\documentclass[12pt]{article} \usepackage{times} \usepackage{graphicx} \oddsidemargin 0.7cm \textwidth 15cm \textheight 20cm \title{\bf Food Web Structure and Habitat Loss} \author{{\bf Carlos J. Meli\'an} and {\bf Jordi Bascompte} \\ \\Estaci\'on Biol\'ogica de Do\~nana, CSIC \\Apdo. 1056, E-41080 Sevilla, Spain.} \\ \date{ } \maketitle \baselineskip=6.1 mm \vspace{0.5 in} \centerline{Short running title: Food Web Structure and Habitat Loss.} \vspace{0.2 in} \centerline{ Type of article: Report.} \centerline{Number of words in abstract=104} \centerline{Number of words in manuscript=4,194} \vspace{0.2 in} Correspondence should be sent to: Carlos J. Meli\'an, Estaci\'on Biol\'ogica de Do\~nana, CSIC. Apdo. 1056, E-41080 Sevilla, Spain. Telephone: (+)34 954 232340. Fax: (+) 34 954 621125. e-mail: cmelian@ebd.csic.es. \vspace{0.2 in} Biosketch: Carlos J. Meli\'an uses both theory and the statistical analysis of data sets to understand the dynamics of ecological webs and their responses to human-induced perturbations. \newpage \begin{abstract} In this paper we explore simple food web models to study how metacommunity structure affects species response to habitat loss. We find that patch abundances and extinction thresholds vary according to the kind of food web. Second, for intermediate species, a slight decrease in the exploration cost of the better competitor has a strong effect on the extinction threshold of the poorer competitor. When predicting extinction risk one should consider not only the amount of habitat destroyed, but also the structure of the food web in which species are embedded. Both direct and indirect interactions are critical for predicting the consequences of habitat destruction. \vspace{0.4 in} \centerline{Keywords: Metacommunity. Habitat destruction. Omnivory.} \centerline{Apparent competition. Intraguild predation. Indirect interactions.} \end{abstract} \newpage \section{Introduction} Ongoing habitat destruction is the primary cause of biodiversity loss (Pimm \& Raven 2000). Still, little is known about how biodiversity is reduced in complex ecological webs. The goal of this paper is to explore how metacommunity structure affects the response of food webs to habitat loss. Previous theoretical studies of habitat loss have investigated single-species (Lande 1987; Bascompte \& Sol\'e 1996), two-species (Nee \& May 1992; May 1994; Nee et al. 1997; Holt 1997; Bascompte \& Sol\'e 1998a,b; Namba et al. 1999; Swihart et al. 2001) and n-competing species models (Hastings 1980; Tilman 1994; Tilman et al. 1994; Kareiva \& Wennergren 1995). These studies emphasize two important findings. First, the existence of a correlation between trophic rank and extinction threshold, whereby specialist predators are driven extinct before their prey (Kareiva 1987; Kruess \& Tscharntke 1994; Bascompte \& Sol\'e 1998a; Gilbert et al. 1998; Holt et al. 1999; Steffan-Dewenter \& Tscharntke 2000). This is in agreement with empirical observations in host-parasitoid (Kruess \& Tscharntke 1994) and butterfly-plant communities (Steffan-Dewenter \& Tscharntke 2000). Consequently, prey species outbreaks may be more common once their natural enemies have been driven extinct by destruction of habitat (Kruess \& Tscharntke 1994). Second, habitat loss has a more severe effect on species that are better competitors but poorer dispersers (Hanski 1983; Nee \& May 1992). Thus, the species most prone to extinction are the highly successful competitor species we might never guess are at risk (Tilman et al 1994; Kareiva \& Wennergren 1995). Few studies have considered the effects of habitat loss in food webs with more than two trophic levels (but see Holt 1993 and 1997 for a related study of metacommunity dynamics of food webs in heterogeneous landscapes). However, habitat destruction may yield qualitatively new consequences when considering species that are embedded in an intricate web of ecological relationships (Nee et al. 1997). A few empirical and experimental papers seem to confirm the context-dependence of the response of food webs to perturbations. Paterson (1984) pointed out that for small mammals in boreal forest fragments, the proportion of