Active Reallocation of Food-Web Interactions under Environmental Change Paper
Human-induced habitat modification is the primary driver of worldwide changes in the diversity and composition of species (Millennium Ecosystem Assessment 2005). However, it is less clear how environmental change affects the patterns of interactions among species (Tylianakis et al. 2008). Although the structure of ecological communities (Memmott et al. 1994; M¨uller et al. 1999) is known to vary across gradients of habitat modification (Tscharntke et al. 1998; Klein et al. 2006; Tylianakis et al. 2007; Albrecht et al. 2007), the processes responsible for these changes are unknown. Here we show that variability in consumer functional response among habitats lead to interaction distributions that cannot be explained purely on the basis of resource availability. We apply a simple model of consumer feeding to data on insect hosts and their natural enemies from four regions.
The model accurately recreates observed changes in quantitative food-web structure following habitat modification. The model highlights two processes responsible for changes to the distribution of interactions: altered selection within a consumer’s existing resource set, and the initiation of novel trophic interactions. In environments where communities are more impacted by habitat modification, interaction patterns increasingly depart from density-dependent resource selection. Our findings are consistent with improved consumer foraging efficiency in simpli- fied environments, where increased resource selectivity can lead to greater than expected specialisation, while increased resource encounters can also lead to greater than expected generalisation. Understanding how variation in trophic specialisation is generated will improve forecasts of the communitylevel impact of environmental change and its implications for ecosystem functioning.
A central goal in ecology is to explain and predict the structure of species interaction networks (Memmott 1999; Lewis et al. 2002; Montoya et al. 2006). Environmental change can lead to the disappearance of species from ecosystems and cause alterations to the abundance of those species that persist (Foley et al. 2005). Consequently, understanding how anthropogenic changes affect the dynamics and function of ecological networks is an important theoretical challenge, but is also likely to have significant practical consequences since humans rely on the ecosystem services associated with species interactions such as pollination, seed dispersal, and biological control (Costanza et al. 1997; Losey & Vaughan 2006). Theoretical studies exploring changes in community composition have typically assumed that food-web topology remains unchanged even as species are removed, although recent work has proposed mechanisms that allow for structural adaptation (Kondoh 2003; Kaiser-Bunbury et al. 2010; Staniczenko et al. 2010).
Advances in field methods that quantify functionally-important variations in the magnitude or frequency of interactions (M¨uller et al. 1999) have generated highly-detailed food webs that not only provide a more robust description of static community structure (Banasek-Richter et al. 2004), but also enable more accurate insights into dynamic and indirect interactions among species (Morris et al. 2004; Lalibert´e & Tylianakis 2010). This increasing availability of rich, community-level, data requires a parallel advance in theoretical models to explain the mechanisms underpinning quantitative, rather than binary (interaction presence-absence), food webs.
Diets of species are largely constrained by their phylogenetic history and morphology (Ives & Godfray 2006). However, the composition of a consumer’s diet can alter depending on resource availability and quality in different environments (Stang et al. 2009). A useful initial null hypothesis that avoids assuming specific behavioural processes is that interactions are primarily determined by resource species density (V´azquez et al. 2007). In the simplest case, we assume a linear response between consumer interaction frequency and resource density, with the explicit form of the relationship remaining independent of environment. We call this constant functional response density-dependent reallocation (i.e., interactions are allocated passively in modified environments, entirely according to changes in resource density). However, consumer functional response is unlikely to remain constant in modified habitats, due to effects such as different preferences for resource species and altered foraging efficiency (Pulliam 1974). We call such flexible functional response active reallocation.
Our simple model of active reallocation quantifies and characterises this dynamic process, and provides significantly better agreement with empirical data compared to density-dependent reallocation. It clarifies the role of novel trophic interactions—also known as switches (Murdoch 1969)—and provides a base model that can help identify more specific ecological mechanisms that lead to altered trophic-breadth in different environments. The model allows consumer selectivity to increase or decrease, so that the corresponding distribution of interactions becomes, respectively, more specific (over-specialisation) or more general (over-generalisation) than would be expected from density-dependent reallocation.
