Describing how resource consumption rates depend on resource density, conventionally termed "functional responses," is crucial to understanding the population dynamics of trophically interacting organisms. Yet, accurately determining the functional response for any given pair of predator and prey remains a challenge. Moreover, functional responses are potentially complex surfaces in multidimensional space, where resource density is only one of several factors determining consumption rates. We explored how three sources of error can be addressed in the design and statistical analysis of functional response experiments: ill-chosen spacing of prey densities, heteroscedastic variance in consumption rates, and non-independence of parameters of the function describing prey consumption in relation to prey density and additional environmental factors. We generated extensive, virtual data sets that simulated feeding experiments in which both prey density and environmental temperature were varied, and for which the true, deterministic functional response surface was known and realistic variance had been added. We compared eight different methods of functional response fitting, one of which stood out as best performing. We subsequently tested several conclusions from the simulation study against experimental data of zooplankton feeding on algae across a broad range of temperatures. We summarize our main findings in three best practice guidelines for the experimental estimation of functional response surfaces, of which the second is the most important: (1) space prey densities logarithmically, starting from very low densities; (2) log-transform prey consumption data prior to fitting; and (3) fit a multivariate functional response surface to all data (including all prey densities and other factors, in our case temperature) in a single step. We also observed that functional response surfaces were fitted more accurately and precisely than their component parameters. The latter occurred because parameter estimates were non-independent, which is an inevitable feature of fitting complex nonlinear functions to data: A given response surface can often be described with near-equal accuracy by multiple parameter combinations. We therefore conclude that fitted functional response models perform better at optimizing the fit of the overall response surface than at determining how component parameters, such as the attack rate or handling time, depend on environmental factors such as temperature.

Online enhancements: appendixes.abstract: Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individualbased models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply both in continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very efficient and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations.

Spatial environmental heterogeneity coupled with dispersal can promote ecological persistence of diverse metacommunities. Does this premise hold when metacommunities evolve? Using a two‐resource competition model, we studied the evolution of resource‐uptake specialisation as a function of resource type (substitutable to essential) and shape of the trade‐off between resource uptake affinities (generalist‐ to specialist‐favouring). In spatially homogeneous environments, evolutionarily stable coexistence of consumers is only possible for sufficiently substitutable resources and specialist‐favouring trade‐offs. Remarkably, these same conditions yield comparatively low diversity in heterogeneous environments, because they promote sympatric evolution of two opposite resource specialists that, together, monopolise the two resources everywhere. Consumer diversity is instead maximised for intermediate trade‐offs and clearly substitutable or clearly essential resources, where evolved metacommunities are characterised by contrasting selection regimes. Taken together, our results present new insights into resource‐competition‐mediated evolutionarily stable diversity in homogeneous and heterogeneous environments, which should be applicable to a wide range of systems.

To understand how functional traits shape ecological communities it is necessary to understand both how traits across the community affect its functioning and how eco-evolutionary dynamics within the community change the traits over time. Of particular interest are so-called evolutionarily stable communities (ESCs), since these are the end points of eco-evolutionary dynamics and can persist over long time scales. One theoretical framework that has successfully been used for assembling ESCs is adaptive dynamics. However, this framework cannot account for intraspecific variationneither locally nor across structured populations. On the other hand, in moment-based approaches, intraspecific variation is accommodated, but community assembly has been neglected. This is unfortunate as some questions regarding for example local adaptation vis-a-vis diversification into multiple species requires both facets. In this paper we develop a general theoretical framework that bridges the gap between these two approaches. We showcase how ESCs can be assembled using the framework, and illustrate various aspects of the framework using two simple models of resource competition. We believe this unifying framework could be of great use to address questions regarding the role of functional traits in communities where population structure, intraspecific variation, and eco-evolutionary dynamics are all important. 1 .

It is well recognized that spatial heterogeneity and overall productivity have important consequences for the diversity and community structure of food webs. Yet, few, if any, studies have considered the effects of heterogeneous spatial distributions of primary production. Here, we theoretically investigate how the variance and autocorrelation length of primary production affect properties of evolved food webs consisting of one autotroph and several heterotrophs. We report the following findings. (1) Diversity increases with landscape variance and is unimodal in autocorrelation length.(2) Trophic level increases with landscape variance and is unimodal in autocorrelation length. (3) The extent to which the spatial distribution of heterotrophs differ from that of the autotroph increases with landscape variance and decreases with autocorrelation length. (4) Components of initial disruptive selection experienced by the ancestral heterotroph predict properties of the final evolved communities. Prior to our study reported here, several authors had hypothesized that diversity increases with the landscape variance of productivity. Our results support their hypothesis and contribute new facets by providing quantitative predictions that also account for autocorrelation length and additional properties of the evolved communities.