Quantitative descriptions of resource choice in ecological models

Food web functional responses

This article reviews the nature of functional responses that have commonly been used to represent feeding relationships in the ecological literature. It compares these with the range of functional response forms that are likely to characterize species in natural communities. The latter set of responses involves many more variables. The article reviews the history of functional response models, and examines previous work that has allowed the functional response of a predator to a single type of prey to depend on additional variables beyond the abundance of that prey type. While a number of more complex functional responses have been discussed over the years, many variables affecting feeding rates are still typically omitted from models of food webs. The influences on functional responses from trophic levels above that of the predator or below that of the prey are particularly likely to be ignored, although models and data have suggested that they can have large effects on the functional response. The influences of adaptive behavior and of the time-scale of response measurement are also too often ignored. Some of the known and unknown consequences of these omissions are discussed.

Fitting stochastic predator-prey models using both population density and kill rate data

Most mechanistic predator-prey modelling has involved either parameterization from process rate data or inverse modelling. Here, we take a median road: we aim at identifying the potential benefits of combining datasets, when both population growth and predation processes are viewed as stochastic. We fit a discrete-time, stochastic predator-prey model of the Leslie type to simulated time series of densities and kill rate data. Our model has both environmental stochasticity in the growth rates and interaction stochasticity, i.e., a stochastic functional response. We examine what the kill rate data brings to the quality of the estimates, and whether estimation is possible (for various time series lengths) solely with time series of population counts or biomass data. Both Bayesian and frequentist estimation are performed, providing multiple ways to check model identifiability. The Fisher Information Matrix suggests that models with and without kill rate data are all identifiable, although correlations remain between parameters that belong to the same functional form. However, our results show that if the attractor is a fixed point in the absence of stochasticity, identifying parameters in practice requires kill rate data as a complement to the time series of population densities, due to the relatively flat likelihood. Only noisy limit cycle attractors can be identified directly from population count data (as in inverse modelling), although even in this case, adding kill rate data - including in small amounts - can make the estimates much more precise. Overall, we show that under process stochasticity in interaction rates, interaction data might be essential to obtain identifiable dynamical models for multiple species. These results may extend to other biotic interactions than predation, for which similar models combining interaction rates and population counts could be developed.

How important is individual foraging specialisation in invasive predators for native-prey population viability?

Predation by invasive species is a major threat to the persistence of naïve prey. Typically, this negative effect is addressed by suppressing the population size of the invasive predator to a point where the predation pressure does not hinder the viability of the prey. However, this type of intervention may not be effective whenever a few specialised predators are the cause of the decline. We investigated the effects of varying levels of specialised invasive stoats (Mustela erminea) abundance on the long-term viability of simulated kiwi (Apteryx spp.) populations. We explored four scenarios with different proportions of highly specialised stoats, which were those that had a ≥ 0.75 probability of predating kiwi eggs and chicks if they were within their home range: (i) a stoat population composed mostly of generalists (mean: 0.5 probability of predation across the population); (ii) 5% of highly specialised stoats and the remaining being generalists; (iii) 10% of highly specialised stoats and the remaining being generalists; and, (iv) half highly specialised stoats and half generalists. We found that stoat home range sizes, rather than stoat density or the density of highly specialised stoats, was the main driver of kiwi population trends. Stoats with large home ranges were more likely to predate kiwi eggs and chicks as these were more likely to fall within a large home range. More broadly, our findings show how the daily individual ranging and foraging behaviour of an invasive predator can scale-up to shape population trends of naïve prey.

Short-term apparent mutualism drives responses of aquatic prey to increasing productivity

According to apparent competition theory, sharing a predator should cause indirect interactions among prey that can affect the structure and the dynamics of natural communities. Though shifts in prey dominance and predator resource use along environmental gradients are rather common, empirical evidence on the role of indirect prey-prey interactions through shared predation particularly with increasing productivity, is still scarce. In an 8-week lake mesocosm experiment, we manipulated both the addition of inorganic nutrients and the presence of generalist fish predators (crucian carp, Carassius carassius L.), to test for the effects of indirect interactions through shared predation along a productivity gradient. We found that apparent mutualism (indirect positive interaction) between benthic and pelagic prey strongly affected short-term responses of aquatic food webs to increasing productivity in the presence of a generalist fish. Increasing productivity favoured the relative abundance of benthic prey, following trends in natural productive lake systems. This led to a shift in fish selectivity from pelagic to benthic prey driven by changes in fish behaviour, which resulted in apparent mutualism due to the lower and delayed top-down control of pelagic prey at increasing productivity. Our results show empirical evidence that the coupling of multiple production pathways can lead to strong indirect interactions through shared predation, whereby prey dynamics on short time-scales are highly dependent on the foraging behaviour of generalist predators. This mechanism may play an important role in short-term responses of food webs across environmental gradients.

