Biodiversity maintenance in food webs with regulatory environmental feedbacks
Introduction
Organisms within an ecosystem are constantly interacting with and altering their abiotic environment. While classic food-web studies have focused mainly on trophic interactions and energy fluxes (Elton, 1927; Lindeman, 1942) unraveling the effects of environmental feedbacks and environmental modification by organisms on biodiversity maintenance is a current focus in ecological research (de Ruiter et al., 2005; Harding, 1999; Hooper et al., 2005; Loladze et al., 2004; Wright and Jones, 2006; Wright et al., 2006). We propose that organismal feedback-coupled interactions with the environment are likely critical components both for sustaining biodiversity in complex, multiple trophic level food webs and for altering their susceptibility to environmental stressors.
Intuitive and empirical conclusions that complexity is a characteristic feature of natural communities of species stand at odds with May's theoretical demonstration that increasing biodiversity and complexity destabilize food webs (May, 1971, May, 1973; and see DeAngelis, 1975; de Ruiter et al., 1995; Hutchinson, 1959; MacArthur, 1955; Neutel et al., 2002; Odum, 1953; Worm and Duffy, 2003; Yodzis, 1981). Current stability–complexity studies continue to be based upon model food webs with diverse predator–prey links or numbers of species. For these food-web structures, predator–prey dynamics are described through increasingly sophisticated systems of differential equations motivated by Lotka–Volterra-like formulations (Brose et al., 2003; Chen and Cohen, 2001; Kondoh, 2003; McCann, 2000). However, these systems are typically prone to significant numbers of species extinctions. Fundamental understanding of the mechanisms—and often identification of the mechanisms—ensuring food-web integrity remains a challenge, and several important schemes leading to increased species persistence have been proposed.
For example, different forms for predator–prey functional responses that alter consumption rates of abundant or rare food resources have successfully been used to promote persistence of large fractions of species in large food webs (Martinez et al., 2006; Williams and Martinez, 2004). Complementary to these studies of large food-web dynamics are explorations addressing the effects of removal of keystone species in increasingly complex food-web structures (Brose et al., 2005). In a different vein, adaptive foraging strategies have been introduced into food-web dynamics whereby predators continuously modify their consumption efforts to focus on those prey yielding above-average energy gains (Brose et al., 2003; Kondoh, 2003, Kondoh, 2006). These strategies are found to increase species persistence in large food webs and to potentially reverse the complexity–stability relationship so that more complex food webs are more stable. Evolutionary schemes in which food-web construction proceeds through sequential species addition leading either to new and persistent predator–prey interactions or to extinction events have been used to create complex food webs with realistic trophic structuring (Drossel et al., 2001; Loeuille and Loreau, 2005; McKane, 2004). Other studies aimed at understanding dynamical food-web persistence have drawn attention to predator–prey body size effects (Emmerson and Raffaelli, 2004) and to coupled fast and slow energy channels for production-to-biomass ratios that exist in natural food webs (Rooney et al., 2006). This latter study connects to earlier work where weak-link interactions between species are shown to promote community persistence (McCann et al., 1998) and resonates with a recent study revealing asymmetric interactions between mutually dependent animal and plant species as an important key to biodiversity maintenance in real food webs (Bascompte et al., 2006). Furthermore, non-dynamical simulations of species removal and subsequent secondary extinctions based upon structural considerations in well-characterized real food webs have contributed to understanding stability–complexity relationships (Dunne et al., 2002).
None of these food-web models, however, take into consideration feedbacks and couplings between organisms and their environment. However, ecosystem function beyond the “who-eats-whom” of food-web dynamics is important to food-web studies (Moorcroft, 2003; Pascual, 2005) and potentially, as in the context of our work, to species persistence. While studies including biogeochemical considerations and ecological stoichiometric constraints (DeAngelis, 1992; Elser et al., 1998; Moe et al., 2005; Schlesinger, 1997; Sterner and Elser, 2002) do place organisms in dynamic physical–chemical environments, effects on multiple trophic level food-web dynamics are not typically addressed: small, often analytically tractable, systems are in focus (Daufresne and Loreau, 2001a, Daufresne and Loreau, 2001b; Grover, 2003; Hall et al., 2006; Kuijper et al., 2004; Loladze et al., 2004). We still lack a basic understanding of how environmental feedbacks impact the dynamics and persistence of structurally realistic food webs. The work presented here is a contribution in that direction.
