Reply from A.A. Berryman and J.A. Millstein

Berryman, Alan A.; Millstein, Jeffrey A.

doi:10.1016/0169-5347(89)90169-9

Cited by 7 publications

(8 citation statements)

References 20 publications

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“…Thus, a moderately abundant species with variable numbers may be at greater risk than a rare species with small but steadier numbers. Our results do corroborate the studies on natural populations (7,17,27,28) to show that the risk of extinction increases with high variability coupled to a small minimum but argues against the notion, based on field data (7,8), that chaotic dynamics is unrealistic. To explain the stable growth dynamics attributed to a large number of insect populations (5,7,29), theoretical studies have shown that the chaotic dynamics exhibited by model populations can be suppressed under many different ecological conditions (5,(9)(10)(11)(12).…”

Section: Temporal Dynamics Under Emigrationsupporting

confidence: 80%

“…Though unstable dynamics such as chaos has been exhibited by both discrete theoretical models of population growth and experimental data (1-6), populations undergoing chaotic oscillations are assumed to run a high risk of extinction due to large variations and low-minimum population size. This and insect field data (7,8) has led to the view that chaotic oscillations are unrealistic and hence are likely to be selected against during evolution. It has been shown that common ecological processes, such as immigration, tend to stabilize chaotic oscillations or reestablish the population (5,(9)(10)(11)(12), thereby suppressing unstable growth dynamics.…”

mentioning

confidence: 99%

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Unusual dynamics of extinction in a simple ecological model.

Sinha

Parthasarathy

1996

Proc. Natl. Acad. Sci. U.S.A.

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In addition, the persistence of populations at high depletion rates has important implications in the considerations of strategies for the management of biological resources.The spatiotemporal organization of a single-species population can show many different dynamics that can change because of migration. Though unstable dynamics such as chaos has been exhibited by both discrete theoretical models of population growth and experimental data (1-6), populations undergoing chaotic oscillations are assumed to run a high risk of extinction due to large variations and low-minimum population size. This and insect field data (7, 8) has led to the view that chaotic oscillations are unrealistic and hence are likely to be selected against during evolution. It has been shown that common ecological processes, such as immigration, tend to stabilize chaotic oscillations or reestablish the population (5, 9-12), thereby suppressing unstable growth dynamics. It is also intuitively apparent and generally borne out by data that emigration or increased depletion and harvesting from a population can cause population extinction, especially if the population size is small (9, 13-15). Models of population growth have been used for predicting optimal use of natural biological resources and deciding on harvesting strategies for the maximum sustainable yield from resources such as fisheries (15, 16). However, both natural and laboratory data have always had cases where populations continue to persist in small numbers without going extinct and where some species of large population size go rapidly extinct (7,(17)(18)(19)(20); the data in ref. 17 on the small populations of five species of birds that never went extinct irrespective of body sizes needs to be noted.). Therefore, the nonlinear interaction of growth rates, population size, and rates of migration (i.e., addition and depletion to populations) is important for an understanding of population behavior, especially the "fourth regime"-i.e., extinction (4).In this study with a common discrete population growth model, which is widely used for modeling population growth and harvesting strategies, we show that (i) populations under- [1] where Xi is the population density in the ith generation and R is the intrinsic growth rate. When such a population undergoes a constant (L) amount of emigration, depletion, or harvesting regularly at every generation, the growth equation (Eq. 1) takes the form,Eq. 1 has been studied extensively (3) and is considered to be a simple model for illustrating the occurrence of chaotic oscillations in one-dimensional maps, where increasing R induces period-doubling bifurcations leading to chaos. Eq. 1 possesses one equilibrium point, and the stability of the fixed point and the consequent dynamics exhibited by the system are dependent on R alone. Inclusion of a constant immigration term in this model has been shown (11) to reduce the occurrence of chaos at higher growth rates. When considering populations undergoing a constant emigration at every generat...

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Section: Temporal Dynamics Under Emigrationsupporting

confidence: 80%

mentioning

confidence: 99%

Unusual dynamics of extinction in a simple ecological model.

