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 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 Temperature-Dependent Functional Response of Harmonia Axyridis Pallas (Coleoptera: Coccinellidae) Preying on Acyrthosiphon Pisum (Harris) (Hemiptera: Aphididae) Nymphs

2021 ◽  
Author(s):  
Yasir Islam ◽  
Farhan Mahmood Shah ◽  
Xu Rubing ◽  
Muhammad Razaq ◽  
Miao Yabo ◽  
...  
Keyword(s):  
Functional Response ◽  
High Performance ◽  
Acyrthosiphon Pisum ◽  
Harmonia Axyridis ◽  
Functional Responses ◽  
Aphid Control ◽  
Host Aphid ◽  
Functional Response Models ◽  
Biocontrol Potential

Abstract Functional response models are often used to understand the foraging interactions and determine the suitable biocontrol agents. We determined the functional response of Harmonia axyridis to nymph Acyrthosiphon pisum at different but constant temperatures (between 15 and 35 °C) and prey densities. Logistic regression and Roger’s random predator models were employed to determine the type and parameters of functional response. Harmonia axyridis larvae and adults exhibited Type II functional responses to different densities of A. pisum. Warming increased both the predation activity and host aphid control mortality. The 4th instar and female H. axyridis consumed the most aphids. Warming contributed markedly in accelerating the predator action. For fourth instar larvae and female H. axyridis adult, the successful attack rates were 0.234 ± 0.014 h−1 and 0.247 ± 0.015 h−1; the handling times were 0.132 ± 0.005 h and 0.156 ± 0.004 h; and the estimated maximum predation rates were 181.28 ± 14.54 and 153.85 ± 4.06, respectively. These findings accentuate the high performance of 4th instar and female H. axyridis and the role of temperature in their efficiency. Further studies exploring intraguild predation and mutual interference will be required to conclude the biocontrol potential of H. axyridis to A. pisum.

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.

Statistical Issues in the Estimation of Functional Responses

2021 ◽  
pp. 115-132
Author(s):  
John P. DeLong
Keyword(s):  
Functional Response ◽  
Individual Variation ◽  
Handling Time ◽  
Trial Data ◽  
Data Sets ◽  
Functional Responses ◽  
Key Issues ◽  
Statistical Issues ◽  
Functional Response Models

In this chapter I cover some key issues in fitting functional response models to data and determining the values of parameters. Because some of these issues have been covered elsewhere, here I focus on the nature of foraging trial data and why noise, stochasticity, and individual variation pose particular challenges for understanding functional responses. I examine several data sets to illustrate methods of determining differences in functional response parameters and types. I also show through simulations that individual variation in functional response parameters may account for the noisiness of foraging data and also lead to underestimates of both space clearance rate and handling time in curve-fitting approaches.

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.

A COMPARISON OF TWO MODELS OF THE FUNCTIONAL RESPONSE WITH EMPHASIS ON PARAMETER ESTIMATION PROCEDURES

1970 ◽  
Vol 102 (9) ◽  
pp. 1094-1101 ◽  
Author(s):  
Norman R. Glass
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Functional Response ◽  
Handling Time ◽  
Logistic Function ◽  
Model Fit ◽  
Response Models ◽  
Nonlinear Functional ◽  
Functional Response Models ◽  
Parameter Values

AbstractThe two primary functional response models extant in recent entomological literature were compared using a common set of data. Use of an iterative least squares parameter estimation routine was shown to be essential to a comparison of these two models. With parameters properly determined, the Watt model fit data on one out of five experiment days best, the Holling model fit data best on four out of five experiment days. The "handling time" submodel was shown to require iterative least squares parameter estimation rather than the usual log transformation and subsequent fitting of this logistic function by standard linear regression techniques. The conclusion was reached that if accuracy in prediction by nonlinear functional response models is desired, proper methods of determining parameter values are of critical importance.

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 Functional response of Harmonia axyridis preying on Acyrthosiphon pisum nymphs: the effect of temperature

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yasir Islam ◽  
Farhan Mahmood Shah ◽  
Xu Rubing ◽  
Muhammad Razaq ◽  
Miao Yabo ◽  
...  
Keyword(s):  
Functional Response ◽  
High Performance ◽  
Acyrthosiphon Pisum ◽  
Harmonia Axyridis ◽  
Effect Of Temperature ◽  
Functional Responses ◽  
Aphid Control ◽  
Host Aphid ◽  
Predator Foraging

AbstractIn the current study, we investigated the functional response of Harmonia axyridis adults and larvae foraging on Acyrthosiphon pisum nymphs at temperatures between 15 and 35 °C. Logistic regression and Roger’s random predator models were employed to determine the type and parameters of the functional response. Harmonia axyridis larvae and adults exhibited Type II functional responses to A. pisum, and warming increased both the predation activity and host aphid control mortality. Female and 4th instar H. axyridis consumed the most aphids. For fourth instar larvae and female H. axyridis adults, the successful attack rates were 0.23 ± 0.014 h−1 and 0.25 ± 0.015 h−1; the handling times were 0.13 ± 0.005 h and 0.16 ± 0.004 h; and the estimated maximum predation rates were 181.28 ± 14.54 and 153.85 ± 4.06, respectively. These findings accentuate the high performance of 4th instar and female H. axyridis and the role of temperature in their efficiency. Further, we discussed such temperature-driven shifts in predation and prey mortality concerning prey-predator foraging interactions towards biological control.

scholarly journals Applying predator-prey theory to modelling immune-mediated, within-host interspecific parasite interactions

Parasitology ◽  
2010 ◽  
Vol 137 (6) ◽  
pp. 1027-1038 ◽  
Author(s):  
ANDY FENTON ◽  
SARAH E. PERKINS
Keyword(s):  
Functional Response ◽  
Interspecific Interactions ◽  
Parasite Load ◽  
Multiple Infections ◽  
Functional Responses ◽  
Predator Prey ◽  
Immune Activity ◽  
Parasite Communities ◽  
Immune Mediated ◽  
Predator Prey Models

SUMMARYPredator-prey models are often applied to the interactions between host immunity and parasite growth. A key component of these models is the immune system's functional response, the relationship between immune activity and parasite load. Typically, models assume a simple, linear functional response. However, based on the mechanistic interactions between parasites and immunity we argue that alternative forms are more likely, resulting in very different predictions, ranging from parasite exclusion to chronic infection. By extending this framework to consider multiple infections we show that combinations of parasites eliciting different functional responses greatly affect community stability. Indeed, some parasites may stabilize other species that would be unstable if infecting alone. Therefore hosts' immune systems may have adapted to tolerate certain parasites, rather than clear them and risk erratic parasite dynamics. We urge for more detailed empirical information relating immune activity to parasite load to enable better predictions of the dynamic consequences of immune-mediated interspecific interactions within parasite communities.

Sign in / Sign up

Export Citation Format

Share Document