predators declined with habitat loss, but the proportion of insectivores remained constant and the proportion of herbivores increased. Similarly, Fox \& Olsen (2000) studied the propagation of indirect effects through food webs having different degrees of complexity. They found that in reticular webs the top predator exhibited more sensitivity to perturbations on basal species than in simpler linear webs. This occurs because indirect effects (i.e., competition between both prey species; Wootton 1994) become increasingly important in complex, reticulate food webs (Fox \& Olsen 2000). Omnivory, defined broadly as feeding on more than one trophic level, occupies a prominent position in discussions about food web structure and dynamics. According to classical results from food web theory, omnivory destabilizes ecological communities (Pimm \& Lawton 1978), whereas more recent conceptual syntheses suggest that it should be a strongly stabilizing factor in food webs (Polis \& Strong 1996; Fagan 1997; McCann \& Hastings 1997; McCann et al. 1998; Holyoak \& Sachdev 1998). This paper complements this perspective by investigating spatial persistence after human-induced habitat loss. \section{Integrating Metapopulation Models} Through this paper we will integrate several basic models derived as extensions of the metapopulation model by Levins (1969). The Levins model, which has become the centerpiece of the metapopulation paradigm in conservation biology (Hanski 1998), can be written as: \begin{eqnarray} {dR \over dt} = c R (1-R)-e R,\label{eq:Levins1} \end{eqnarray} where $R$ is the proportion of patches occupied, $c$ is the colonization rate, and $e$ is the local extinction rate. The rate of newly colonized sites is given by the product of propagule production by the occupied sites, $c R$, and the proportion of sites that are not yet occupied, $1-R$. Similarly, the rate at which occupied sites become vacant is given by the product of the extinction rate $e$, and the proportion of occupied sites $R$. This equation has a globally stable non-trivial equilibrium given by $R^*= 1 - e/c$. Building on the Levins' framework, Lande (1987) allowed only a fraction $h$ of the habitat (i.e., territories) to be available. His results emphasize that we do not have to destroy all patches to extinguish a metapopulation that persists by virtue of a balance between local extinctions and recolonizations in a mosaic environment. Similarly, habitat destruction (Tilman 1994; Tilman et al. 1994; Kareiva \& Wennergren 1995) has been represented as $d = 1-h$ in a model derived from equation (1). But, how do interactions among species change patch abundances and extinction thresholds? Nee \& May (1992) and Tilman et. al (1994) expanded the Levins' metapopulation model to two and n-competing species assuming a trade-off between competition and colonization (Tilman 1994; Tilman et. al 1994). Hence, Tilman (1994) considers two competing species whose interactions are structured to give a competitive hierarchy. This leads to the following equations: \begin{eqnarray} {dR_1 \over dt}= c_1 R_1 (1-R_1)-e_1 R_1,\label{eq:Tilman1}\\ {dR_2 \over dt}= c_2 R_2 (1-R_1-R_2)-e_2 R_2-c_1 R_1 R_2. \label{eq:Tilman2} \end{eqnarray} The superior competitor, $R_1$, is described by the same equation as would a species living by itself (identical to Levins' metapopulation model in equation (1)), and thus it is totally unaffected by the inferior competitor. The superior competitor always displaces the inferior competitor when both species co-occur in a site, but the inferior competitor can neither invade nor displace the superior competitor from a site. The inferior competitor, $R_2$, can colonize only sites in which both it and species $R_1$ are absent (the term ($1-R_1-R_2$) in equation (3)). This represent interference or direct competition between both competitors. Furthermore, species $R_1$ can invade and displace species $R_2$ (the term $-c_1 R_1 R_2$ in equation (3)). A fraction $d$ of patches destroyed can be incorporated as ($1-R_1-d$) in equation (2) and ($1-R _1-R_2-d$) in equation (3). Tilman assumed a trade-off between colonization and competition and showed that habitat loss induces the selective extinction of the best competitors (Tilman et al. 1994). Habitat destruction lowers effective colonization rates of all species, but most greatly impacts species with lower colonization rates, the better competitors in Tilman's model. The third model considered here is a specialist predator-prey metapopulation model (May 1994; Bascompte \& Sol\'e 1998a). The model can be expressed as follows: \begin{eqnarray} {dR \over dt}= c_1 R (1-R)-e_1 R-\mu C,\label{eq:Bascompte1}\\ {dC \over dt}= c_2 C (R-C)-e_2 C.