Community dynamics and sensitivity to model structure: towards a probabilistic view of process-based model predictions

Functional Responses Shape Node and Network Level Properties of a Simplified Boreal Food Web

Ecological communities are fundamentally connected through a network of trophic interactions that are often complex and difficult to model. Substantial variation exists in the nature and magnitude of these interactions across various predators and prey and through time. However, the empirical data needed to characterize these relationships are difficult to obtain in natural systems, even for relatively simple food webs. Consequently, prey-dependent relationships and specifically the hyperbolic form (Holling’s Type II), in which prey consumption increases with prey density but ultimately becomes saturated or limited by the time spent handling prey, are most widely used albeit often without knowledge of their appropriateness. Here, we investigate the sensitivity of a simplified food web model for a natural, boreal system in the Kluane region of the Yukon, Canada to the type of functional response used. Intensive study of this community has permitted best-fit functional response relationships to be determined, which comprise linear (type I), hyperbolic (type II), sigmoidal (type III), prey- and ratio-dependent relationships, and inverse relationships where kill rates of alternate prey are driven by densities of the focal prey. We compare node- and network-level properties for a food web where interaction strengths are estimated using best-fit functional responses to one where interaction strengths are estimated exclusively using prey-dependent hyperbolic functional responses. We show that hyperbolic functional responses alone fail to capture important ecological interactions such as prey switching, surplus killing and caching, and predator interference, that in turn affect estimates of cumulative kill rates, vulnerability of prey, generality of predators, and connectance. Exclusive use of hyperbolic functional responses also affected trends observed in these metrics over time and underestimated annual variation in several metrics, which is important given that interaction strengths are typically estimated over relatively short time periods. Our findings highlight the need for more comprehensive research aimed at characterizing functional response relationships when modeling predator-prey interactions and food web structure and function, as we work toward a mechanistic understanding linking food web structure and community dynamics in natural systems.

Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

The assessment of relative model performance using information criteria like AIC and BIC has become routine among functional-response studies, reflecting trends in the broader ecological literature. Such information criteria allow comparison across diverse models because they penalize each model's fit by its parametric complexity—in terms of their number of free parameters—which allows simpler models to outperform similarly fitting models of higher parametric complexity. However, criteria like AIC and BIC do not consider an additional form of model complexity, referred to as geometric complexity, which relates specifically to the mathematical form of the model. Models of equivalent parametric complexity can differ in their geometric complexity and thereby in their ability to flexibly fit data. Here we use the Fisher Information Approximation to compare, explain, and contextualize how geometric complexity varies across a large compilation of single-prey functional-response models—including prey-, ratio-, and predator-dependent formulations—reflecting varying apparent degrees and forms of non-linearity. Because a model's geometric complexity varies with the data's underlying experimental design, we also sought to determine which designs are best at leveling the playing field among functional-response models. Our analyses illustrate (1) the large differences in geometric complexity that exist among functional-response models, (2) there is no experimental design that can minimize these differences across all models, and (3) even the qualitative nature by which some models are more or less flexible than others is reversed by changes in experimental design. Failure to appreciate model flexibility in the empirical evaluation of functional-response models may therefore lead to biased inferences for predator–prey ecology, particularly at low experimental sample sizes where its impact is strongest. We conclude by discussing the statistical and epistemological challenges that model flexibility poses for the study of functional responses as it relates to the attainment of biological truth and predictive ability.

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.

Hidden layers of density dependence in consumer feeding rates

Functional responses relate a consumer's feeding rates to variation in its abiotic and biotic environment, providing insight into consumer behaviour and fitness, and underpinning population and food-web dynamics. Despite their broad relevance and long-standing history, we show here that the types of density dependence found in classic resource- and consumer-dependent functional-response models equate to strong and often untenable assumptions about the independence of processes underlying feeding rates. We first demonstrate mathematically how to quantify non-independence between feeding and consumer interference and between feeding on multiple resources. We then analyse two large collections of functional-response data sets to show that non-independence is pervasive and borne out in previously hidden forms of density dependence. Our results provide a new lens through which to view variation in consumer feeding rates and disentangle the biological underpinnings of species interactions in multi-species contexts.

Systematic bias in studies of consumer functional responses

Functional responses are a cornerstone to our understanding of consumer-resource interactions, so how to best describe them using models has been actively debated. Here we focus on the consumer dependence of functional responses to evidence systematic bias in the statistical comparison of functional-response models and the estimation of their parameters. Both forms of bias are universal to nonlinear models (irrespective of consumer dependence) and are rooted in a lack of sufficient replication. Using a large compilation of published datasets, we show that - due to the prevalence of low sample size studies - neither the overall frequency by which alternative models achieve top rank nor the frequency distribution of parameter point estimates should be treated as providing insight into the general form or central tendency of consumer interference. We call for renewed clarity in the varied purposes that motivate the study of functional responses, purposes that can compete with each other in dictating the design, analysis and interpretation of functional-response experiments.

Emerging Frontiers in the Study of Molecular Evolution

A collection of the editors of Journal of Molecular Evolution have gotten together to pose a set of key challenges and future directions for the field of molecular evolution. Topics include challenges and new directions in prebiotic chemistry and the RNA world, reconstruction of early cellular genomes and proteins, macromolecular and functional evolution, evolutionary cell biology, genome evolution, molecular evolutionary ecology, viral phylodynamics, theoretical population genomics, somatic cell molecular evolution, and directed evolution. While our effort is not meant to be exhaustive, it reflects research questions and problems in the field of molecular evolution that are exciting to our editors.