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.

scholarly journals Holling meets habitat selection: functional response of large herbivores revisited

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Claudia Dupke ◽  
Anne Peters ◽  
Nicolas Morellet ◽  
Marco Heurich
Keyword(s):  
Habitat Selection ◽  
Land Cover ◽  
Functional Response ◽  
Discrete Choice Models ◽  
Time Of Day ◽  
Functional Responses ◽  
Response Curves ◽  
Large Herbivores ◽  
Land Cover Types ◽  
Selection Of

Abstract Background Holling (Can Entomol 91(5):293–320, 1959) was the first to describe a functional response between a predator’s consumption-rate and the density of its prey. The same concept can be applied to the habitat selection of herbivores, specifically, the change in relative habitat use with the change in habitat availability. Functional responses in habitat selection at a home-range scale have been reported for several large herbivores. However, a link to Holling’s original functional response types has never been drawn, although it could replace the current phenomenological view with a more mechanistically based understanding of functional responses. Methods In this study, discrete choice models were implemented as mixed-effects baseline-category logit models to analyze the variation in habitat selection of a large herbivore at seasonal and diurnal scales. Thus, changes in the use of land cover types with respect to their availability were investigated by monitoring 11 land cover types commonly used by roe deer (Capreolus capreolus) in the Bavarian Forest National Park, Germany. Functional response curves were then fitted using Holling’s formulas. Results Strong evidence of non-linear functional responses was obtained for almost all of the examined land cover types. The shape of the functional response curves varied depending on the season, the time of day, and in some cases between sexes. These responses could be referenced to Holling’s types, with a predominance of type II. Conclusions Our results indicate that Holling’s types can be applied to describe general patterns of the habitat selection behavior of herbivores. Functional responses in habitat selection may occur in situations requiring a trade-off in the selection of land cover types offering different resources, such as due to the temporally varying physiological needs of herbivores. Moreover, two associated parameters defining the curves (prey density and predation rate) can aid in the identification of temporal variations and in determinations of the strength of the cost-benefit ratio for a specific land cover type. Application of our novel approach, using Holling’s equations to describe functional responses in the habitat selection of herbivores, will allow the assignment of general land cover attraction values, independent of availability, thus facilitating the identification of suitable habitats.

Estimation of Functional Responses of Predators on Juvenile Salmon

1978 ◽  
Vol 35 (6) ◽  
pp. 797-808 ◽  
Author(s):  
Randall M. Peterman ◽  
Marino Gatto
Keyword(s):  
Functional Response ◽  
Chum Salmon ◽  
Pink Salmon ◽  
Experimental Studies ◽  
Functional Responses ◽  
Response Curves ◽  
Response Component ◽  
Predation Mortality ◽  
Salmon Fry ◽  
Salmon Population

Several studies have shown that predators can eat large portions (up to 85%) of emerging salmon (Oncorhynchus spp.) fry populations. To understand salmon population dynamics and the effect of salmon enhancement projects, it is necessary to determine how present predation mortality varies with prey density. To predict the shape of this relation outside the range of past observations, we must examine the basic components of the predation process, the functional and numerical responses. A review of past, sparse data on the functional response component shows that predators of salmon fry and smolts were mostly not being saturated (i.e. maximum attack rates were not being achieved) at high prey densities. A method to estimate functional responses from certain types of existing field data is derived and applied to Hooknose Creek pink salmon (O. gorbuscha) and chum salmon (O. keta) information. Results from 7 out of 9 yr corroborate earlier observations that predators are normally operating on the low end of their functional response curves and are therefore capable of causing high mortality on larger prey populations. Also, competition among predators is demonstrated to be significant, resulting in changes in slopes of functional responses. More experimental studies of functional responses are needed, and such research should be carried out in conjunction with perturbations in salmon fry abundance which will result from enhancement projects. Key words: salmon fry, predation, freshwater survival, enhancement, functional response, predator competition

scholarly journals Multistage Curve Fitting

1977 ◽  
Vol 9 (1-2) ◽  
pp. 191-202 ◽  
Author(s):  
Christoph Haehling von Lanzenauer ◽  
Don Wright
Keyword(s):  
Distribution Function ◽  
Method Of Moments ◽  
Curve Fitting ◽  
Maximum Likelihood Method ◽  
Graphical Method ◽  
Decision Makers ◽  
Third Party ◽  
Likelihood Method ◽  
Bodily Injury ◽  
Image Position

