Global redistribution and local migration in semi-discrete host-parasitoid population dynamic models

ABSTRACTHost-parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving ordinary differential equations that mechanistically describe interactions when hosts become vulnerable to parasitoid attacks. We use this semi-discrete formalism to study two key spatial effects: local movement (migration) of parasitoids between patches during the vulnerable period; and yearly redistribution of populations across patches outside the vulnerable period. Our results show that in the absence of any redistribution, constant density-independent migration and parasitoid attack rates are unable to stabilize an otherwise unstable host-parasitoid population dynamics. Interestingly, inclusion of host redistribution (but not parasitoid redistribution) before the start of the vulnerable period can lead to stable coexistence of both species. Next, we consider a Type-III functional response (parasitoid attack rate increases with host density), where the absence of any spatial effects leads to a neutrally stable host-parasitoid equilibrium. As before, density-independent parasitoid migration by itself is again insufficient to stabilize the population dynamics and host redistribution provides a stabilizing influence. Finally, we show that a Type-III functional response combined with density-dependent parasitoid migration leads to stable coexistence, even in the absence of population redistributions. In summary, we have systematically characterized parameter regimes leading to stable/unstable population dynamics with different forms of spatial heterogeneity coupled to the parasitoid’s functional response using mechanistically formulated semi-discrete models.

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Warming can destabilise predator-prey interactions by shifting the functional response from Type III to Type II

10.1101/498030 ◽

2018 ◽

Author(s):

Uriah Daugaard ◽

Owen Petchey ◽

Frank Pennekamp

Keyword(s):

Population Dynamics ◽

Functional Response ◽

Conversion Efficiency ◽

Trophic Interactions ◽

Clearance Rate ◽

Temperature Effects ◽

Type Ii ◽

Predator Prey ◽

Type Iii ◽

Population Dynamic Model

The potential for climate change and temperature shifts to affect community stability remains relatively unknown. One mechanism by which temperature may affect stability is by altering trophic interactions. The functional response quantifies the per capita resource consumption by the consumer as a function of resource abundance and is a suitable framework for the description of nonlinear trophic interactions. We studied the effect of temperature on a ciliate predator-prey pair (Spathidium sp. and Dexiostoma campylum) by estimating warming effects on the functional response and on the associated conversion efficiency of the predator. We recorded prey and predator dynamics over 24 hours and at three temperature levels (15, 20 and 25 C). To these data we fitted a population dynamic model including the predator functional response, such that the functional response parameters (space clearance rate, handling time, and density dependence of space clearance rate) were estimated for each temperature separately. To evaluate the ecological significance of temperature effects on the functional response parameters we simulated predator-prey population dynamics. We considered the predator-prey system to be destabilised, if the prey was driven extinct by the predator. Effects of increased temperature included a transition of the functional response from a Type III to a Type II and an increase of the conversion efficiency of the predator. The simulated population dynamics showed a destabilisation of the system with warming, with greater risk of prey extinction at higher temperatures likely caused by the transition from a Type III to a Type II functional response. Warming-induced shifts from a Type III to II are not commonly considered in modelling studies that investigate how population dynamics respond to warming. Future studies should investigate the mechanism and generality of the effect we observed and simulate temperature effects in complex food webs including shifts in the type of the functional response as well as consider the possibility of a temperature dependent conversion efficiency.

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Fluctuations in population densities inform stability mechanisms in host-parasitoid interactions

10.1101/2020.12.30.424820 ◽

2021 ◽

Cited By ~ 1

Author(s):

Abhyudai Singh

Keyword(s):

Population Dynamics ◽

Population Density ◽

Functional Response ◽

Discrete Time ◽

Host Population ◽

Reproduction Rate ◽

Population Densities ◽

Type Iii ◽

Time Formalism ◽

Large Fluctuations

AbstractPopulation dynamics of host-parasitoid interactions has been traditionally studied using a discrete-time formalism starting from the classical work of Nicholson and Bailey. It is well known that differences in parasitism risk among individual hosts can stabilize the otherwise unstable equilibrium of the Nicholson-Bailey model. Here, we consider a stochastic formulation of these discrete-time models, where the host reproduction is a random variable that varies from year to year and drives fluctuations in population densities. Interestingly, our analysis reveals that there exists an optimal level of heterogeneity in parasitism risk that minimizes the extent of fluctuations in the host population density. Intuitively, low variation in parasitism risk drives large fluctuations in the host population density as the system is on the edge of stability. In contrast, high variation in parasitism risk makes the host equilibrium sensitive to the host reproduction rate, also leading to large fluctuations in the population density. Further results show that the correlation between the adult host and parasitoid densities is high for the same year, and gradually decays to zero as one considers cross-species correlations across different years. We next consider an alternative mechanism of stabilizing host-parasitoid population dynamics based on a Type III functional response, where the parasitoid attack rate accelerates with increasing host density. Intriguingly, this nonlinear functional response makes qualitatively different correlation signatures than those seen with heterogeneity in parasitism risk. In particular, a Type III functional response leads to uncorrelated adult and parasitoid densities in the same year, but high cross-species correlation across successive years. In summary, these results argue that the cross-correlation function between population densities contains signatures for uncovering mechanisms that stabilize consumer-resource population dynamics.

