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Modeling Foundation Species in Food Webs 1,3, 2 1 BENJAMIN BAISER, NATHANIEL WHITAKER, and AARON M

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Modeling Foundation Species in Food Webs 1,3, 2 1 BENJAMIN BAISER, NATHANIEL WHITAKER, and AARON M Modeling foundation species in food webs 1,3, 2 1 BENJAMIN BAISER, NATHANIEL WHITAKER, AND AARON M. ELLISON 1Harvard University, Harvard Forest, 324 N. Main Street, Petersham, Massachusetts 01366 USA 2Department of Mathematics and Statistics, University of Massachusetts at Amherst, 1424 Lederle Graduate Research Center, Amherst, Massachusetts 01003-9305 USA Citation: Baiser, B., N. Whitaker, and A. M. Ellison. 2013. Modeling foundation species in food webs. Ecosphere 4(12):146. http://dx.doi.org/10.1890/ES13-00265.1 Abstract. Foundation species are basal species that play an important role in determining community composition by physically structuring ecosystems and modulating ecosystem processes. Foundation species largely operate via non-trophic interactions, presenting a challenge to incorporating them into food web models. Here, we used non-linear, bioenergetic predator-prey models to explore the role of foundation species and their non-trophic effects. We explored four types of models in which the foundation species reduced the metabolic rates of species in a specific trophic position. We examined the outcomes of each of these models for six metabolic rate ‘‘treatments’’ in which the foundation species altered the metabolic rates of associated species by one-tenth to ten times their allometric baseline metabolic rates. For each model simulation, we looked at how foundation species influenced food web structure during community assembly and the subsequent change in food web structure when the foundation species was removed. When a foundation species lowered the metabolic rate of only basal species, the resultant webs were complex, species-rich, and robust to foundation species removals. On the other hand, when a foundation species lowered the metabolic rate of only consumer species, all species, or no species, the resultant webs were species-poor and the subsequent removal of the foundation species resulted in the further loss of species and complexity. This suggests that in nature we should look for foundation species to predominantly facilitate basal species. Key words: food web modeling; foundation species; metabolic rate; network; non-linear dynamics. Received 20 August 2013; revised 5 October 2013; accepted 8 October 2013; final version received 30 October 2013; published 9 December 2013. Corresponding Editor: D. P. C. Peters. Copyright: Ó 2013 Baiser et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://creativecommons.org/licenses/by/3.0/ 3 Present address: Department of Wildlife Ecology and Conservation, University of Florida, P.O. Box 110430, Gainesville, Florida 32611-0430 USA. E-mail: [email protected] INTRODUCTION tion species in ecological communities (reviewed by Ellison et al. 2005, 2010, Van der Putten 2012). Foundation species (sensu Dayton 1972) are Numerous field studies have shown that foun- basal species that structure ecological communi- dation species can alter trajectories of the ties by creating physical structure and modulat- assembly of ecological communities (e.g., Gibson ing ecosystem processes (Ellison et al. 2005). et al. 2012, Scho¨eb et al. 2012, Butterfield et al. Recent declines (e.g., Tsuga canadensis)and 2013, Martin and Goebel 2013, Orwig et al. extirpations (e.g., Castanea dentata) of foundation 2013). However, general models of how foun- species in terrestrial ecosystems have called dation species affect ecological systems are attention to the need for new methods for scarce and generally qualitative (Ellison and identifying and quantifying the role of founda- Baiser, in press). v www.esajournals.org 1 December 2013 v Volume 4(12) v Article 146 BAISER ET AL. Foundation species can interact trophically Noumi et al. 2012, Butterfield et al. 2013). within a community, but they exert their influ- We developed four different foundation spe- ence primarily through non-trophic effects (Elli- cies models to explore non-trophic effects of son and Baiser, in press). Some examples of non- foundation species in food webs. In each, the trophic actions of foundation species include: foundation species influences target species at altering local climates and microclimates (e.g., different trophic positions in the food web: (1) a Scho¨eb et al. 2012, Butterfield et al. 2013); basal model, in which the foundation species changing soil temperature, moisture, and acidity reduces the metabolic rates of only other, albeit (e.g., Prevey et al. 2010, Lustenhouwer et al. 2012, non-foundation, basal species; (2) a consumer Martin and Goebel 2013); providing refuge for model, in which the foundation species reduces prey species and perches for predators (e.g., the metabolic rates of only consumers; (3) a total Yakovis et al. 2008, Tovar-Sa´nchez et al. 2013); model, in which the foundation species