One of the most important properties of a distribution function is that it fits the data well enough for the decision-makers' or analysts' purposes. The statisticians' problem is to select a specific form for the distribution function and to determine its parameters from the available data. Various methods (graphical method, method of moments, maximum likelihood method) are available for that purpose.In many real world situations a single distribution function, however, may not be appropriate over the entire range of the available data. This suggests that the underlying process changes over the range of the respective variable. This fact should be considered in curve fitting. A typical example of such a situation is given in Figure 1 representing third party liability losses for trucks.It is interesting to speculate about the different raisons d'être (Seal [5]) for the observed discontinuity. It may be the result of out-of-court or in-court settlements or could stem from differences between bodily injury and property damages.

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 Estimating predator functional responses using the times between prey captures

2020 ◽  
Author(s):  
Kyle E. Coblentz ◽  
John P. DeLong
Keyword(s):  
Experimental Design ◽  
Statistical Method ◽  
Experimental Method ◽  
Functional Response ◽  
List Type ◽  
Proof Of Concept ◽  
Functional Responses ◽  
Predator Prey ◽  
Jumping Spiders ◽  
Wide Range

AbstractPredator functional responses, which describe how predator feeding rates change with prey densities, are a core component of predator-prey theory. Given their importance, ecologists have measured thousands of predator functional responses. However, most of these studies have used a single standard experimental method that is ill-suited to address many current, pressing questions regarding functional responses.We derive a new experimental design and statistical analysis that quantifies the parameters of predator functional responses by using the time between a predator’s feeding events and can be used with individual predators requiring only one or a few trials. We examine the feasibility of this experimental method and analysis by using simulations to examine the ability of the statistical model to estimate the ‘true’ functional response parameters from simulated data. We also perform a proof-of-concept experiment estimating the functional responses of two individual jumping spiders feeding on midges.Our simulations show that the statistical method is capable of reliably estimating functional response parameters under a wide range of parameter values and sample sizes. Our proof-of-concept experiment illustrates that the experimental design and statistical method provided reasonable estimates of functional response parameters and good fits to the data for individual jumping spiders using only a few trials per individual.By virtue of the fewer number of trials required to measure a functional response, the method derived here promises to expand the questions that can be addressed using functional response experiments and the systems for which functional responses can be measured. For example, this method is well-poised to address questions such as intraspecific variation in predator functional response parameters and the role of predator and prey traits and abiotic conditions on shaping functional responses. We hope, therefore, that this time-between-captures method will refine our understanding of functional responses and thereby our understanding of predator-prey interactions more generally.

Comparison of Functional Response and Mutual Interference Between Two Aphelinid Parasitoids of Bemisia argentifolii (Homoptera: Aleyrodidae)

2001 ◽  
Vol 36 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Shoil M. Greenberg ◽  
Benjamin C. Legaspi ◽  
Walker A. Jones
Keyword(s):  
Functional Response ◽  
Handling Time ◽  
Mass Rearing ◽  
Mutual Interference ◽  
Host Feeding ◽  
Bemisia Argentifolii ◽  
Functional Responses ◽  
Response Curves ◽  
Eretmocerus Mundus ◽  
Type Ii Functional Response

Functional responses and mutual interference were compared in an indigenous parasitoid, Encarsia pergandiella Howard (Hymenoptera: Aphelinidae), with that of an exotic parasitoid, Eretmocerus mundus Mercet (Aphelinidae) from Spain, attacking the silverleaf whitefly, Bemisia argentifolii Bellows and Perring (Homoptera: Aleyrodidae). Type II functional response curves were fitted to the data and were used to calculate handling time. Eretmocerus mundus attacked more whitefly nymphs than E. pergandiella. Handling times estimated from the functional responses were 72 min for E. pergandiella and 12 min for E. mundus, suggesting that lower attack rates for the former parasitoid may be attributed to longer handling times. The statistically estimated handling time for E. mundus was compared with an estimate derived from empirical observations of parasitoid behavior. Actual observations of handling time, defined as oviposition, host feeding and associated preening, yielded a mean handling time of <2 min, suggesting that functional response experiments may not produce reliable estimates of handling time. The mutual interference coefficient m of E. mundus was numerically higher than that for E. pergandiella (0.238 vs 0.184, respectively). Although there were no significant differences in m, the comparison raises the interesting question of whether parasitoids with higher attack rates may also have higher levels of mutual interference under conditions of high parasitoid density (e.g., mass rearing).