\label{eq:Bascompte2} \end{eqnarray} Where $R$ is the patch occupancy of a resource or prey, and $C$ is the patch occupancy of a consumer or predator. This model assumes that predators need prey in order to survive in a patch, that is, $C$ is a subset of $R$ (this is the reason for the term $R-C$ in equation (5)). This model further incorporates the effect of varying levels of predator control on prey populationīs via the parameter $\mu$. In this model, specialist predators are driven extinct by habitat loss before their prey (Bascompte and Sol\'e 1998a). Finally, we introduce Swihart et al.'s (2001) model, an expansion of Bascompte and Sol\'e's (1998a) model constructed to understand the effect of habitat destruction on a generalist predator. The novelty is that the predator colonization of a patch occurs independently of patch occupation by the preferred prey. Therefore, in patches without prey, predators pay an added cost ($\psi$) in terms of an increase in the rate of local extinction for mistakenly colonizing an inferior resource patch. The model is written as: \begin{eqnarray} {dR \over dt}= c_1 R (1-R)-e_1 R-\mu R C ,\label{eq:Swihart1}\\ {dC \over dt}= c_2 C (1-C)-e_2 C-\psi C(1-R).\label{eq:Swihart2} \end{eqnarray} In contrast to specialist predators, Swihart et al. (2001) found that habitat destruction is not as detrimental for generalist predators. Thus, habitat loss does not necessarily reduce the length of food chains as showed for specialist predators (Bascompte \& Sol\'e 1998a). In summary, much of the theory about how habitat loss affects the dynamics of multi-species interactions deals only with simple 2 species interactions or n competing species. The question we address in the remainder of this paper is how do these results change when we consider increasing food web complexity and indirect effects? \section{Metacommunity Models} Over the past decade, the view that food webs are highly interconnected assemblages characterized by recurrent structures has overcome the former concept of ecosystems as linear food chains. Because combinations of competition and predation can represent these common food web structures, the use of simple food web modules has been advocated to explore the repercussions of these ubiquitous interactions (McCann 2000 and references therein). We synthesize trophic and competitive interactions using models assuming that all the species have a similar population structure and habitat requirements; they are influenced by habitat loss in exactly the same way. We consider four types of food web illustrated in Fig. 1: a simple food chain, an omnivorous food web (e.g. Fagan 1997), a food web with apparent competition (e.g. Holt \& Lawton 1994; Bonsall \& Hassell 1997), and finally a food web with intraguild predation (e.g. Polis \& Holt, 1992). The model for the simple food chain (Fig. 1) can be described as: \begin{eqnarray} {dR \over dt}= c_1 R (1-R-d)-e_1 R-\mu_1 R C,\label{eq:Simple1}\\ {dC \over dt}= c_2 C (1-C-d)-e_2 C-\psi_1 C(1-R)-\mu_2 C P,\label{eq:Simple2}\\ {dP \over dt}= c_3 P (1-P-d)-e_3 P-\psi_2 P(1-C).