resource, a single top predator and many competing middle species. The predators
   have either fixed preferences for their prey, or they switch between available
   prey in a way that maximizes their fitness. Dependence of these food web dynamics
   on environmental carrying capacity and food web connectance is studied. The
   results predict that optimal flexible foraging strongly weakens apparent
   competition and promotes species coexistence. Food web robustness (defined here
   as the proportion of surviving species) does not decrease with increased
   connectance in these food-webs. Moreover, it is shown that flexible prey
   switching leads to the same population equilibria as in corresponding food webs
   with highly specialized predators. The results show that flexible [21]foraging
   behavior by predators can have very strong impact on species richness, as well as
   the response of communities to changes in resource enrichment and food-web
   connectance when compared to the same food-web topology with inflexible top
   predators. Several results on global stability using Lyapunov functions are
   provided.

Introduction

   Understanding coexistence of competing species on a limited number of resources
   has been one of the most challenging tasks for ecologists. The "competitive
   exclusion principle" states that two complete competitors cannot coexist at an
   equilibrium when feeding on a single resource (e.g., Gause, 1934, Hardin, 1960).
   More generally, n competing species cannot coexist at a population equilibrium if
   they are limited by less than n limiting factors (Levin, 1970). How is it then
   possible that many species do survive in nature? One such example is the large
   number of phytoplankton species surviving on just a few common resources. This
   puzzling discrepancy between empirical observations and theoretical predictions
   has been termed "the paradox of phytoplankton" (Hutchinson, 1961). Since that
   time, several possible mechanisms explaining competing species coexistence were
   proposed. Hutchinson (1961) proposed that species coexistence can be achieved due
   to fluctuating environment that prevents population densities to settle at an
   equilibrium and favors different species at different times. Similarly, intrinsic
   oscillations in species abundances can promote species coexistence (e.g.,
   Armstrong and McGehee, 1980, Huisman and Weissing, 1999). Predation is another
   mechanism that can relax competition among competitors. This was experimentally
   verified by Slobodkin (1964) with his hydra experiments and on a larger spatial
   scale by Paine (1969) who showed that removal of starfish Pisaster ochraceus
   resulted in the competitive exclusion of most barnacle species on which the
   starfish normally feeds. Thus, barnacle co-existence was facilitated by the
   common predator.

   As specialized predators act as limiting factors, it is not surprising that in
   food-webs where each competitor is limited by its own predator, coexistence is
   possible. The question is when a single predator species can enhance survival of
   several competing species. Leibold (1996) and Holt et al. (1994) showed that two
   competing species can coexist in a diamond-like food web where they both compete
   for a common resource and are consumed by a common generalist predator. These
   predictions do not violate the competitive exclusion principle because in the
   diamond-like food web with two competing middle species there are exactly two
   limiting factors: the common resource and the predator. However, Krivan (2003)
   showed that even with two competitors coexistence is limited to a narrow range of
   demographic parameters. The situation dramatically changed when top predators
   were flexible foragers with foraging preferences that maximized their fitness. In
   this case, the set of parameters for which the two species coexisted was much
   larger when compared to the same system with fixed predator preferences. Similar
   results were obtained by several authors who studied two-consumer-one-predator
   food webs with optimally foraging predators (e.g., Abrams, 1982, Holt, 1983,
   Fryxell and Lundberg, 1993, Fryxell and Lundberg, 1994, Holt et al., 1994,
   Krivan, 1996, Krivan, 1997, Fryxell and Lundberg, 1997, Abrams, 2010). These
   works focused mostly on simple food-web modules (sensu Holt, 1997) such as
   exploitative or apparent competition (Holt, 1977, Holt, 1984) between consumers.
   While analyses of these modules are instrumental in our understanding of basic
   mechanisms of species coexistence, it is much more difficult to extrapolate these
   results to complex food-webs.

   One of the fundamental questions of ecology asks how diversity relates to species
   coexistence. A general early belief was that higher diversity creates greater
   opportunities for negative regulatory feedbacks in food webs which, in turn,
   enhance species coexistence and stability (Odum, 1971). The assumption that
   complexity begets stability was challenged by May (1972) (see also Gardner and
   Ashby, 1970) who showed that for randomly assembled food webs with fixed
   interaction strength between species, there is a sharp transition from stability
   to instability when complexity measured as the food-web connectance (i.e., the
   number of realized links in the food web divided by the number of all possible
   links) exceeds a critical threshold. It was also shown that robustness (defined
   as the proportion of surviving species) decreases with increasing connectance
   (e.g., Brose et al., 2003, Berec et al., 2010). May's work was challenged by
   Kondoh (2003) who showed that when predators are flexible foragers (i.e., when
   interaction strength adaptively changes with changes in population densities),
   complexity can enhance community persistence. However, some subsequent works
   revealed that this prediction depends on other factors such as population
   dynamics (Brose et al., 2003), food web topology (Brose et al., 2003, Kondoh,
   2006, Garcia-Domingo and Saldaña, 2007, Uchida and Drossel, 2007), and details of
   foraging behavior (Berec et al., 2010).

   In this article I will focus on four food web modules (Fig. 1) with a fixed
   topology and many species. The deterministic food webs considered in this article
   are more complex when compared with simple food-web modules consisting of a few
   (usually 2-4) species, but they are simpler when compared with stochastic food
   webs generated e.g. by the cascade or niche model (Williams and Martinez, 2000).
   Such an intermediate level of complexity can allow one to discern ties to
   preexisting ecological theory more cleanly than is often the case with models
   dealing with stochastic complex food webs. In particular, I will study apparent
   competition (Fig. 1A) and combined apparent and exploitative competition (Fig.
   1C) among many species when top predators are generalists. I will also compare
   these food webs with similar food-web modules with highly specialized top
   predators (Fig. 1B and D). For generalist predators I consider two possibilities:
   either predators have fixed foraging preferences for their prey (called
   non-flexible predators), or they switch between available prey in a way that
   maximizes their fitness (called flexible predators). Dependence of the number of
   surviving species and the mean population abundances on the mean environmental
   carrying capacity and food web connectance is studied. I will show that
   population dynamics in the two food webs with a single flexible top predator
   (Fig. 1, panels A and C) are very similar to population dynamics with specialized
   predators (Fig. 1, panels B and D). The situation is strikingly different for
   inflexible generalist predators.

Section snippets

Di-trophic food webs

   In this section I will study a di-trophic food web consisting of several
   resources (
   [MATH: x1,...,xn :MATH]
   ) and their common generalist consumer (y, Fig. 1A). Such a food web can model
   mobile consumers feeding on patchily distributed immobile resources.
   Corresponding population dynamics can be conceptualized by the Lotka-Volterra
   model of apparent competition (Holt, 1977, Holt, 1984):
   [MATH: dxidt=rixi(1-xiKi)-liuixiy,i=1,...,ndydt=y\sumi=1nui(eilixi-mi), :MATH]
   where
   [MATH: 0