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Population dynamics of multi-host communities attacked by a common parasitoid

10.1101/2021.01.04.425210 ◽

2021 ◽

Author(s):

Abhyudai Singh

Keyword(s):

Population Dynamics ◽

Functional Response ◽

Host Species ◽

Attack Rate ◽

Host Density ◽

Apparent Competition ◽

Species Interaction ◽

Type I ◽

Type Iii ◽

Time Formalism

AbstractWe model population dynamics of two host species attacked by a common parasitoid using a discrete-time formalism that captures their population densities from year to year. It is well known starting from the seminal work of Nicholson and Bailey that a constant parasitoid attack rate leads to an unstable host-parasitoid interaction. However, a Type III functional response, where the parasitoid attack rate accelerates with increasing host density stabilizes the population dynamics. We first consider a scenario where both host species are attacked by a parasitoid with the same Type III functional response. Our results show that sufficient fast acceleration of the parasitoid attack rate stabilizes the population dynamics of all three species. For two symmetric host species, the extent of acceleration needed to stabilize the three-species equilibrium is exactly the same as that needed for a single host-parasitoid interaction. However, asymmetry can lead to scenarios where the removal of a host species from a stable interaction destabilizes the interaction between the remaining host species and the parasitoid. Next, we consider a situation where one of the host species is attacked at a constant rate (i.e., Type I functional response), and the other species is attacked via a Type III functional response. We identify parameter regimes where a Type III functional response to just one of the host species stabilizes the three species interaction. In summary, our results show that a generalist parasitoid with a Type III functional response to one or many host species can play a key role in stabilizing population dynamics of host-parasitoid communities in apparent competition.

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Stochasticity in host-parasitoid models informs mechanisms regulating population dynamics

Scientific Reports ◽

10.1038/s41598-021-96212-y ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Abhyudai Singh

Keyword(s):

Population Dynamics ◽

Population Density ◽

Functional Response ◽

Discrete Time ◽

Host Population ◽

Reproduction Rate ◽

Population Densities ◽

Type Iii ◽

Time Formalism ◽

Large Fluctuations

AbstractPopulation dynamics of host-parasitoid interactions have been traditionally studied using a discrete-time formalism starting from the classical work of Nicholson and Bailey. It is well known that differences in parasitism risk among individual hosts can stabilize the otherwise unstable equilibrium of the Nicholson-Bailey model. Here, we consider a stochastic formulation of these discrete-time models, where the host reproduction is a random variable that varies from year to year and drives fluctuations in population densities. Interestingly, our analysis reveals that there exists an optimal level of heterogeneity in parasitism risk that minimizes the extent of fluctuations in the host population density. Intuitively, low variation in parasitism risk drives large fluctuations in the host population density as the system is on the edge of stability. In contrast, high variation in parasitism risk makes the host equilibrium sensitive to the host reproduction rate, also leading to large fluctuations in the population density. Further results show that the correlation between the adult host and parasitoid densities is high for the same year, and gradually decays to zero as one considers cross-species correlations across different years. We next consider an alternative mechanism of stabilizing host-parasitoid population dynamics based on a Type III functional response, where the parasitoid attack rate accelerates with increasing host density. Intriguingly, this nonlinear functional response makes qualitatively different correlation signatures than those seen with heterogeneity in parasitism risk. In particular, a Type III functional response leads to uncorrelated adult and parasitoid densities in the same year, but high cross-species correlation across successive years. In summary, these results argue that the cross-correlation function between population densities contains signatures for uncovering mechanisms that stabilize consumer-resource population dynamics.

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BIFURCATION AND CHAOS IN A DISCRETE PREDATOR–PREY MODEL WITH HOLLING TYPE-III FUNCTIONAL RESPONSE AND HARVESTING EFFECT

Journal of Biological System ◽

10.1142/s021833902140009x ◽

2021 ◽

pp. 1-28

Author(s):

ANURAJ SINGH ◽

PREETI DEOLIA

Keyword(s):

Functional Response ◽

Sufficient Conditions ◽

Flip Bifurcation ◽

Bifurcation Structure ◽

Bifurcation And Chaos ◽

Predator Prey ◽

Type Iii ◽

Predator Prey Model ◽

Prey Model ◽

Wide Range

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting.

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Optimal Flow Control and Single Split Architecture Exploration for Fluid-Based Thermal Management

Volume 2A: 44th Design Automation Conference ◽

10.1115/detc2018-86148 ◽

2018 ◽

Cited By ~ 2

Author(s):

Satya R. T. Peddada ◽

Daniel R. Herber ◽

Herschel C. Pangborn ◽

Andrew G. Alleyne ◽

James T. Allison

Keyword(s):

Flow Control ◽

Thermal Management ◽

High Performance ◽

Dynamic Models ◽

Cooling System ◽

Rooted Tree ◽

Modeling Framework ◽

System Architectures ◽

Tree Graphs ◽

Heat Loads

High-performance cooling is often necessary for thermal management of high power density systems. Both human intuition and vast experience may not be adequate to identify optimal thermal management designs as systems increase in size and complexity. This paper presents a design framework supporting comprehensive exploration of a class of single phase fluid-based cooling architectures. The candidate cooling system architectures are represented using labeled rooted tree graphs. Dynamic models are automatically generated from these trees using a graph-based thermal modeling framework. Optimal performance is determined by solving an appropriate fluid flow control problem, handling temperature constraints in the presence of exogenous heat loads. Rigorous case studies are performed in simulation, with components having variable sets of heat loads and temperature constraints. Results include optimization of thermal endurance for an enumerated set of 4,051 architectures. In addition, cooling system architectures capable of steady-state operation under a given loading are identified.

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The effects of host-feeding on stability of discrete-time host–parasitoid population dynamic models

Mathematical Biosciences ◽

10.1016/j.mbs.2015.11.011 ◽

2016 ◽

Vol 272 ◽

pp. 54-63 ◽

Cited By ~ 12

Author(s):

Brooks Emerick ◽

Abhyudai Singh

Keyword(s):

Discrete Time ◽

Population Dynamic ◽

Dynamic Models ◽

Host Feeding ◽

Parasitoid Population

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Effects of buprofezin and imidacloprid on the functional response of Eretmocerus mundus Mercet

Plant Protection Science ◽

10.17221/64/2012-pps ◽

2014 ◽

Vol 50 (No. 3) ◽

pp. 145-150 ◽

Cited By ~ 7

Author(s):

F. Sohrabi ◽

P. Shishehbor ◽

M. Saber ◽

M.S. Mosaddegh

Keyword(s):

Functional Response ◽

Bemisia Tabaci ◽

Natural Enemies ◽

Attack Rate ◽

Sublethal Effects ◽

Handling Time ◽

Type Ii ◽

Type Iii ◽

Eretmocerus Mundus

Eretmocerus mundus Mercet is one of the key natural enemies of Bemisia tabaci (Gennadius). In this study, the sublethal effects of LC<sub>25</sub> of imidacloprid and field-recommended concentration of buprofezin on the functional response of E. mundus to different densities of second instar B. tabaci nymphs were evaluated. The results revealed a type III functional response in the control and imidacloprid treatment. The type III functional response was altered into a type II by buprofezin. Although imidacloprid did not alter the type of functional response of E. mundus compared to the control, it negatively affected the handling time and maximum attack rate of the parasitoid. Therefore, the use of this insecticide should be evaluated carefully in IPM programs.

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The functional and numerical responses ofTrissolcus basalis(Hymenoptera: Platygastridae) parasitizingNezara viridula(Hemiptera: Pentatomidae) eggs in the field

Bulletin of Entomological Research ◽

10.1017/s0007485313000023 ◽

2013 ◽

Vol 103 (4) ◽

pp. 441-450 ◽

Cited By ~ 4

Author(s):

G.G. Liljesthröm ◽

M.F. Cingolani ◽

J.E. Rabinovich

Keyword(s):

Functional Response ◽

Attack Rate ◽

Sex Allocation ◽

Biological Control Agent ◽

Theoretical Models ◽

Control Agent ◽

Trissolcus Basalis ◽

Main Host ◽

Absolute Density ◽

Parasitoid Population

AbstractTrissolcus basalishas been used as a biological control agent of its main host,Nezara viridula, in many countries. However, estimations of its functional and numerical responses in the field are lacking. We estimated the density ofN. viridulaeggs, the proportion of parasitizedN. viridulaeggs, and the number ofT. basalisadults/trap in the field. We transformed relative parasitoid density to an absolute density, and estimated the parasitoid's attack rate,a, and the mutual interference parameter,m, in two ways: following Arditi & Akçakaya (1990) and using the Holling–Hassell–Varley model with two iterative techniques. The attack rate estimated by both methods werea=1.097 anda=0.767, respectively. Parametermvaried less between methods:m=0.563 andm=0.586, respectively, and when used to calculate the number of parasitizedN. viridulaeggs per m2, differences with the observed values were not significant. The numerical response ofT. basaliswas affected by the sex allocation of their progeny and the proportion of adult parasitoids trapped decreased with field parasitoid population density. Theoretical models show that 0<m<1 is a stabilizing factor and previous re-analysis of field data showed a meanmvalue of 0.8. The Holling–Hassell–Varley model leads to a flexible description of the functional response allowing to predict acceptable weekly host parasitism. The pre-imaginal parasitoid survival and the change in sex ratio as a function of parasitoid density adequately describe the numerical functional response of the parasitoid.

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