\label{eq:Simple3} \end{eqnarray} Here $R$ is the basal species patch density, $C$ is the patch density of the intermediate species, and $P$ is the patch density of the top species. $d$ is the fraction of sites destroyed. $c_i$ and $e_i$ represent colonization and extinction rates of species $i$. As noted above, we assume that colonization of a patch by the predator occurs independently of patch occupancy by its main prey. Therefore, in patches without prey, intermediate and top species pay an added cost ($\psi_1$ and $\psi_2$ in equations (9) and (10)) in terms of an increase in the rate of local extinction for mistakenly colonizing an inferior resource patch. That is, extreme specialist predators go immediately extinct in patches without their prey. When $C$ and $P$ are extreme generalists, $\psi_1$ and $\psi_2$ are equal to $0$ (Swihart et al. 2001). Finally, $\mu_i$ represents the increase in mortality due to predation. Our model extends the basic ignorant predator model by Swihart et al. (2001) by adding an additional trophic level, with new direct and indirect interactions. In the omnivorous food web (Fig. 1), vertical complexity is now increased relative to the simple food chain, via feeding links between the top species and the two lower trophic levels. The model can be written as: \begin{eqnarray} {dR\over dt}=c_1 R (1-R-d)-e_1R-\mu_1RC-\mu_2RP,\label{eq:Omn1}\\ {dC\over dt}=c_2 C (1-C-d)-e_2C-\psi_1C(1-R)-\mu_3CP,\label{eq:Omn2}\\ {dP\over dt}=c_3 P (1-P-d)-e_3P-\frac{\psi_2}{2}P(1-R)-\frac{\psi_3}{2}P(1-C),\label{eq:Omn3} \end{eqnarray} where all parameters are defined as above (equations (8-10)). We consider omnivory in a restrictive sense, that is, top species' persistence is maximum when both prey species are present in the same patch. We assume that omnivorous top species needs species from two trophic levels in each patch to minimize the foraging cost (Ball 1994; Sih \& Christensen 2001). Thus, if $\psi_2$ is the cost for a top predator in a simple food web, then the cost associated in the omnivorous food web when one of the prey species is absent would be $\psi_2/2$ or $\psi_3/2$ (equation (13)). As a result, when omnivorous top species colonize a new patch and none of the prey species are present, the total cost, $\psi_t$, is: \begin{equation} \psi_t = \frac{\psi _2}{2} + \frac{\psi _3}{2}, \label{eq:Cost1} \end{equation} and the extinction rate in such an empty patch is $e_3$ + $\psi_2/2$ + $\psi_3/2$. In a similar way, when only one of the two prey species (i.e., basal or intermediate) is absent in a patch, the extinction rate is $e_3$ + $\psi_i/2$. The extinction term for the top species when there is apparent competition (Fig. 1), or intraguild predation (Fig. 1) is defined similarly as that for the omnivorous top species. We assume that the top species needs the two prey species in each patch to minimize the foraging cost. In both cases, the top species feeds on two intermediate species, $C_1$ and $C_2$. Thus, species $C_1$ and $C_2$ are engaged in apparent competition by sharing the same predator (see Fig. 1). They are also engaged in indirect competition since they share the same resource (the basal species). We assume a trade-off between competition and colonization: $C_1$ is a better competitor but $C_2$ is a better disperser. The asymmetry in colonization rates allows the coexistence of $C_1$ and $C_2$. $C_2$ can not occupy patches already occupied by $C_1$ (this is described by the term $1-C_1-C_2-d$ in equations (17) and (21)), and $C_1$ can occupy either empty patches or patches occupied by $C_2$. Here, we do not assume that $C_1$ displaces species $C_2$ from patches occupied by both $C_1$ and $C_2$ as assumed by Tilman (1994). These are a less severe assumptions than that made for a purely competitive system (e.g., Tilman 1994; see equation (3)), and represents a less intensive competition between $C_1$ and $C_2$. This can be translated into the following model (Fig. 1): \begin{eqnarray} {dR\over dt}=c_1R(1-R-d)-e_1R-\mu_1RC_1-\mu_2RC_2, \label{eq:Apparent1}\\ {dC_1\over dt}=c_2C_1(1-C_1-d)-e_2C_1-\psi_1C_1(1-R)-\mu_3C_1P, \label{eq:Apparent2}\\ {dC_2\over dt}=c_3C_2(1-C_1-C_2-d)-e_3C_2-\psi_2C_2(1-R)-\mu_4C_2P, \label{eq:Apparent3}\\ {dP\over dt}=c_4P(1-P-d)-e_4P-\frac{\psi_3}{2}P(1-C_1)-\frac{\psi_4}{2}P(1-C_2). \label{eq:Apparent4} \end{eqnarray} Finally, when allowing $C_1$ to also feed on $C_2$ (with a similar extinction term as for the top species), we can write the following model for the food web with intraguild predation (Fig. 1): \begin{eqnarray} {dR\over dt}=c_1R(1-R-d)-e_1 R-\mu_1RC_1-\mu_2RC_2,\label{eq:Intraguild1}\\ {dC_1\over dt}=c_2C_1(1-C_1-d)-e_2C_1-\frac{\psi_1}{2}C_1(1-R)-\frac{\psi_2}{2}C_1(1-C_2)-\mu_3C_1P, \label{eq:Intraguild2}\\ {dC_2\over dt}=c_3C_2(1-C_1-C_2-d)-e_3C_2-\psi_3C_2(1-R)-\mu_4C_2P-\mu_5C_2C_1, \label{eq:Intraguild3}\\ {dP\over dt}=c_4P(1-P-d)-e_4P-\frac{\psi_4}{2}P(1-C_1)-\frac{\psi_5}{2}P(1-C_2). \label{eq:Intraguild4} \end{eqnarray} We will focus on the extinction thresholds, that is, the critical values of habitat destruction, $d_c$, at which a given species goes extinct. The inverse of such an extinction threshold could be considered as a measure of vulnerability to extinction due to habitat loss. In addition to the extinction threshold, {\em the dependence of patch occupancy on habitat destruction} is also important to understand the effects of habitat loss on metacommunity persistence, and we will also consider this as a benchmark for comparison. As we will show, both extinction thresholds and {\em the decline of patch occupancy} can be difficult to predict when indirect interactions are at work. \section{Results} Our goal is to consider how food web structure alters the top species ($P$) response to habitat loss for two different ecological scenarios, namely donor control and top-down control. To explore this question we analyze the metacommunity models developed in the previous section. Through this paper we explore a broad range of biologically realistic parameter combinations. The results presented here are qualitatively robust for all parameter combinations examined. Specifically, we have used numerical methods to derive the non-trivial solutions for symmetrical parameter combinations,{\em that is, all species have equal parameter values}, ranging from donor control $\mu_i=0$ to top-down control $\mu_i=0.7$; colonization/extinction from $c_i=0.4$, $e_i=0.1$ to $c_i=0.7$,$e_i=0.3$; and exploration cost from $\psi_i=0.3$ to $\psi_i=0.7$. This range of parameter combinations meets our criteria of (i) biological realism, and (ii) existence of stable non-trivial solutions. To begin with, let us start with a donor control scenario (i.e., prey dynamics constrain the distribution of the predator, without reciprocal effects by the predator on its prey, $\mu_i=0$). We consider intermediate ($C_1$ and $C_2$) and top species ($P$) as specialists, but not extreme specialists, that is, they have a high degree of selective searching behavior. They have an increased rate of local extinction for mistakenly colonizing an inferior resource patch ($\psi_i > 0$). We start with symmetric demographic rates, in which basal, intermediate, and top species have the same colonization/extinction rates. Note that the top species' persistence is maximum when both prey species are present in the same patch. We also explored a less restrictive assumption and qualitative results remained. For the above parameter values, a positive numerical equilibrium exists. We plot this equilibrium patch occupancy as a function of habitat destruction in Fig. 2a. We find that: \begin{enumerate} \item The extinction threshold for the top species in an omnivorous web occurs at a higher level of habitat destruction ($d_c=0.30$) than for webs with apparent competition ($d_c=0.24$) and simple linear chains ($d_c=0.24$). The top species goes extinct sooner in webs with intraguild predation ($d_c=0.17$). \item The top species decreases linearly but with different slopes for each type of food web. The steepest decline is for the simple and apparent competition food web, followed by the omnivory food web. The decline is less steep for intraguild predation. \end{enumerate} Let us now consider an example of top-down control. We find that the pattern is qualitatively similar to donor control. All else being equal, patch abundances are lower for top-down control, and the top species' extinction threshold occurs at a lower fraction of sites destroyed (compare Figs. 2a and 2b). Until now, we have only considered the response of the top species. What happens with the rest of the community? We plot the decline in the number of species for each food web as more habitat is destroyed in Fig. 3. Each step corresponds to the extinction of one of the species. The first species going extinct is the top species ($P$), and the last is the basal species ($R$). We find that the basal