scholarly journals Functional Responses ofNephus arcuatusKapur (Coleoptera: Coccinellidae), the Most Important Predator of Spherical MealybugNipaecoccus viridis(Newstead)

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Sara Zarghami ◽  
Mohammad Saeed Mossadegh ◽  
Farhan Kocheili ◽  
Hossein Allahyari ◽  
Arash Rasekh
Keyword(s):  
Functional Response ◽  
Developmental Stages ◽  
Handling Time ◽  
Predation Rate ◽  
Adult Males ◽  
Functional Responses ◽  
Adult Females ◽  
Important Predator ◽  
Citrus Orchards ◽  
Southwestern Iran

Nephus arcuatusKapur is an important predator ofNipaecoccus viridis(Newstead), in citrus orchards of southwestern Iran. This study examined the feeding efficiency of all stages ofN. arcuatusat different densities ofN. viridiseggs by estimating their functional responses. First and 2nd instar larvae as well as adult males exhibited a type II functional response. Attack rate and handling time were estimated to be 0.2749 h−1and 5.4252 h, respectively, for 1st instars, 0.5142 h−1and 1.1995 h for 2nd instars, and 0.4726 h−1and 0.7765 h for adult males. In contrast, 3rd and 4th instar larvae and adult females ofN. arcuatusexhibited a type III functional response. Constantband handling time were estimated to be 0.0142 and 0.4064 h for 3rd instars, respectively, 0.00660 and 0.1492 h for 4th instars, and 0.00859 and 0.2850 h for adult females. The functional response of these six developmental stages differed in handling time. Based on maximum predation rate, 4th instar larvae were the most predatory (160.9 eggs/d) followed by adult females (84.2 eggs/d). These findings suggest thatN. arcuatusis a promising biocontrol agent ofN. viridiseggs especially for 4th instar larvae and adult females.

scholarly journals Holling Meets Habitat Selection - Functional Response of Large Herbivores Revisited

2021 ◽  
Author(s):  
Claudia Dupke ◽  
Anne Peters ◽  
Nicolas Morellet ◽  
Marco Heurich
Keyword(s):  
Habitat Selection ◽  
Habitat Use ◽  
Functional Response ◽  
Time Of Day ◽  
Habitat Availability ◽  
Functional Responses ◽  
Habitat Types ◽  
Response Curves ◽  
Large Herbivores ◽  
Selection Of

Abstract Background: Holling (1959) was the first to describe a functional response between a predator’s consumption-rate and the density of its prey. The same concept may be applied to the habitat selection of herbivores, by considering the change in relative habitat use with the change in habitat availability. Functional responses in habitat selection at a home-range scale has been reported for several large herbivores. However, a link to Holling’s original functional response types has never been drawn despite its potential to understand availability dependence in habitat selection more profoundly. Methods: Discrete choice models were implemented as mixed-effects baseline-category logit models to analyze the variation in habitat selection of a large herbivore over seasonal and diurnal scales. Specifically, changes in habitat use with respect to habitat availability were investigated by monitoring 11 habitat types commonly used by roe deer ( Capreolus capreolus ) in the Bavarian Forest National Park, Germany. Functional response curves were then fitted using Holling’s formulas. Results: Strong evidence of non-linear functional responses was obtained for almost all of the examined habitat types. The shape of the functional response curves varied depending on the season, time of day and in some cases between sexes. These responses could be referenced to Holling’s types, with a predominance of type II.Conclusions: Our results indicate that Holling’s types could be applied to describe general patterns in habitat selection behaviour of herbivores. Functional response in habitat selection may occur in situations of trade-off in the selection of habitats offering different resources, due to temporally varying physiological needs of herbivores. Moreover, the two associated parameters defining the curves helps to identify the temporal variations and clarify how strongly the cost-to-benefit ratio is pronounced for a specific habitat. The presented novel approach of using Holling’s equations to describe functional response in habitat selection of herbivores could be used for assigning general habitat attraction values, independent of habitat availability, which might facilitate the identification of suitable habitats.

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.

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