Trophic interaction modifications: an empirical and theoretical framework

Consumer-resource interactions are often influenced by other species in the community. At present these 'trophic interaction modifications' are rarely included in ecological models despite demonstrations that they can drive system dynamics. Here, we advocate and extend an approach that has the potential to unite and represent this key group of non-trophic interactions by emphasising the change to trophic interactions induced by modifying species. We highlight the opportunities this approach brings in comparison to frameworks that coerce trophic interaction modifications into pairwise relationships. To establish common frames of reference and explore the value of the approach, we set out a range of metrics for the 'strength' of an interaction modification which incorporate increasing levels of contextual information about the system. Through demonstrations in three-species model systems, we establish that these metrics capture complimentary aspects of interaction modifications. We show how the approach can be used in a range of empirical contexts; we identify as specific gaps in current understanding experiments with multiple levels of modifier species and the distributions of modifications in networks. The trophic interaction modification approach we propose can motivate and unite empirical and theoretical studies of system dynamics, providing a route to confront ecological complexity.

Trait adaptation promotes species coexistence in diverse predator and prey communities

Species can adjust their traits in response to selection which may strongly influence species coexistence. Nevertheless, current theory mainly assumes distinct and time-invariant trait values. We examined the combined effects of the range and the speed of trait adaptation on species coexistence using an innovative multispecies predator-prey model. It allows for temporal trait changes of all predator and prey species and thus simultaneous coadaptation within and among trophic levels. We show that very small or slow trait adaptation did not facilitate coexistence because the stabilizing niche differences were not sufficient to offset the fitness differences. In contrast, sufficiently large and fast trait adaptation jointly promoted stable or neutrally stable species coexistence. Continuous trait adjustments in response to selection enabled a temporally variable convergence and divergence of species traits; that is, species became temporally more similar (neutral theory) or dissimilar (niche theory) depending on the selection pressure, resulting over time in a balance between niche differences stabilizing coexistence and fitness differences promoting competitive exclusion. Furthermore, coadaptation allowed prey and predator species to cluster into different functional groups. This equalized the fitness of similar species while maintaining sufficient niche differences among functionally different species delaying or preventing competitive exclusion. In contrast to previous studies, the emergent feedback between biomass and trait dynamics enabled supersaturated coexistence for a broad range of potential trait adaptation and parameters. We conclude that accounting for trait adaptation may explain stable and supersaturated species coexistence for a broad range of environmental conditions in natural systems when the absence of such adaptive changes would preclude it. Small trait changes, coincident with those that may occur within many natural populations, greatly enlarged the number of coexisting species.

When Michaelis and Menten met Holling: towards a mechanistic theory of plant nutrient foraging behaviour

Plants are adept at assessing and responding to nutrients in soil, and generally proliferate roots into nutrient-rich patches. An analogy between this growth response and animal foraging movement is often drawn, but because of differences between plants and animals it has not always been clear how to directly apply existing foraging theory to plants. Here we suggest one way to unite pre-existing ideas in plant nutrient uptake with foraging theory. First, we show that the Michaelis-Menten equation used by botanists and the Holling disc equation used by zoologists are actually just rearrangements of the same functional response. This mathematical unity permits the translation of existing knowledge about the nutrient uptake physiology of plants into the language of foraging behaviour, and as a result gives botanists direct access to foraging theory. Second, we developed a model of root foraging precision based on the Holling disc equation and the marginal value theorem, and parameterize it from the literature. The model predicts (i) generally plants should invest in higher quality patches compared to lower quality patches, and as patch background-contrast increases; (ii) low encounter rates between roots and nutrients result in high root foraging precision; and (iii) low handling times for nutrients should result in high root foraging precision. The available data qualitatively support these predictions. Third, to parameterize the model above we undertook a review of the literature. From that review we obtained parameter estimates for nitrate and/or ammonium uptake for 45 plant species from 38 studies. We observe that the parameters ranged over six orders of magnitude, there was no trade-off in foraging ability for nitrate versus ammonium: plants that were efficient foragers for one form of nitrogen were efficient foragers for the other, and there was also no phylogenetic signal in the parameter estimates.

