scholarly journals How patch size and habitat complexity changes interaction strength and population dynamics: a combined individual-based and population-based modeling experiment

2016 ◽  
Author(s):  
Yuanheng Li ◽  
Ulrich Brose ◽  
Katrin Meyer ◽  
Björn C Rall
Keyword(s):  
Functional Response ◽  
Habitat Complexity ◽  
Patch Size ◽  
Interaction Strength ◽  
Population Based ◽  
Functional Responses ◽  
Predator Prey Model ◽  
Population Dynamic Model ◽  
Modeling Experiment ◽  
Feeding Interactions

Understanding how functional responses (non-linear prey density dependent feeding interactions) are affected by patch size and habitat complexity is crucial as functional responses are the major determinants of food web stability and subsequently biodiversity. Due to its laborious character, measuring empirical functional responses systematically across large gradients of patch sizes and habitat complexity independently is almost impossible. Here we overcame this issue by using an individual-based predator-prey model allowing to simulate functional responses in patches ranging from the size of petri dishes to natural patches in the field. Moreover we are able to vary the habitat complexity independent of the patch size. Contradicting to the pervasive type II functional response that is still assumed as the appropriate model to describe feeding interactions we found a type III functional response in our simulations, independent of patch size and habitat complexity. Moreover, half-saturation density determining the feeding success at low prey densities decrease only with increasing habitat complexity and is only marginally influenced by patch size. Subsequent population dynamic model simulations indicate that small patches do not allow for survival of the predator, caused by a mismatch of the nearly constant functional response but an increasing extinction boundary with decreasing patch size. This effect is counteracted by increasing habitat complexity allowing both, the prey and the predator to co-exist. Our results underline the need for protecting large patches with high habitat complexity to sustain biodiversity.

scholarly journals How patch size and refuge availability change interaction strength and population dynamics: a combined individual- and population-based modeling experiment

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e2993 ◽  
Author(s):  
Yuanheng Li ◽  
Ulrich Brose ◽  
Katrin Meyer ◽  
Björn C. Rall
Keyword(s):  
Population Dynamics ◽  
Habitat Complexity ◽  
Patch Size ◽  
Feeding Rate ◽  
Interaction Strength ◽  
Time Frame ◽  
Feeding Rates ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model

Knowledge on how functional responses (a measurement of feeding interaction strength) are affected by patch size and habitat complexity (represented by refuge availability) is crucial for understanding food-web stability and subsequently biodiversity. Due to their laborious character, it is almost impossible to carry out systematic empirical experiments on functional responses across wide gradients of patch sizes and refuge availabilities. Here we overcame this issue by using an individual-based model (IBM) to simulate feeding experiments. The model is based on empirically measured traits such as body-mass dependent speed and capture success. We simulated these experiments in patches ranging from sizes of petri dishes to natural patches in the field. Moreover, we varied the refuge availability within the patch independently of patch size, allowing for independent analyses of both variables. The maximum feeding rate (the maximum number of prey a predator can consume in a given time frame) is independent of patch size and refuge availability, as it is the physiological upper limit of feeding rates. Moreover, the results of these simulations revealed that a type III functional response, which is known to have a stabilizing effect on population dynamics, fitted the data best. The half saturation density (the prey density where a predator consumes half of its maximum feeding rate) increased with refuge availability but was only marginally influenced by patch size. Subsequently, we investigated how patch size and refuge availability influenced stability and coexistence of predator-prey systems. Following common practice, we used an allometric scaled Rosenzweig–MacArthur predator-prey model based on results from ourin silicoIBM experiments. The results suggested that densities of both populations are nearly constant across the range of patch sizes simulated, resulting from the constant interaction strength across the patch sizes. However, constant densities with decreasing patch sizes mean a decrease of absolute number of individuals, consequently leading to extinction of predators in the smallest patches. Moreover, increasing refuge availabilities also allowed predator and prey to coexist by decreased interaction strengths. Our results underline the need for protecting large patches with high habitat complexity to sustain biodiversity.

scholarly journals How patch size and refuge availability change interaction strength and population dynamics: a combined individual- and population-based modeling experiment

2016 ◽  
Author(s):  
Yuanheng Li ◽  
Ulrich Brose ◽  
Katrin Meyer ◽  
Björn C Rall
Keyword(s):  
Population Dynamics ◽  
Habitat Complexity ◽  
Patch Size ◽  
Feeding Rate ◽  
Interaction Strength ◽  
Time Frame ◽  
Feeding Rates ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model

