Predicting Extinction: Progress with an Individual-Based Model of Protozoan Predators and Prey

Holyoak, Marcel; Lawler, Sharon P.; Crowley, Philip H.

doi:10.2307/177496

Cited by 3 publications

(8 citation statements)

References 61 publications

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“…The experiment continued for 21 days, by which time food webs in undivided 270 mL volumes had collapsed to just C. striatum and bacteria, or these species with B. americanum. These species combinations are capable of persisting for long periods, even in small undivided habitats (Holyoak & Lawler 1996b; Morin 1999; Holyoak et al . 2000).…”

Section: Methodsmentioning

confidence: 99%

“…The interpretation of zero densities is complicated by the fact that zero density values from subsamples have a certain probability of representing a real extinction from an entire 30 mL bottle (a patch). In an earlier experiment, the probability of a single recorded zero density value representing a real extinction was 0.39, which was calculated by comparing subsamples with entire bottle contents (Holyoak, in press). For simplicity, the raw numbers of recorded zero densities for C. striatum (in Table 1) were used as an indicator of the frequency of actual extinction within array bottles and the duration of periods of absence.…”

Section: Methodsmentioning

confidence: 99%

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Habitat subdivision causes changes in food web structure

Holyoak¹

2000

Ecology Letters

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Theory suggests that the response of communities to habitat subdivision depends on both species' characteristics and the extent to which species interact. For species with dynamics that are independent of other species, subdivision is expected to promote regional extinction as populations become small and isolated. By contrast, intermediate levels of subdivision can facilitate persistence of strongly interacting species. Consistent with this prediction, experimental subdivision lengthened persistence of some species, altering the extent of food web collapse through extinction. Extended persistence was associated with immigration rescuing a basal prey species from local extinction. As predicted by food web theory, habitat subdivision reduced population density of a top predator. Removal of this top predator from undivided microcosms increased the abundance of two other predator species, and these changes paralleled those produced by habitat subdivision. These results show that species interactions structured this community, and illustrate the need for investigations of other communities.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Habitat subdivision causes changes in food web structure

Holyoak¹

2000

Ecology Letters

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“…The precise time of population extinction is invariably unpredictable due to the contributions of demographic stochasticity (MacArthur and Wilson 1967, Richter-Dyn and Goel 1972, Melbourne and Hastings 2008, environmental catastrophe (Lande 1993, Casagrandi andGatto 2002) and interspecific interactions (Chesson and Ellner 1989, Holyoak et al 2000, Tilman 2004, Ferguson and Ponciano 2014 to the final stages of decline. Accordingly, the majority of dynamical models used to study extinction are stochastic with the consequence that the extinction time is a random variable.…”

Section: Introductionmentioning

confidence: 99%

“…Previous theoretical work has examined stochastic extinction for predator-prey systems (Donalson and Nisbet 1999, Holyoak et al 2000, Grasman 2001, Sabo 2005, Kramer and Drake 2010 and Lotka-Volterra models of competition (Allen 1983, Renshaw 1993, Roeger and Allen 2004, Chan and Franke 2004, Baxter et al 2005, Fiasconaro and Spagnolo 2007. Studies of predator-prey systems make it clear that details of the interaction mechanism, such as predator functional response during hunting, may have a large effect on extinction probability (Kramer and Drake 2010).…”

Section: Introductionmentioning

confidence: 99%

Time to competitive exclusion

Kramer

Drake

2014

Ecosphere

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Abstract. A predictive theory of population extinction for natural populations requires integrating the effects of stochasticity with the interactions engaged in with populations of other species. The theory of competitive exclusion predicts that inferior competitors for a limiting resource will be driven to extinction, but the effects of resource competition on time to extinction have not been examined. We studied a stochastic version of Tilman's resource competition model to examine two species competition-driven extinction. Simulations showed that competitive imbalance, population size and demographic rates of the ''inferior'' competitor were the most important determinants of mean extinction time, while factors including resource supply and nutrient uptake had negligible influence. However, when competitors were more evenly matched and had small initial population sizes the ''superior'' competitor often went extinct. In these cases the distribution of extinction times shifted from the familiar exponential tail towards a heavytailed distribution with characteristically longer extinction times that may be indicative of the transition between exclusion and coexistence. These results provide new insight into the quantitative effects of competition and demographic stochasticity on extinction risk. Further work is needed to understand how extinction of superior competitors affects coexistence and extinction in natural communities.

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“…Holyoak et al. () argues that “with cyclical dynamics, the timing and likelihood of extinction may be [amongst others] a function of the density cycles”.…”

Section: Methodsmentioning

confidence: 99%

Viability of cyclic populations

Singer

Frank

2016

Ecology

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Theory on viability of small populations is well developed and has led to the standard methodology of population viability analysis (PVA) to assess vulnerability of single species. However, more complex situations involving community dynamics or environmental change violate theoretical assumptions. Synthesizing concepts from population, community, and conservation ecology, we develop a generic theory on the viability of cyclic populations. The interplay of periodic population decline and demography causes varying risk patterns that aggregate during cycles and modify the temporal structure of viability. This variability is visualized and quantitatively assessed. For two standard viability metrics that summarize immediate extinction risk and the general long-term conditions of populations, we mathematically describe the impact of population cycles. Finally, we suggest and demonstrate PVA for cyclic populations that respond to, e.g., seasonality, interannual variation, or trophic interactions. Our theoretical and methodological advancement opens a route to viability analysis in food webs and trophic meta-communities and equips biodiversity conservation with a long-missing tool.

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Predicting Extinction: Progress with an Individual-Based Model of Protozoan Predators and Prey

Cited by 3 publications

References 61 publications

Habitat subdivision causes changes in food web structure

Habitat subdivision causes changes in food web structure

Time to competitive exclusion

Viability of cyclic populations

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