3.2 Materials and Methods
The information contained in food webs can be summarised in various ways. Quantitative, weighted, equivalents of binary food-web statistics have been developed (Bersier et al. 2002) and used extensively. The weighted connectance (Cq) quantifies the amount of potential interactions that are realised in the food web; the interaction diversity (Iq) quantifies the evenness of the interactions between species; the generality (Gq) quantifies the average number of resource species weighted by consumer abundance; and the vulnerability (Vq) quantifies the average number of consumer species weighted by resource abundance (see Appendix 3.5.1). This set of metrics provide consumer-centric, resource-centric and complete food-web summaries of interactions and we used them to assess the structure of food webs across different gradients of habitat modification in Germany, Ecuador, Indonesia and Switzerland.
These food webs focus on a subset of interactions involving insects at two trophic levels: parasitoid species (consumers) and their host species (resources). Similar methods were used to collect food-web data from the different regions presented here, facilitating comparison. Pooling of replicate webs within regions was necessary to maximise resolution on the webs and minimise the possibility of artefacts due to low sampling effort (Tylianakis et al. 2010). Patterns of parasitoid-host interactions have been shown previously to differ between forested and unforested habitats (including no to few individual trees), and more complex compared to more simple environments (Tylianakis et al. 2007; Lalibert´e & Tylianakis 2010). Therefore, we assembled quantitative bipartite webs representative of less-open (hereafter complex) and more-open (hereafter simple) environments in each region (Table 3.1, Figure 3.1). These categorisations were based on replicate web metadata such as ground-level light intensity and plant species richness. There are clear differences in the distribution of interaction frequencies among environments and among regions (Table 3.2).
We used the difference in the Shannon evenness index (Krebs 1989) of host species between webs (∆, Table 3.1) as a measure of the community impact generated by habitat modification. The Shannon evenness for each region was normalised by the maximum value it could take to get a measure in the range [0,1]:
where the numerator is the Shannon entropy for N host species, pi is the
proportional density for host species i, and the denominator is the maximum possible evenness of the distribution. We compare the environments of complex and simple webs using ∆ = Ecomplex − Esimple. ∆ close to zero indicates little change in host distribution, implying little impact due to modification between complex and simple environments; larger values suggest increased impact. Negative values imply increasing homogenisation in the distribution of host species, with positive values implying increasing heterogeneity. This analysis leads to the following ordering from least-to-most severely altered region: Indonesia, Germany, Ecuador, and Switzerland (Table 3.1).
We model quantitative food-web structure in simple environments using data from complex environments. We begin by assuming that each interaction between host i and parasitoid j in the complex food web follows a linear functional response
where mij is the observed per-capita attack rate (i.e., the empirical number of parasitism events divided by the host density). To assess whether the assumption of linear functional response is reasonable, we fit Type I (linear) and Type II (saturating) functional forms to complex web interactions where more than three replicate web interactions contribute to a pooled web interaction. For the Type II functional response, we performed a non-linear least-squares fit with a Michaelis-Menten form
where vij is the saturation interaction strength, and Kij is the rate constant. We assigned a classification—linear or saturating—as the form giving the lowest mean square error following the least-squares procedure (assuming the saturating form has biologically-reasonable parameters, i.e., the rate constant should not be negative). In our complex web data, we found that the majority (72%) of interactions permitting classification were better fit by a linear rather than saturating functional form.
A Type III (sigmoidal) response was not considered here because the limited number of data points for each pooled web interaction would make distinguishing between Type II and Type III forms very difficult. The majority of interactions (73% across Indonesia, Ecuador and Switzerland) in each pooled web were observed in only one of the contributing replicate webs. For these interactions, we can only assume the most parsimonious possibility of a linear response between interaction frequency and resource density. Germany did not have a sufficient number of replicate webs for this analysis.
