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

2021 ◽  
Vol 9 ◽  
Author(s):  
Mark Novak ◽  
Daniel B. Stouffer
Keyword(s):  
Experimental Design ◽  
Functional Response ◽  
Information Criteria ◽  
Mathematical Form ◽  
Experimental Sample ◽  
Geometric Complexity ◽  
Functional Responses ◽  
Response Models ◽  
Model Flexibility ◽  
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.

scholarly journals Geometric complexity and the information-theoretic comparison of functional-response models

2021 ◽  
Author(s):  
Mark Novak ◽  
Daniel B Stouffer
Keyword(s):  
Experimental Design ◽  
Functional Response ◽  
Information Criteria ◽  
Model Complexity ◽  
Mathematical Form ◽  
Experimental Sample ◽  
Geometric Complexity ◽  
Functional Responses ◽  
Response Models ◽  
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 criterion 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 levels of phenomenological generality and 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 geometric complexity 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 the relative effects of geometric complexity are strongest. We conclude by discussing the statistical and epistemological challenges that geometric complexity poses for the study of functional responses as it relates to the attainment of biological truth and predictive ability.

scholarly journals Space race functional responses

2015 ◽  
Vol 282 (1801) ◽  
pp. 20142121 ◽  
Author(s):  
Henrik Sjödin ◽  
Åke Brännström ◽  
Göran Englund
Keyword(s):  
Functional Response ◽  
Community Dynamics ◽  
Simple Structure ◽  
Functional Responses ◽  
Response Models ◽  
Predator Prey ◽  
Prey System ◽  
Space Race ◽  
Functional Response Models ◽  
The Relationship

We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis–Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka–Volterra predator–prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats.

scholarly journals Hidden layers of density dependence in consumer feeding rates

2020 ◽  
Author(s):  
Daniel B. Stouffer ◽  
Mark Novak
Keyword(s):  
Density Dependence ◽  
Functional Response ◽  
Species Interactions ◽  
Feeding Rates ◽  
Functional Responses ◽  
Response Models ◽  
Multiple Resources ◽  
Functional Response Models ◽  
Biotic Environment ◽  
Insight Into

AbstractFunctional responses relate a consumer’s feeding rates to variation in its abiotic and biotic environment, providing insight into consumer behavior 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 analyze two large collections of functional-response datasets 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.

scholarly journals Systematic bias in studies of consumer functional responses

2020 ◽  
Author(s):  
Mark Novak ◽  
Daniel B. Stouffer
Keyword(s):  
Functional Response ◽  
Nonlinear Models ◽  
Systematic Bias ◽  
Functional Responses ◽  
Response Models ◽  
Point Estimates ◽  
Resource Interactions ◽  
Functional Response Models ◽  
Consumer Dependence ◽  
Insight Into

AbstractFunctional 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.

scholarly journals Fitting functional responses: Direct parameter estimation by simulating differential equations

2017 ◽  
Author(s):  
Benjamin Rosenbaum ◽  
Bjoern C. Rall
Keyword(s):  
Parameter Estimation ◽  
Functional Response ◽  
Marine Biology ◽  
Prediction Models ◽  
Functional Responses ◽  
Food Web Structure ◽  
Ode Models ◽  
Background Mortality ◽  
Functional Response Models ◽  
Scientific Fields

The feeding functional response is one of the most widespread mathematical frameworks in Ecology, Marine Biology, Freshwater Biology, Microbiology and related scientific fields describing the resource-dependent uptake of a consumer. Since the exact knowledge of its parameters is crucial in order to predict, for example, the efficiency of biocontrol agents, population dynamics, food web structure and subsequently biodiversity, a trustful parameter estimation is of utmost importance for scientists using this framework. Classical approaches for estimating functional response parameters lack flexibility and can often only serve as approximation for a correct parameter estimation. Moreover, they do not allow to incorporate side effects such as resource growth or background mortality. Both call for a new method to be established solving these problems. Here, we combined ordinary differential equation models (ODE models), that were numerically solved using computer simulations, with an iterative maximum likelihood fitting approach. We compared our method to classical approaches of fitting functional responses, using data both with and without additional resource growth and mortality. We found that for classical functional response models, like the often used type II and type III functional response, the established fitting methods are reliable. However, using more complex and flexible functional responses, our new established method outperforms the traditional methods. Additionally, only our method allows to analyze experiments correctly when resources experience growth or background mortality. Our method will enable researchers from different scientific fields that are measuring functional responses to estimate parameters correctly. These estimates will enable community ecologists to parameterize their models more precisely, allowing for a deeper understanding of complex ecological systems, and will increase the quality of ecological prediction models.

