The Basics and Origin of Functional Response Models

2021 ◽  
pp. 9-25
Author(s):  
John P. DeLong
Keyword(s):  
Functional Response ◽  
Model Parameters ◽  
Response Model ◽  
Response Models ◽  
Ground Floor ◽  
Biological Interpretation ◽  
Functional Response Models ◽  
Forward Looking

This chapter is the essential beginner’s guide to the functional response, its derivation, the various forms, its connection to other models in the literature, and what the parameters mean. It is the ground floor for the rest of the book, covering the four main types of functional response, what the parameters mean in biological terms, and how we arrived at these equations. Surprisingly, our understanding of the functional response as represented in the literature is quite muddled, with confusion ranging from the terminology used, to the various mathematical forms the functional response takes, to the biological interpretation of functional response model parameters. I provide a summary and forward-looking perspective on these issues.

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 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.

DSM criteria for major depression: evaluating symptom patterns using latent-trait item response models

2004 ◽  
Vol 35 (4) ◽  
pp. 475-487 ◽  
Author(s):  
STEVEN H. AGGEN ◽  
MICHAEL C. NEALE ◽  
KENNETH S. KENDLER
Keyword(s):  
Major Depression ◽  
Item Response ◽  
Latent Trait ◽  
Risk Measurement ◽  
Measurement Properties ◽  
Model Parameters ◽  
Response Model ◽  
Item Response Model ◽  
Response Models ◽  
Item Response Models

Background. Expert committees of clinicians have chosen diagnostic criteria for psychiatric disorders with little guidance from measurement theory or modern psychometric methods. The DSM-III-R criteria for major depression (MD) are examined to determine the degree to which latent trait item response models can extract additional useful information.Method. The dimensionality and measurement properties of the 9 DSM-III-R criteria plus duration are evaluated using dichotomous factor analysis and the Rasch and 2 parameter logistic item response models. Quantitative liability scales are compared with a binary DSM-III-R diagnostic algorithm variable to determine the ramifications of using each approach.Results. Factor and item response model results indicated the 10 MD criteria defined a reasonably coherent unidimensional scale of liability. However, person risk measurement was not optimal. Criteria thresholds were unevenly spaced leaving scale regions poorly measured. Criteria varied in discriminating levels of risk. Compared to a binary MD diagnosis, item response model (IRM) liability scales performed far better in (i) elucidating the relationship between MD symptoms and liability, (ii) predicting the personality trait of neuroticism and future depressive episodes and (iii) more precisely estimating heritability parameters.Conclusions. Criteria for MD largely defined a single dimension of disease liability although the quality of person risk measurement was less clear. The quantitative item response scales were statistically superior in predicting relevant outcomes and estimating twin model parameters. Item response models that treat symptoms as ordered indicators of risk rather than as counts towards a diagnostic threshold more fully exploit the information available in symptom endorsement data patterns.

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

Evaluation of alternative prey-, predator-, and ratio-dependent functional response models in a zooplankton microcosm

2017 ◽  
Vol 95 (3) ◽  
pp. 177-182 ◽  
Author(s):  
Christina M. Prokopenko ◽  
Katrine Turgeon ◽  
John M. Fryxell
Keyword(s):  
Functional Response ◽  
Theoretic Approach ◽  
Type Ii ◽  
Predator Density ◽  
Response Models ◽  
Predator Interference ◽  
Kill Rate ◽  
Ratio Dependent ◽  
Functional Response Models ◽  
Rotifer Brachionus Calyciflorus

There is strenuous debate among ecologists regarding the inclusion of predator density into the originally prey-dependent functional response. We provided comprehensive empirical comparisons of alternative functional response models for the predatory ostracod Heterocypris incongruens (Ramdohr, 1808) and the rotifer Brachionus calyciflorus (Pallas, 1766) as its prey in small freshwater microcosms. Prey killed was measured at factorial combinations of four predator densities and five prey densities, and was recorded at 3 min intervals over 60 min experiments. To support the potential effect of predator interference on per capita kill rate, we recorded ostracod activity and aggression. Kill rate increased following a saturating function with increasing prey density and decreased with increasing predator density. Model evaluation using an information–theoretic approach indicated that the Arditi–Ginzburg type II ratio-dependent model performed best, followed by the Arditi–Akcakaya and Beddington–DeAngelis type II predator-dependent models, suggesting that predator interference was important in predicting kill rates. Interference among predators increased and their activity decreased with increasing predator density, providing confirmation that interference was responsible for the predator-dependent effect. By combining a microcosm experiment and behavioral observations, our results suggest that predator interference at realistic population densities influences ostracod kill rates and this form of interference was best accommodated by predator-dependent models.

Using Data Augmentation and Markov Chain Monte Carlo for the Estimation of Unfolding Response Models

2003 ◽  
Vol 28 (3) ◽  
pp. 195-230 ◽  
Author(s):  
Matthew S. Johnson ◽  
Brian W. Junker
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Item Response ◽  
Data Augmentation ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Response Model ◽  
Response Models ◽  
Mcmc Estimation

Unfolding response models, a class of item response theory (IRT) models that assume a unimodal item response function (IRF), are often used for the measurement of attitudes. Verhelst and Verstralen (1993) and Andrich and Luo (1993) independently developed unfolding response models by relating the observed responses to a more common monotone IRT model using a latent response model (LRM; Maris, 1995 ). This article generalizes their approach, and suggests a data augmentation scheme for the estimation of any unfolding response model. The article introduces two Markov chain Monte Carlo (MCMC) estimation procedures for the Bayesian estimation of unfolding model parameters; one is a direct implementation of MCMC, and the second utilizes the data augmentation method. We use the estimation procedure to analyze three data sets, one simulated, and two from real attitudinal surveys.

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