With density-dependent reallocation, by definition, the set of m-coefficients is independent of the environment. Consequently, we can use Equation 3.2 (parameterised from the complex environment) to model the interaction distribution for each parasitoid species in a simple environment (e.g., after habitat modification), given a new empirical distribution of host species. We compare this density-dependent deterministic model to empirical data from the simple environment by running stochastic simulations of parasitoid-host interactions that incorporate two sources of uncertainty: i) error arising from differences in observed per-capita attack rates among replicate webs; and ii) error arising from requiring integer numbers for interaction events.
We quantified variation in the per-capita attack rate (the number of parasitism events divided by the host density, mij in Equation 3.2) between replicate webs using linear least-squares regression. Where more than three replicate web interactions contributed to a pooled interaction, we recorded the standard deviation of the residuals and the pooled number of parasitism events (pooled interaction frequency). Since we are conducting a least-squares minimisation, residuals are approximately normally distributed (mean zero) with their standard deviation representing the error on the true value of a pooled interaction.
Compiling all interactions, we fit a linear relationship between pooled interaction frequency, J, and the expected error in that value: σJ = a+bJ, where a and b are constants from a linear regression. We used this relationship to incorporate per-capita attack-rate uncertainty into simulations of species interactions in simplified environments. For a given deterministic prediction for the frequency of an interaction, the error on that value is drawn from a normal distribution with mean zero and standard deviation σJ .
Simulations provided an expected frequency-weighted interaction generality for each parasitoid species, with an associated standard deviation, which was compared to empirical data using the z-score. The diversity of interaction inflows to a consumer k is,
where bik is the interaction contribution from resource i and b•k is the total interaction frequency into k, for a total of r resource species. The number of resource species a consumer has (weighted according to their use frequency) is then nk = 2Hk . The empirical value for nk can be compared to the interaction distribution generated by density-dependent reallocation (Null model 1, see below) using the
where n ∗ k is the empirical value, hnkiis the average value of an ensemble of model randomisations and σnk is the standard deviation of the same quantity. Values of zk > 0 indicate over-specialisation and zk < 0 indicate overgeneralisation.
The active reallocation model is deterministic and, as with density-dependent reallocation, begins by assuming that interactions follow a linear functional response (see Appendix 3.5.2). However, the set of m-coefficients for a parasitoid species can be altered between environments by two community-level parameters, R (resource-based changes) and S (switch-specific changes). The parameters take positive values and adjust the dispersion of m-coefficients for each parasitoid species: R, S > 1 “stretches” consumer interaction distributions (m-coefficients become more different), thereby promoting preference of some hosts over others; whereas R, S < 1 “compresses” consumer interaction distributions (m-coefficients become more similar), thereby homogenising host preference.
The model permits two additional modes of consumer behaviour compared to density-dependent reallocation: i) consumer interaction frequencies can change in a non-linear way following changes in resource density (through R); and ii) switches—interactions that are absent in the complex web but present in the simple web—are afforded a separate role to existing interactions in determining quantitative food-web structure (through S). We set parameter values giving closest agreement with the empirical data (deterministic model, Table 3.1) and run stochastic simulations as with density-dependent reallocation.
We compare the reallocation model to two null models. Null model 1 corresponds to density-dependent reallocation and assumes that changes in interaction frequency (including switches) are solely determined by changes in resource density. Null model 2 is as Null model 1 but does not include switches; it assumes that the maximum possible set of interactions in the simple food web remains the same as in the complex food web.
The closeness of a model quantitative food-web metric, Q∗ , to the empirical value, Q, is
values closer to 0 indicate better agreement with the empirical value. Closeness to empirical data is measured by assessing all four metrics jointly for each simulation run, and we use the largest value of δQ as our measure. However, we find similar qualitative results if the average of the individual metric closeness values is used rather than taking the maximum value for the closeness.
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