species has a similar response in each configuration (that is, its extinction threshold is the same for each configuration). This is not a surprise since after the rest of species have gone extinct, we have the same single Levins' species model. For the intermediate species ($C_1$ and $C_2$), the extinction threshold is the same for both the simple (Fig. 3a) and the omnivorous (Fig. 3b) food web. On the other hand, the extinction thresholds for the intermediate species depend on whether they are embedded in the web with apparent competition or intraguild predation. With apparent competition, $C_1$ and $C_2$ have similar extinction thresholds (Fig. 3c), while $C_1$ goes extinct before $C_2$ for intraguild predation (Fig. 3d). Top-down control exacerbates these differences. In general, all species go extinct sooner when control is top-down as opposed to donor (see Fig. 3). Finally, we may ask how indirect effects and non-linearities in the interactions affect the predictability of metapopulation responses to habitat loss. We explore this response in (i) an intraguild predation web, and (ii) an apparent competition web where intermediate species ($C_1$ and $C_2$) engage in direct competition. We study asymmetric demographic and exploration cost rates. Again, we have studied a broad range of biologically realistic parameter values corresponding to stable non-trivial solutions. Specifically, the range of parameter values explored here is as follows: $\mu_i=0$ (donor control) to $\mu_i=0.7$ (top-down control); $c_i=0.4$, $e_i=0.1$ to $c_i=0.7$, $e_i=0.3$; $c_2=0.3$ to $c_2=0.5$; $\psi_i=0.4$ to $\psi_i=0.7$ with $\psi_1$ (i.e., the exploration cost of the better competitor) from $\psi_1=0$ to $\psi_1=1$. Our results are robust for this entire suite of asymmetric parameter combinations. For the case of apparent competition, we observe in Fig. 4a that the better competitor ($C_1$ -dotted line) has a higher patch occupancy and a lower extinction threshold than the better colonizator, poorer competitor ($C_2$ -continuous line). We observe in Fig. 4b that a small reduction in the exploration cost of the better competitor $C_1$ (from $\psi_1=0.3$ to $\psi_1=0.1$) has a nonlinear indirect effect on the extinction threshold of the less abundant, poorer competitor species ($C_2$). Fig. 5a shows the extinction threshold of both the better ($C_1$) and poorer ($C_2$) competitors for different values of the exploration cost for the better competitor. Fig. 5b shows how the extinction threshold for the poorer competitor depends on the colonization rates of the better competitor. Evolutionary changes in the demographic parameters of one species can cascade through the food web with unanticipated consequences for the other species. \section{Summary and Discussion} The following remarks emphasize some of our conclusions: \begin{enumerate} \item Food web structure alters the top species response to habitat loss. \item Direct and indirect interactions between two intermediate prey decrease the patch occupancy of top predators. \item Omnivory confers higher persistence for the top species for a specific value of habitat loss. \item The extinction threshold of the top species is lower for top-down control than for donor control, but the difference attenuates with decreasing trophic level. \item Although the top species' regional abundance is lower for top-down control, its rate of decrease as habitat is destroyed is also lower. That is, all else being equal, donor control would lead to situations with high abundance but low resistance to habitat destruction, while the contrary would happen for top-down control. \item In apparent competition and intraguild predation with direct and indirect competition between intermediate species, a slight decrease in the exploration cost of the better competitor ($C_1$) results in a strong effect on the extinction threshold of the poorer competitor ($C_2$). \end{enumerate} The present results confirm the finding that predators with high selective searching behavior are driven extinct for lower destruction values than their prey. But many natural communities are dominated by non-specialized consumers (Polis \& Strong 