The environmental feedbacks we consider are regulatory in nature. That is, within a food web a subset of species regulates an environmental variable through feedback couplings with it. Regulatory feedbacks add functional complexity to food-web models, thereby introducing a new dimension to the stability–complexity debate.
Specifically, we have extended food-web models constructed through the niche model (Williams and Martinez, 2000)—which results in realistic structural characteristics including hierarchical trophic structure, cannibalism, and looping—to include simple regulatory environmental feedbacks in the form of Lovelock's Daisyworld (DW) (Lovelock, 1992; Watson and Lovelock, 1983). Although a theoretical construct, DW's elegant simplicity and well-understood mathematical structure make it an excellent candidate for studying species persistence in food webs coupled to environmental feedbacks.
In the original DW system, two daisy species, white and black, populate the surface of a virtual planet. White daisies reflect sunlight and so cool their local environment, while black daisies absorb sunlight and cause warming. These environmental feedbacks result in a self-organized ratio of black to white daisies for temperature regulation over a wide range of the sun's luminosity. It is in this sense that we refer to “regulatory environmental feedbacks.” In our food webs, the autotrophs are modeled upon the daisies of DW for their environmental coupling.
By generating food webs with the niche-model algorithm (Williams and Martinez, 2000), we are able to study the effects of environmental feedbacks on a multitude of realistic and structurally diverse food webs. To our knowledge only two previous studies consider DW function in a food-web context (Harding, 1999; Lovelock, 1992). Unlike these studies, we examine the effects of environmental feedbacks on the extinction probability of species within systems featuring high trophic diversity, realistic structural characteristics, and multi-species predator–prey dynamics.
Two natural systems may feature comparable regulatory mechanisms. Hunt and Wall report that the adaptive homeostatic changes they observe in their study of carbon and nitrogen transfers in a soil ecosystem are “reminiscent” of DW (Hunt and Wall, 2002). Furthermore, mutualistic interactions between deep-sea tubeworms L. luymesi, their symbionts and external microbial consortia create a feedback system allowing for emergent matching of sulfide supply and demand to the tubeworms (Cordes et al., 2005). We propose that the regulatory features of these systems can also be embedded within niche-model food webs.
Section snippets
Methods
The focus of this paper is species persistence in food webs with environmental feedbacks: after simulation of predator–prey dynamics, species persistence is reported specifically as the ratio of the number of surviving species to the starting number in a given web.
Collections of 10-, 15-, and 20-species food webs were constructed through the niche-model algorithm developed by Williams and Martinez (2000). Briefly, in order to generate an N-species food web each species is assigned a random
Results and analysis
The number of species extinctions and, consequently, species persistence are calculated for every food web at each connectance value, with and without environmental feedbacks, that is, with the parameter γ=0.00326 and with γ=0. Species persistence, again with and without regulatory feedbacks, is averaged over all food webs at a given connectance. We find that for food webs at each level of biodiversity (10-, 15-, and 20-species) average species persistence increases when temperature feedbacks
Discussion and conclusions
Daisyworld, although a theoretical construct, provides a powerful inroad to identifying features leading to species persistence in real food webs. We suggest that food webs featuring realistic environmental couplings with attractor dynamics for an environmental variable will also manifest increased overall species persistence.
In their study of soil biodiversity and ecosystem function, Hunt and Wall (2002) studied carbon and nitrogen transfers among plants, microbes, and soil fauna using
Acknowledgments
We thank Neo Martinez for insight into the niche model, Jim Elser for discussions, and Volker Rudolf for a critical reading of the manuscript. We are grateful for thoughtful input and suggestions from three anonymous reviewers. The Jeffress Memorial Trust, The College of William and Mary, Harvard University, and the Howard Hughes Medical Institute extended financial support.
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Present address: Monitoring and Assessment of Biodiversity Program, National Zoological Park, Smithsonian Institution, 1100 Jefferson Drive, SW, Suite 3123, Washington DC 20560, USA.
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These authors contributed equally to this work.