reduces and stabilizing stream banks and shorelines the metabolic rates of all species; and (4) a control against erosion (reviewed by Ellison et al. model, in which the foundation species is only 2005). Because foundation species exert system- consumed and has no effect on the metabolic wide effects on biodiversity and ecosystem rates of any associated species. We examined the functioning primarily through these (and other) outcomes of each of these models for six non-trophic interactions, it has proven difficult to metabolic rate ‘‘treatments’’ in which the foun- link effects of foundation species into theories of dation species alters the metabolic rates of the structure and function of food webs. Food associated species by one-tenth to ten times their web theory aims to elucidate the persistence of allometric baseline metabolic rates. For each the types of complex, species-rich webs that we model simulation, we looked at how foundation see in nature (e.g., May 1972, Allesina and Tang species influence different measures of food web 2012). Measures of network properties, such as structure during community assembly and the connectance, compartmentalization, and species subsequent change of food web structure when richness,aswellasthestrengthofspecies the foundation species was removed. interactions, all can influence the stability and persistence of food webs (e.g., May 1972, Dunne METHODS et al. 2002, Gravel et al. 2011, Stouffer and Bascompte 2011). Adding non-trophic interac- We modeled dynamic ecological networks tions, such as those exhibited by foundation using a four-step process (Brose et al. 2006, species or mutualists in general, provides an Berlow et al. 2009, Ke´fi et al. 2012): (1) model additional step towards understanding persis- initial network structure; (2) calculate body mass tence and stability of ecological networks (The- for each species based on trophic level; (3) bault and Fontaine 2010, Allesina and Tang 2012, simulate population dynamics using an allome- Ke´fi et al. 2012) tric predator-prey model; and (4) add non- Here, we adapt non-linear, bioenergetic pred- trophic interactions into the allometric predator- ator-prey models to explore non-trophic roles of prey model. foundation species in food webs. To make explicit linkages between trophic and non-tro- Network structure phic interactions, we model the metabolic rate of We used the niche model of Williams and individual ‘‘species’’ as a function of foundation Martinez (2000) to designate trophic links in our species biomass. Metabolic rate is good proxy for model food webs. The niche model is an a wide variety of positive non-trophic species algorithm with two parameter inputs: species interactions (sensu Ke´fi et al. 2012), because richness (S) and connectance (C ¼ L/S2, where L ¼ ‘‘stressful conditions’’ may be reduced when the number of trophic links). Each species in the foundation species ameliorate temperature ex- web has a niche value uniformly drawn from [0, tremes, provide associated species with habitat 1] and a niche range that is placed on a one- resources or shelters, or enhance their growth dimensional axis. Any one species whose niche rate (Schiel 2006, Shelton 2010, Gedan et al. 2011, value falls within the niche range of another is Angelini and Silliman 2012, Dijkstra et al. 2012, defined to be the latter’s prey (for specific details v www.esajournals.org 2 December 2013 v Volume 4(12) v Article 146 BAISER ET AL. on the niche model see Williams and Martinez j; and fij is the fraction of biomass removed from 2000). The niche model has been shown to the resource biomass that is actually ingested. reproduce accurately a wide range of food web The functional response, Fij, describes how network properties for many empirical webs consumption rate varies as a function of prey (Williams and Martinez 2000, Dunne et al. 2004, biomass. We used a type II functional response: Williams and Martinez 2008). xijBj Fij ¼ X : ð3Þ Body mass B0 þ xikBk We calculated body mass, Mi, for species i as: k¼resources TÀ1 In Eq. 3, x is the uniform relative consumption Mi ¼ Z : ð1Þ ij rate of consumer i preying on resource j (i.e., the In Eq. 1, Z is the predator-prey biomass ratio and preference of consumer i for resource j) when the T is the average trophic level of species i consumer has n total resources (xij ¼ 1/n) and B0 calculated using the prey-averaged method is the half-saturation constant (i.e., resource (Williams and Martinez 2004). We set basal biomass at which consumer reaches half of its species M to unity and used a predator-prey maximum consumption rate). In all of our biomass ratio of Z ¼ 102. We used body mass to models, B0 was set equal to 0.5. allometrically scale biological parameters in the Body size is an important component of both predator-prey model. predator-prey interactions (Warren and Lawton 1987, Woodward and Hildrew 2002, Brose et al. Allometric predator–prey model 2006) and metabolic functioning of organisms We simulated food web population dynamics (Brown et al.
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