Sinha

Parthasarathy

1996

Proc. Natl. Acad. Sci. U.S.A.

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“…This demonstrates a potential route to chaos for this predator-prey system dependent on the relationship between predator and prey density. The role of density-dependence in ecological chaos and in population stability and robustness has been widely supported in theory and simulation [15,17,32]. This behaviour may also represent an adaptive form of the Paradox of Enrichment presented in a highly controversial and influential paper by Rossenzweig [53] in which de-stabilization of both populations can result from lowering the resource restrictions on prey.…”

Section: Dimensionality and Chaosmentioning

confidence: 93%

“…The model is also partially motivated by recognising the role played by density-dependence in both stochastic and dynamical complex behaviour in ecology (e.g. in inducing population level chaos in classical ecological models [17]). However, density considerations only describe the frequency, not the strength or type of individual interactions between members of two species.…”

Section: Model Justification and Formulationmentioning

confidence: 99%

“…Since then, a vast array of models have been produced in an attempt to characterise the most important elements of the erratic ecological time series and to ascertain the deterministic or stochastic nature of these complex signals [16][17][18][19]. Decades later debate still rages as to the very definition of chaos and noise in ecol-ogy [20,21], however much work has been done to suggest that explaining factors such as density dependence and persistent long-term autocorrelation will be necessary to produce a complete description of ecological dynamics [22,23].…”

Section: Introductionmentioning

confidence: 99%

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Evolutionary fields can explain patterns of high-dimensional complexity in ecology

2017

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One of the properties that make ecological systems so unique is the range of complex behavioural patterns that can be exhibited by even the simplest communities with only a few species. Much of this complexity is commonly attributed to stochastic factors which have very high-degrees of freedom. Orthodox study of the evolution of these simple networks has generally been limited in its ability to explain complexity, since it restricts evolutionary adaptation to an inertia-free process with few degrees of freedom in which only gradual, moderately complex behaviours are possible. We propose a model inspired by particle mediated field phenomena in classical physics in combination with fundamental concepts in adaptation, that suggests that small but high-dimensional chaotic dynamics near to the adaptive trait optimum could help explain complex properties shared by most ecological datasets, such as aperiodicity and pink, fractal noise spectra. By examining a simple predator-prey model and appealing to real ecological data, we show that this type of complexity could be easily confused for or confounded by stochasticity, especially when spurred on or amplified by stochastic factors that share variational and spectral properties with the underlying dynamics.

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Food web structure and the evolution of ecological communities

Quince

Higgs

McKane

Biological Evolution and Statistical Physics

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Simulations of the coevolution of many interacting species are performed using the Webworld model. The model has a realistic set of predator-prey equations that describe the population dynamics of the species for any structure of the food web. The equations account for competition between species for the same resources, and for the diet choice of predators between alternative prey according to an evolutionarily stable strategy. The set of species present undergoes long-term evolution due to speciation and extinction events. We summarize results obtained on the macro-evolutionary dynamics of speciations and extinctions, and on the statistical properties of the food webs that are generated by the model. Simulations begin from small numbers of species and build up to larger webs with relatively constant species number on average. The rate of origination and extinction of species are relatively high, but remain roughly balanced throughout the simulations. When a 'parent' species undergoes speciation, the 'child' species usually adds to the same trophic level as the parent. The chance of the child species surviving is significantly higher if the parent is on the second or third trophic level than if it is on the first level, most likely due to a wider choice of possible prey for species on higher levels. Addition of a new species sometimes causes extinction of existing species. The parent species has a high probability of extinction because it has strong competition with the new species. Non-parental competitors of the new species also have a significantly higher extinction probability than average, as do prey of the new species. Predators of the new species are less likely than average to become extinct.

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Reply from A.A. Berryman and J.A. Millstein

Cited by 7 publications

References 20 publications

Unusual dynamics of extinction in a simple ecological model.

Unusual dynamics of extinction in a simple ecological model.

Evolutionary fields can explain patterns of high-dimensional complexity in ecology

Food web structure and the evolution of ecological communities

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