Evolution of specialization under non-equilibrium population dynamics

We analyze the evolution of specialization in resource utilization in a mechanistically underpinned discrete-time model using the adaptive dynamics approach. We assume two nutritionally equivalent resources that in the absence of consumers grow sigmoidally towards a resource-specific carrying capacity. The consumers use resources according to the law of mass-action with rates involving trade-off. The resulting discrete-time model for the consumer population has over-compensatory dynamics. We illuminate the way non-equilibrium population dynamics affect the evolutionary dynamics of the resource consumption rates, and show that evolution to the trimorphic coexistence of a generalist and two specialists is possible due to asynchronous non-equilibrium population dynamics of the specialists. In addition, various forms of cyclic evolutionary dynamics are possible. Furthermore, evolutionary suicide may occur even without Allee effects and demographic stochasticity.

Learning predator promotes coexistence of prey species in host-parasitoid systems

Ecological theory suggests that frequency-dependent predation, in which more common prey types are disproportionately favored, promotes the coexistence of competing prey species. However, many of the earlier empirical studies that investigated the effect of frequency-dependent predation were short-term and ignored predator-prey dynamics and system persistence. Therefore, we used long-term observation of population dynamics to test how frequency-dependent predation influences the dynamics and coexistence of competing prey species using insect laboratory populations. We established two-host-one-parasitoid populations with two bruchid beetles, Callosobruchus chinensis and C. maculatus, as the hosts and the pteromalid wasp Anisopteromalus calandrae as their common parasitoid. When the parasitoid was absent, C. chinensis was competitively excluded in ∼20 wk. Introducing the parasitoid greatly enhanced the coexistence time to a maximum of 118 wk. In the replicates of long-lasting coexistence, the two host species C. maculatus and C. chinensis exhibited periodic antiphase oscillations. Behavioral experiments showed frequency-dependent predation of A. calandrae that was caused by learning. Females of A. calandrae learned host-related olfactory cues during oviposition and increased their preference for the common host species. Numerical simulations showed that parasitoid learning was the essential mechanism that promoted persistence in this host-parasitoid system. Our study is an empirical demonstration that frequency-dependent predation has an important role in greatly enhancing the coexistence of prey populations, suggesting that predator learning affects predator-prey population dynamics and shapes biological communities in nature.

The roles of spatial heterogeneity and adaptive movement in stabilizing (or destabilizing) simple metacommunities

Adaptive consumer movement and between-patch heterogeneity have both been suggested to reduce population fluctuations in spatially subdivided systems. These conjectures are explored using models of two-patch consumer-resource systems with fitness dependent consumer movement and cyclic dynamics in at least one of the patches; neither conjecture applies generally to such systems. Under relatively low heterogeneity, highly accurate and rapid adaptive movement most often increases both the between-patch correlation of density and the variation in the total density of both species compared to a similar system having a low rate of random movement. However, such adaptive movement can decrease between-patch correlation and global population variability when (1) the consumer's movement is moderately sensitive to fitness differences and heterogeneity is relatively low, or (2) one of the patches would be stable in isolation, and the stable patch supports a sufficiently large consumer population. In both cases, the dynamics are typically either a stable equilibrium or a simple anti-phase cycle with low variation in total population size. Under adaptive movement, population variability is often lowest for intermediate levels of heterogeneity, but monotonic increases or decreases with increasing spatial heterogeneity are possible, depending on the fitness sensitivity of movement and how the characteristic that differs between patches affects within-patch stability and population size. High rates of random movement can lead to greater stability than adaptive movement when consumers are very efficient.

Modifying modifiers: what happens when interspecific interactions interact?

1. The strength of the trophic link between any given pair of species in a food web is likely to depend on the presence and/or densities of other species in the community. How these trophic interaction modifications (TIMs) interact with one another to produce a net modifying effect is an important but under-explored issue. 2. We review several specific types of TIMs that are well understood to address whether the magnitude of the net modification changes with the number of modifiers, and whether modifiers usually increase or decrease each other's effects. 3. Modifications of interactions are generally not independent. It is likely that TIMs interact antagonistically in the majority of cases; the magnitudes of TIMs decrease as more modifiers are added, or new TIMs reduce the magnitudes of modifications that are already present. 4. Individual modifications are likely to have a smaller effect in many-species systems than expected from independent combination of modifications measured in systems with relatively few species. Thus, models that lack explicit TIMs may in some cases yield adequate predictions for species-level perturbations, provided that the net effects of TIMs are implicitly included in measured interaction strengths. 5. Many types of TIMs share structural similarities. Nevertheless, a complete understanding of their effects may require theory that distinguishes different 'functional groups' of modifiers and addresses how these are structured according to trophic relationships.