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

Emerick, Brooks; Singh, Abhyudai

doi:10.1016/j.mbs.2015.11.011

Cited by 27 publications

(13 citation statements)

References 31 publications

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“…For host-parasitoid systems, two types of mathematical models have been developed, discrete models normally for systems with non-overlapping generations [11,17,33,42] and continuous models for generation-round systems [10,17,52]. Continuous models usually assume fixed development times to describe developmental stages of hosts and parasitoids.…”

Section: Model Formulationmentioning

confidence: 99%

“…Godfray and Hassell [17] discussed population cyclic behaviours of host-parasitoid interactions from the point of view of both endogenous factors in constant environment and exogenous mechanisms in varying environment. Host feeding, as a specific behaviour, has also been widely studied to recognize its dynamical effects on population development [6,11,12]. Furthermore, experimental approaches were proposed and then widely applied to the research of interactions between hosts and their parasitoids under controlled conditions in microcosm [27,40,44].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a negative binomial host–parasitoid model with two maturation delays and impulsive resource input

Huang

Liu

et al. 2019

Journal of Biological Dynamics

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To study the interaction of parasitoids and their insect hosts in laboratory environment, we propose a mathematical model incorporating impulsive resource inputs, stage-structure, maturation times and negative binomial distribution of parasitoid attacks. According to the adaptability of the insect host to the environment, we obtain conditions under which the system is uniformly permanent in two cases, which guarantee that the host and its parasitoid can coexist. By applying fixed point theory, we show existence of the positive periodic solution where the host and its parasitoid can coexist, and also obtain the conditions that ensure the existence of the parasitoidextinction periodic solution. Our numerical analysis confirms and extends our theoretical results. The simulations show that when the total amount of resource is fixed, a smaller amount of recourse inputs with a shorter period of impulsive delivery results in smaller oscillation amplitude in the insect host population. However, the development of parasitoid population is not affected by the resource management strategy. It is also demonstrated that larger maturation times, either the host's or the parasitoid's, lead to the decline of the parasitoid population. But larger parasitoid's maturation time does accelerate the host's population growth. These are helpful for us to acquire a deeper knowledge of the host-parasitoid interaction in laboratory environment.

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Section: Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of a negative binomial host–parasitoid model with two maturation delays and impulsive resource input

Huang

Liu

et al. 2019

Journal of Biological Dynamics

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“…Our aim is to formulate a general two-patch migration model using the semi-discrete modeling framework [7,30], and analyze the conditions for coexistence with respect to migration parameters. As we have seen in past models, stability of the coexistence equilibrium point usually occurs when the parasitoid is inefficient, indicating that if there is an interaction that inhibits the parasitoid's ability to oviposit then coexistence is more likely to occur.…”

Section: Introductionmentioning

confidence: 99%

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

Emerick

Singh

Chhetri

2020

Mathematical Biosciences

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Host-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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“…In order to resolve biological questions, a biological experiment must be organized, as that the results can be used to create the mathematical model, which connects the various biological variables in the study and determines the parameters relevant to the biological question . Biomathematics is thus a vital tool in the study of various biological fields, such as evolution, immunology, population studies, and areas of neuroscience …”

Section: Introductionmentioning

confidence: 99%

Mathematical equations for dental implant stability patterns during the osseointegration period, based on previous resonance frequency analysis studies

Charatchaiwanna

Rojsiraphisa

Aunmeungtong

et al. 2019

Clin Implant Dent Rel Res

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Background Total stability of dental implant can be obtained from resonance frequency analysis (RFA) device, but without primary and secondary stability values. Purpose To formulate mathematical equations for dental implant stability patterns during the osseointegration period. Materials and Methods An online systematically search of the literature between January 1996 and December 2017 was performed for all prospective clinical trials that measured implant stability using RFA device during the osseointegration period. Initial mathematical function with adjustable parameters were created. Then curve‐fitting was performed using a computerized program to formulate mathematical equations stability patterns. Results Nine publications (24 study groups) were included in the mathematical analysis. Curve fitting with low sum of squared errors could be applied in all studies, except one. The stability has been divided into high, medium, and low stability. The curve fitting showed stability dip areas and intersection point which predict the returning of the stability to reach the primary stability. The study groups with low primary stability showed the poorest results, the high and medium stability group showed the stability pattern following the assumed primary stability pattern according to the mathematic equations. Conclusions The model of primary and secondary stability could be predicted from the proposed equations.

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

Cited by 27 publications

References 31 publications

Analysis of a negative binomial host–parasitoid model with two maturation delays and impulsive resource input

Analysis of a negative binomial host–parasitoid model with two maturation delays and impulsive resource input

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

Mathematical equations for dental implant stability patterns during the osseointegration period, based on previous resonance frequency analysis studies

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