1996). In the latter scenario, habitat destruction will favor generalist predators with low exploration cost (Mikkelson 1993; Swihart et al. 2001). In both cases, patch abundance and extinction thresholds depend on the food web structure in which the top species are embedded. Trophic generalization can lead to a wide range of indirect interactions in food webs such as exploitative competition, apparent competition, and intraguild predation (Holt et al. 1999). Additionally, there is a surprising number of cases in which the removal of a predator leads to a decrease in the abundance of the focal prey (Sih et al. 1985). Many of these cases seem to involve indirect interactions in multispecies assemblages (e.g., competitive interactions among prey held in check by a generalist predator, Holt 1997). In this paper we have first explored the relative effect of direct and indirect interactions in the context of habitat loss. We have shown that indirect interactions from apparent competition (Fig. 1) and intraguild predation (Fig. 1) depress the extinction threshold for the top species (Figs. 2a and 2b). That is, direct and indirect interactions reduce the fraction of habitat destroyed at which the top species is driven extinct. This has been demonstrated empirically by Fox \& Olsen (2000). By using microcosms, these authors showed that perturbations had a larger impact on predators embedded in reticulated food webs. Our results add a complementary perspective to the empirical evidence pointing towards higher stability for multichannel omnivory food webs (Polis \& Strong 1996; Fagan 1997; Holyoak \& Sachdev 1998; McCann et al. 1998). In this paper, we provide evidence showing how top species may persist at higher values of habitat destruction when embedded in a food web with high levels of omnivory. {\em Fagan (1997) observed in a multipatch scale that the return to the equilibrium after a range of disturbances was faster in omnivorous structure}, although there is still a lack of theoretical interpretations (Fagan 1997). The present paper represents a first step in this direction. Note that we use stability in the sense of spatial persistence in response to habitat loss, rather than return to the equilibrium after a local perturbation such as a reduction in abundance (Pimm \& Lawton 1978; Fagan 1997). The extinction threshold is lower for the better competitor ($C_1$) than for the worse competitor ($C_2$) for a broad range of parameter values. This result is in agreement with previous results from single trophic-level models (Tilman 1994; Tilman et al. 1994; 1997), according to which the initially most abundant species in undisturbed habitat fragments can be the most susceptible to eventual extinction. However, as shown in this paper, the order of extinction can dramatically change depending on the exploration cost of the best competitor. Species are typically enmeshed in an entangled web of direct and indirect interactions. Our results suggest that the response of the metacommunity to disturbances can be a complex interaction of different trends. These results call for extreme caution when the goal is the management of endangered species in fragmented habitats. Also, minor changes in the exploration cost of better competitors can have a large influence on the regional abundance of poorer competitors. This emphasizes how evolutionary changes at the level of generalization of one species may cascade through the rest of the community (Schmitz 1998). In summary, patch abundances and extinction thresholds are not only determined by demographic rates (Levins 1969), behavioral and life history traits (Lande 1987), competitive-colonization abilities (Tilman 1994) and landscape properties (Bascompte \& Sol\'e 1996), but also by the structure of the food web in which the species are embedded. \section{Acknowledgements} We thank Bill Fagan, Shane Richards, John Sabo, and Pedro Jordano for useful comments on a previous draft. 