Knowledge on how functional responses (a measurement of feeding interaction strength) are affected by patch size and habitat complexity (represented by refuge availability) is crucial for understanding food-web stability and subsequently biodiversity. Due to their laborious character, it is almost impossible to carry out systematic empirical experiments on functional responses across wide gradients of patch sizes and refuge availabilities. Here we overcame this issue by using an individual-based model (IBM) to simulate feeding experiments. The model is based on empirically measured traits such as body size dependent speed and capture success. We simulated these experiments in patches ranging from size of petri dishes to natural patches in the field. Moreover, we varied the refuge availability within the patch independently of patch size, allowing for an independent analyses of both variables. The maximum feeding rate (the maximum number of prey a predator can consume in a given time frame) is independent of patch size and refuge availability, as it is the physiological upper limit of feeding rates. Moreover, the results of these simulations revealed that a type III functional response, which is known to have a stabilizing effect on population dynamics, fits the data best. The half saturation density (the prey density where a predator consumes half of its maximum feeding rate) increased with refuge availability but was only marginally influenced by patch size. Subsequently, we investigated how patch size and refuge availability influence stability and coexistence of predator-prey systems. Following common practice, we used an allometric scaled Rosenzweig-MacArthur predator-prey model based on results from our in silico IBM experiments. The results suggested that densities of both populations are nearly constant across the range of patch sizes simulated, resulting from the constant interaction strength across the patch sizes. However, constant densities with decreasing patch sizes mean a decrease of absolute number of individuals, consequently leading to extinction of predators in smallest patches. Moreover, increasing refuge availabilities also allowed predator and prey to coexist by decreased interaction strengths. Our results underline the need for protecting large patches with high habitat complexity to sustain biodiversity.

scholarly journals How patch size and refuge availability change interaction strength and population dynamics: a combined individual- and population-based modeling experiment

2016 ◽  
Author(s):  
Yuanheng Li ◽  
Ulrich Brose ◽  
Katrin Meyer ◽  
Björn C Rall
Keyword(s):  
Population Dynamics ◽  
Habitat Complexity ◽  
Patch Size ◽  
Feeding Rate ◽  
Interaction Strength ◽  
Time Frame ◽  
Feeding Rates ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model

Knowledge on how functional responses (a measurement of feeding interaction strength) are affected by patch size and habitat complexity (represented by refuge availability) is crucial for understanding food-web stability and subsequently biodiversity. Due to their laborious character, it is almost impossible to carry out systematic empirical experiments on functional responses across wide gradients of patch sizes and refuge availabilities. Here we overcame this issue by using an individual-based model (IBM) to simulate feeding experiments. The model is based on empirically measured traits such as body size dependent speed and capture success. We simulated these experiments in patches ranging from size of petri dishes to natural patches in the field. Moreover, we varied the refuge availability within the patch independently of patch size, allowing for an independent analyses of both variables. The maximum feeding rate (the maximum number of prey a predator can consume in a given time frame) is independent of patch size and refuge availability, as it is the physiological upper limit of feeding rates. Moreover, the results of these simulations revealed that a type III functional response, which is known to have a stabilizing effect on population dynamics, fits the data best. The half saturation density (the prey density where a predator consumes half of its maximum feeding rate) increased with refuge availability but was only marginally influenced by patch size. Subsequently, we investigated how patch size and refuge availability influence stability and coexistence of predator-prey systems. Following common practice, we used an allometric scaled Rosenzweig-MacArthur predator-prey model based on results from our in silico IBM experiments. The results suggested that densities of both populations are nearly constant across the range of patch sizes simulated, resulting from the constant interaction strength across the patch sizes. However, constant densities with decreasing patch sizes mean a decrease of absolute number of individuals, consequently leading to extinction of predators in smallest patches. Moreover, increasing refuge availabilities also allowed predator and prey to coexist by decreased interaction strengths. Our results underline the need for protecting large patches with high habitat complexity to sustain biodiversity.

scholarly journals Impact of Fear and Habitat Complexity in a Predator-Prey System with Two Different Shaped Functional Responses: A Comparative Study

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Debgopal Sahoo ◽  
Guruprasad Samanta ◽  
Manuel De la Sen
Keyword(s):  
Steady State ◽  
Functional Response ◽  
Habitat Complexity ◽  
Lower Degree ◽  
Encounter Rate ◽  
Reproduction Rate ◽  
Stable Limit ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model

Habitat complexity or the structural complexity of habitat reduces the available space for interacting species, and subsequently, the encounter rate between the prey and predator is decreased significantly. Different experimental shreds of evidence validate that the presence of the predator strongly affects the physiological behaviour of prey individuals and dramatically reduces their reproduction rate. In this study, we investigate the interplay between the level of fear and the degree of habitat complexity in a predator-prey model with two different shaped functional responses. We, therefore, develop the functional response using the timescale separation method, and the shape of the resulting functional response depends upon the monotonous property of catch rate, g N where N is the prey biomass. Whenever g N increases strictly, a saturating functional response occurs, but for nonmonotonic g N , a dome-shaped functional response arises. For saturating case, it has been revealed that both prey and predator biomass may oscillate for lower levels of fear and a lower degree of habitat complexity. To stabilize this oscillatory behaviour to a coexistence state, we have to adequately increase the level of fear or degree of habitat complexity. However, for dome-shaped case, more complicated dynamics are observed. In this case, coexistence steady state, if exists, may be locally asymptotically stable for a lower degree of habitat complexity, but for intermediate values, the system is capable of producing multiple coexistence steady states with a bistable phenomenon between predator-free steady state and a coexistence steady state. Moreover, if the level of fear is sufficiently low, the system may experience a supercritical or/and subcritical Hopf bifurcation. In the dynamics of parametric disturbance for the degree of habitat complexity parameter, dome-shaped functional response predicts that disturbance may trap the system into a nearest attractor (either a large amplitude stable limit cycle or predator-free steady state); this can be overcome only by a larger alteration, or sometimes it is impossible to overcome (hysteresis phenomena), whereas the saturating-shaped functional response predicts a system resilience. For both the functional responses, a higher degree of habitat complexity always increases the extinction possibility of the predator, and no level of fear can compensate this biodiversity loss.

scholarly journals Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Can-Yun Huang ◽  
Min Zhao ◽  
Hai-Feng Huo
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Ii Functional Response

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

scholarly journals Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response

2020 ◽  
Vol 99 (99) ◽  
pp. 1-12
Author(s):  
Yinshu Wu ◽  
Wenzhang Huang
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Local Stability ◽  
Positive Equilibrium ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Prey Models ◽  
Global And Local

A predator-prey model with Ivlev-Type functional response is studied. The main purpose is to investigate the global stability of a positive (co-existence) equilibrium, whenever it exists. A recently developed approach shows that for certain classes of models, there is an implicitly defined function which plays an important rule in determining the global stability of the positive equilibrium. By performing a detailed analytic analysis we demonstrate that a crucial property of this implicitly defined function is governed by the local stability of the positive equilibrium, which enable us to show that the global and local stability of the positive equilibrium, whenever it exists, is equivalent. We believe that our approach can be extended to study the global stability of the positive equilibrium for predator-prey models with some other types of functional responses.

Bifurcation and Stability in a Delayed Predator–Prey Model with Mixed Functional Responses

2015 ◽  
Vol 25 (07) ◽  
pp. 1540014 ◽  
Author(s):  
R. Yafia ◽  
M. A. Aziz-Alaoui ◽  
H. Merdan ◽  
J. J. Tewa
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Functional Response ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
The Third ◽  
Trivial Equilibrium ◽  
Model Set ◽  
Bifurcation And Stability

The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie–Gower functional response as well as that of Beddington–DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values.

Prey herd behavior modeled by a generic non-differentiable functional response

2018 ◽  
Vol 13 (3) ◽  
pp. 26 ◽  
Author(s):  
Karina Vilches ◽  
Eduardo González-Olivares ◽  
Alejandro Rojas-Palma
Keyword(s):  
Functional Response ◽  
Antipredator Behavior ◽  
Direct Consequence ◽  
Herd Behavior ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Separatrix Curve ◽  
Points Of View ◽  
Well Posed

Over the past decade, many works have studied an antipredator behavior (APB) named prey herd behavior. Analyzes have been conducted by modifying the classical predator consumption rate to be dependent only on the prey population size assuming the square root functional response. This work focuses analyzing the dynamics of a Gause-type predator-prey model considering that social behavior of prey. However, we model this phenomenon using a Holling type II non-differentiable rational functional response, which is more general than that mentioned above. The studied model exhibits richer dynamics than those with differentiable functional responses, and one the main consequences of including this type of function is the existence of initial values for which the extinction of prey occurs within a finite time for all parameter conditions, which is a direct consequence of the non-uniqueness of the solutions over the vertical axes and of the existence of a separatrix curve dividing the phase plane. A discussion on what represents a well-posed problem from both the mathematical and the ecological points of view is presented. Additionally, the differences in other social behaviors of the prey are also established. Numerical simulations are provided to validate the mathematical results.

scholarly journals Trait-Based Variation in the Foraging Performance of Individuals

2021 ◽  
Vol 9 ◽  
Author(s):  
John P. DeLong ◽  
Stella F. Uiterwaal ◽  
Anthony I. Dell
Keyword(s):  
Functional Response ◽  
Individual Variation ◽  
Interaction Strength ◽  
Leg Length ◽  
Functional Responses ◽  
Predator Prey ◽  
Individual Level ◽  
Foraging Performance ◽  
Body Velocity ◽  
Males And Females

Although average, species-level interaction strength plays a key role in driving population dynamics and community structure, predator-prey interactions occur among individuals. As a result, individual variation in foraging rates may play an important role in determining the effects of predator-prey interactions on communities. Such variation in foraging rates stems from individual variation in traits that influence the mechanistic components of the functional response, such as movements that determine encounters and behaviors such as decisions to attack. However, we still have little information about individual-level variation in functional responses or the traits that give rise to such variation. Here we combine a standard functional response experiment with wolf spiders foraging on fruit flies with a novel analysis to connect individual morphology, physiology, and movement to individual foraging performance. We found substantial variation in traits between males and females, but these were not clearly linked to the differences in the functional response between males and females. Contrary to expectations, we found no effect of body velocity, leg length, energetic state, or metabolic rate on foraging performance. Instead, we found that body mass interacted with body rotations (clockwise turns), such that larger spiders showed higher foraging performance when they turned more but the reverse was true for smaller spiders. Our results highlight the need to understand the apparent complexity of the links between the traits of individuals and the functional response.

Sign in / Sign up

Export Citation Format

Share Document