scholarly journals Population Dynamic Regulators In An Empirical Predator-Prey System

2020 ◽  
Author(s):  
Anna S. Frank ◽  
Sam Subbey ◽  
Melanie Kobras ◽  
Harald Gjøsæter
Keyword(s):  
Prey Availability ◽  
Critical Time ◽  
Growth Period ◽  
System Stability ◽  
Model Parameters ◽  
Predator Prey ◽  
Delay Term ◽  
Prey System ◽  
Fitting Model ◽  
Empirical System

ABSTRACTThis paper investigates stability conditions of an empirical predator-prey system using a model that includes a single delay term, τ, in description of the predator dynamics. We derive theoretical conditions on τ, in terms of other model parameters, and determine how changes in these conditions define different stability regimes of the system. We derive optimal model parameters by fitting model to empirical data, using unconstrained optimization. The optimization results are combined with those from the theoretical analysis, to make inference about the empirical system stability.Our results show that Hopf bifurcation occurs in the predatory-prey system when τ exceeds a theoretically derived value τ* > 0. This value represents the critical time for prey availability in advance of the optimal predator growth period. Set into an ecological context, our findings provide mathematical evidence for validity of the match-mismatch hypothesis, for this particular species.

scholarly journals Cooperative hunting in a discrete predator–prey system

2020 ◽  
Vol 13 (07) ◽  
pp. 2050063
Author(s):  
Yunshyong Chow ◽  
Sophia R.-J. Jang ◽  
Hua-Ming Wang
Keyword(s):  
Growth Rate ◽  
Discrete Time ◽  
Reproductive Number ◽  
Model Parameters ◽  
Predator Population ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Cooperative Hunting ◽  
Prey System ◽  
Dependent Growth

We propose and investigate a discrete-time predator–prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson–Bailey host-parasitoid system with density dependent growth rate. A sufficient condition based on the model parameters for which both populations can coexist is derived, namely that the predator’s maximal reproductive number exceeds one. We study existence of interior steady states and their stability in certain parameter regimes. It is shown that the system behaves asymptotically similar to the model with no cooperative hunting if the degree of cooperation is small. Large cooperative hunting, however, may promote persistence of the predator for which the predator would otherwise go extinct if there were no cooperation.

scholarly journals Crowding Effects in an Empirical Predator-Prey System

2020 ◽  
Author(s):  
Sam Subbey ◽  
Anna S. Frank ◽  
Melanie Kobras
Keyword(s):  
Hopf Bifurcation ◽  
System Dynamics ◽  
Empirical Data ◽  
Modeling Framework ◽  
Predator Prey ◽  
System Parameters ◽  
Crowding Effects ◽  
Ode System ◽  
Prey System ◽  
Empirical System

AbstractThis paper uses a Lotka-Volterra (predator-prey) modeling framework to investigate the dynamical link between the biomass of an empirical predator, and that of its prey. We use a system of ordinary (ODE) differential equations to describe the system dynamics, and derive theoretical conditions for stability, in terms of system parameters. We derive the empirical system parameters by fitting the ODE system to empirical data, using non-constrained optimization.We present results to show that the predator biomass is regulated by that of the prey. Furthermore, that the system dynamics is subject to Hopf bifurcation, conditioned on independent second-order terms in the ODE system. In ecological terms, the findings translate into evidence for existence of population crowding (density) effects.

scholarly journals Temperature alters the shape of predator–prey cycles through effects on underlying mechanisms

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9377 ◽  
Author(s):  
John P. DeLong ◽  
Shelby Lyon
Keyword(s):  
Population Dynamics ◽  
Model Parameters ◽  
Cycle Period ◽  
Short Term ◽  
Ecological Dynamics ◽  
Predator Prey ◽  
Prey System ◽  
Wide Range ◽  
Underlying Mechanisms ◽  
Temperature Dependance

Background Predicting the effects of climate warming on the dynamics of ecological systems requires understanding how temperature influences birth rates, death rates and the strength of species interactions. The temperature dependance of these processes—which are the underlying mechanisms of ecological dynamics—is often thought to be exponential or unimodal, generally supported by short-term experiments. However, ecological dynamics unfold over many generations. Our goal was to empirically document shifts in predator–prey cycles over the full range of temperatures that can possibly support a predator–prey system and then to uncover the effect of temperature on the underlying mechanisms driving those changes. Methods We measured the population dynamics of the Didinium-Paramecium predator–prey system across a wide range of temperatures to reveal systematic changes in the dynamics of the system. We then used ordinary differential equation fitting to estimate parameters of a model describing the dynamics, and used these estimates to assess the long-term temperature dependance of all the underlying mechanisms. Results We found that predator–prey cycles shrank in state space from colder to hotter temperatures and that both cycle period and amplitude varied with temperature. Model parameters showed mostly unimodal responses to temperature, with one parameter (predator mortality) increasing monotonically with temperature and one parameter (predator conversion efficiency) invariant with temperature. Our results indicate that temperature can have profound, systematic effects on ecological dynamics, and these can arise through diverse and simultaneous changes in multiple underlying mechanisms. Predicting the effects of temperature on ecological dynamics may require additional investigation into how the underlying drivers of population dynamics respond to temperature beyond a short-term, acute response.

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