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The nature and consequences of indirect effects in ecological communities. {\em Annual Review of Ecology and Systematics}, 25, 443-466. \vspace{0.15 in} \newpage \section{Figure Legends} \vspace{0.2 in} $\bullet$[Fig. 1] The four types of food-web studied are: from left to right, a simple food chain, a food web including omnivory, a food web with the top species feeding on two intermediate consumers (apparent competition), and a food web with consumer 1, $C_1$, feeding on the basal species and on the second consumer $C_2$, (intraguild predation). $R$ denotes the basal species; $C_1$ and $C_2$ denote intermediate species; $P$ denotes the top species. Note that in this paper we introduce a spatial component, and the food web may be incomplete in some patches. \vspace{0.2 in} $\bullet$ [Fig. 2] The patch occupancy of the top species ($P$) is plotted as a function of the fraction of habitat destroyed ($d$). As we explicitly point out in the figure, the different lines represent an omnivorous food web ($orange$ $square$), a simple food chain ($red$ $square$), a food web with apparent competition ($red$ $line$), and a food web with intraguild predation ($blue$ $square$). Fig. 2a represents donor control ($\mu_i=0$), while Fig. 2b represents top-down control ($\mu_i=0.7$). A high exploration cost or selective searching behavior ($\psi_i=0.6$) is assumed. Other parameters are as follows: $c_i=0.7$, and $e_i=0.1$. \vspace{0.2 in} $\bullet$ [Fig. 3] The fraction of extant species relative to the initial number of species is plotted as a function of the fraction of habitat destroyed. Continuous line represents donor control ($\mu_i=0$), and dotted line represents top-down control ($\mu_i=0.7$). The simple food chain (a) the omnivorous web (b) have three species, while the food web with apparent competition (c), and intraguild predation (d), have four species. This explains the difference in the y-axis scale. Parameter values are similar to those in Fig. 2a (for donor control) and 2b (for top-down control). Each step represents the extinction of one species. From left to right, the order of extinction is for the top species ($P$), the intermediate species ($C$), and the basal species ($R$). \vspace{0.2 in} $\bullet$ [Fig. 4] The patch occupancy of the two competing species ($C_1$ and $C_2$ ) in the food web with apparent competition are plotted as a function of the fraction of habitat destroyed ($d$). Continuous and discontinuous line represent intermediate species ($IS$), that is, the poorer ($C_2$) and the better competitor ($C_1$) respectively. The colonization rate of the better competitor is $c_2=0.3$ in both cases. The other parameter values are $\mu_i=0$, $e_i=0.1$, $c_i=0.7$, and $\psi_i=0.7$. As noted, a slight decrease in the exploration cost of $C_1$ implies a big change in the extinction threshold for both competing species. \vspace{0.2 in} $\bullet$ [Fig.5] (a) The extinction thresholds for both competitors ($C_1$ and $C_2$) in the food web with apparent competition are plotted as a function of the exploration cost of the better competitor ($\psi_1$). $Orange$ $circle$ corresponds to $C_1$ and $red$ $circle$ corresponds to $C_2$. Parameter values are as in Fig. 4. (b) Represents the extinction thresholds for $C_2$ as a function of the exploration cost of the better competitor for three colonization rates of the better competitor ($C_1$). Colonization rates of $C_1$ are plotted as $c_2= 0.3$, ($red$ $circle$), $c_2=0.4$, ($maroon$ $circle$) and $c_2=0.5$, ($orange$ $square$). Other parameter values are as in Fig. 4. As noted, there is a strong interaction between the exploration cost of the better competitor and the extinction threshold of the poorer competitor. Similar results remain for intraguild predation and top down-control for all the range of parameter values explored. \newpage \begin{center} \includegraphics[width=16cm]{Fig1.eps} \caption{Fig. 1} \end{center} \begin{center} \includegraphics[width=16cm]{Fig2.eps} \caption{Fig. 2a-2b} \end{center} \begin{center} \includegraphics[width=16cm]{Fig3.eps} \caption{Fig. 3a-3d} \end{center} \begin{center} \includegraphics[width=16cm]{Fig4.eps} \caption{Fig. 4a-4b} \end{center} \newpage \begin{center} \includegraphics[width=16cm]{Fig5.eps} \caption{Fig. 5a-5b} \end{center} \end{document} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End: