Coexistence conditions in generalized discrete-time models of insect population dynamics

Singh, Abhyudai; Emerick, Brooks

doi:10.1016/j.ecolmodel.2022.110148

Cited by 4 publications

(3 citation statements)

References 38 publications

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“…Future work will extend this study in several directions, such as incorporating a Type II functional response implemented using the semi-discrete approach, exploring how spatial effects alter the fundamental limits of biological control [61]- [65], and considering multiple parasitoid species attacking differed host stages. Related to the last point, recent work has provided novel conditions for the coexistence of multiple parasitoids on a single host [66], and in many cases the requirement (4) of adult equilibrium host density increasing with R emerges as a universal criterion for population stability in these complex ecological communities.…”

Section: Discussionmentioning

confidence: 99%

Limits of parasitoid-mediated host population density suppression: Implications for biological control

Singh

2023

Preprint

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Parasitoid wasps are increasingly being used to control insect pest populations, where the pest is the host species parasitized by the wasp. Here we use the discrete-time formalism of the Nicholson-Bailey model to investigate a fundamental question - are there limits to parasitoid-driven suppression of the host population density while still ensuring a stable coexistence of both species? Our model formulation imposes an intrinsic self-limitation in the host’s growth resulting in a carrying capacity in the absence of the parasitoid. Different versions of the model are considered with parasitism occurring at a developmental stage that is before, during, or after the growth-limiting stage. For example, the host’s growth limitation may occur at its larval stage due to intraspecific competition, while the wasps attack either the host egg, larval or pupal stage. For slow-growing hosts, models with parasitism occurring at different life stages are identical in terms of their host suppression dynamics but have contrasting differences for fast-growing hosts. In the latter case, our analysis reveals that wasp parasitism occurring after host growth limitation yields the lowest pest population density conditioned on stable host-parasitoid coexistence. For ecologically relevant parameter regimes we estimate this host suppression to be roughly 10-20% of the parasitoid-free carrying capacity. We further expand the models to consider a fraction of hosts protected from parasitism (i.e., a host refuge). Our results show that for a given host reproduction rate there exists a critical value of protected host fraction beyond which, the system dynamics are stable even for high levels of parasitism that drive the host to arbitrary low population densities. In summary, our systematic analysis sheds key insights into the combined effects of density-dependence in host growth and parasitism refuge in stabilizing the host-parasitoid population dynamics with important implications for biological control.

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Section: Discussionmentioning

confidence: 99%

Limits of parasitoid-mediated host population density suppression: Implications for biological control

Singh

2023

Preprint

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“…Future work will extend this study in several directions, such as incorporating a Type II functional response implemented using the semi-discrete approach, exploring how spatial effects alter the fundamental limits of biological control [71][72][73][74][75], and considering multiple parasitoid species attacking different host stages. Related to the last point, recent work has provided novel conditions for the coexistence of multiple parasitoids on a single host [76], and in many cases the requirement (6) of adult equilibrium host density…”

Section: Plos Onementioning

confidence: 99%

Fundamental limits of parasitoid-driven host population suppression: Implications for biological control

Singh

2023

PLoS ONE

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Parasitoid wasps are increasingly being used to control insect pest populations, where the pest is the host species parasitized by the wasp. Here we use the discrete-time formalism of the Nicholson-Bailey model to investigate a fundamental question—are there limits to parasitoid-driven suppression of the host population density while still ensuring a stable coexistence of both species? Our model formulation imposes an intrinsic self-limitation in the host’s growth resulting in a carrying capacity in the absence of the parasitoid. Different versions of the model are considered with parasitism occurring at a developmental stage that is before, during, or after the growth-limiting stage. For example, the host’s growth limitation may occur at its larval stage due to intraspecific competition, while the wasps attack either the host egg, larval or pupal stage. For slow-growing hosts, models with parasitism occurring at different life stages are identical in terms of their host suppression dynamics but have contrasting differences for fast-growing hosts. In the latter case, our analysis reveals that wasp parasitism occurring after host growth limitation yields the lowest pest population density conditioned on stable host-parasitoid coexistence. For ecologically relevant parameter regimes we estimate this host suppression to be roughly 10-20% of the parasitoid-free carrying capacity. We further expand the models to consider a fraction of hosts protected from parasitism (i.e., a host refuge). Our results show that for a given host reproduction rate there exists a critical value of protected host fraction beyond which, the system dynamics are stable even for high levels of parasitism that drive the host to arbitrary low population densities. In summary, our systematic analysis sheds key insights into the combined effects of density-dependence in host growth and parasitism refuge in stabilizing the host-parasitoid population dynamics with important implications for biological control.

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“…It is well known that this fixed point is unstable resulting in population density oscillations that increase in amplitude over time, eventually leading to parasitoid extinction [5]. A myriad of ecological mechanisms have been characterized that stabilize the hostparasitoid population dynamics including, some hosts protected from parasitism [6], host-to-host differences in susceptibility to parasitism [7]- [13], and host feeding [14]. While Type III functional responses have a stabilizing effect under specific parameter regimes [15]- [17], Type II responses are destabilizing [18], [19].…”

Section: Introductionmentioning

confidence: 99%

Linking parasitoid-driven host density suppression with density-dependence in host growth

Singh

2023

Preprint

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Leveraging the discrete-time formalism of the Nicholson-Bailey model, we investigate the ecological population dynamics of host-parasitoid interactions with an arbitrary form of density-dependence in the host growth rate, andmap out regimes allowing stable coexistence of the consumer (parasitoid) and the resource (host). If the parasitoid-free host population dynamics is stable, we provide sufficient conditions that ensure stability is maintained with the inclusion of the parasitoid irrespective of the level of parasitism. When parasitoids parasitize hosts at a constant rate, high parasitism levels are shown to always destabilize the population dynamics. This results in a limit of host suppression that we quantify using the ratio of host density (just before stability is lost for high parasitism levels) and the host's parasitoid-free carrying capacity. We systematically examine this limit for different types of intrinsic self-limitations in host growth. Our analysis shows that for both Ricker and Beverton-Holt-type host population dynamics, this parasitoid-driven host suppression limit is $33\%$ for slow-growing hosts and $10-20\%$ for fast-growing hosts. Moreover, our results reveal that these limits can be much higher for Hill-type density-dependence in host growth rate. In summary, this contribution characterizes the impact of coupling different forms of intrinsic host population dynamics with and without additional stabilizing factors (such as a fraction of hosts protected from parasitism). These results have important implications for using parasitoids as natural enemies against arthropod pest populations, and the success of such biological control is inherently tied to the form of self-limitation in host growth.

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Coexistence conditions in generalized discrete-time models of insect population dynamics

Cited by 4 publications

References 38 publications

Limits of parasitoid-mediated host population density suppression: Implications for biological control

Limits of parasitoid-mediated host population density suppression: Implications for biological control

Fundamental limits of parasitoid-driven host population suppression: Implications for biological control

Linking parasitoid-driven host density suppression with density-dependence in host growth

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