scholarly journals Building a mechanistic understanding of predation with GPS-based movement data

2010 ◽  
Vol 365 (1550) ◽  
pp. 2279-2288 ◽  
Author(s):  
Evelyn Merrill ◽  
Håkan Sand ◽  
Barbara Zimmermann ◽  
Heather McPhee ◽  
Nathan Webb ◽  
...  
Keyword(s):  
Functional Response ◽  
Handling Time ◽  
Response Models ◽  
Movement Data ◽  
Global Positioning ◽  
Important Challenge ◽  
Sources Of Variation ◽  
Functional Response Models ◽  
Kill Site ◽  
The Right

Quantifying kill rates and sources of variation in kill rates remains an important challenge in linking predators to their prey. We address current approaches to using global positioning system (GPS)-based movement data for quantifying key predation components of large carnivores. We review approaches to identify kill sites from GPS movement data as a means to estimate kill rates and address advantages of using GPS-based data over past approaches. Despite considerable progress, modelling the probability that a cluster of GPS points is a kill site is no substitute for field visits, but can guide our field efforts. Once kill sites are identified, time spent at a kill site (handling time) and time between kills (killing time) can be determined. We show how statistical models can be used to investigate the influence of factors such as animal characteristics (e.g. age, sex, group size) and landscape features on either handling time or killing efficiency. If we know the prey densities along paths to a kill, we can quantify the ‘attack success’ parameter in functional response models directly. Problems remain in incorporating the behavioural complexity derived from GPS movement paths into functional response models, particularly in multi-prey systems, but we believe that exploring the details of GPS movement data has put us on the right path.

Predicting Predation through Prey Ontogeny Using Size-Dependent Functional Response Models

2011 ◽  
Vol 177 (6) ◽  
pp. 752-766 ◽  
Author(s):  
Michael W. McCoy ◽  
Benjamin M. Bolker ◽  
Karen M. Warkentin ◽  
James R. Vonesh
Keyword(s):  
Functional Response ◽  
Response Models ◽  
Size Dependent ◽  
Functional Response Models

THE COMPARATIVE STUDY OF FUNCTIONAL RESPONSES: EXPERIMENTAL DESIGN AND STATISTICAL INTERPRETATION

1985 ◽  
Vol 117 (5) ◽  
pp. 617-629 ◽  
Author(s):  
Marilyn A. Houck ◽  
Richard E. Strauss
Keyword(s):  
Experimental Design ◽  
Functional Response ◽  
Maximum Likelihood Method ◽  
Graphical Method ◽  
Predation Rate ◽  
Likelihood Method ◽  
Statistical Interpretation ◽  
Functional Responses ◽  
Response Curves ◽  
The Comparative Study

AbstractMathematical discussions of models of functional response (predation rate as a function of prey density) have usually emphasized description of the shape of the functional-response curve. However, lack of congruence between experimental design and data analysis and under-utilization of appropriate statistical methods of analysis have hindered an empirical synthetic treatment of such feeding behavior. Here we review existing experimental and statistical procedures with reference to Holling's generalized model of functional response, and describe: (1) an experimental design compatible with the assumptions of the model; (2) a maximum-likelihood method for fitting the model; (3) several methods for statistical comparison of sets of functional-response curves; and (4) an exploratory graphical method for examining patterns of variation among larger numbers of samples.

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