The effects of seasonality on discrete models of population growth

Kot, Mark; Schaffer, William M.

doi:10.1016/0040-5809(84)90038-8

Cited by 83 publications

(58 citation statements)

References 25 publications

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“…We note that mortality is usually a continuous-time process whereas reproduction often occurs during a discrete breeding season, although the reproductive rate may depend on conditions prior to the reproductive season Tate 1982, Albon et al 1983). An alternative approach is to use difference equations in discrete time (Kot andSchaffer 1984, ~s t r o m et al 1996). To demonstrate how seasonality can result in compensation, we will use a discretetime approach.…”

Section: Seasonally Explicit Modelsmentioning

confidence: 99%

“…The reason for the apparent contradiction is the fact that most population models ignore the details of annual seasonality. Seasonality can complicate the dynamics of population models and can yield dynamical behaviours that may not emerge from models that do not incorporate seasonality (Kot and Schaffer 1984, Batzli 1999, Jonzen and Lundberg 1999. We explain how seasonality in density dependence is one mechanism that underlies compensatory mortality and natality.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Seasonal Compensation of Predation and Harvesting

Boyce¹,

Sinclair²,

White³

1999

Oikos

226

216

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Section: Seasonally Explicit Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Seasonal Compensation of Predation and Harvesting

Boyce¹,

Sinclair²,

White³

1999

Oikos

226

216

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“…This is not the first contribution on periodically forced ecosystems. Discrete-time models (maps), in which the unit time step coincides with the period of the forcing function, have been used to show that quasi-periodic and chaotic solutions are possible in population dynamics (see, for example, May, 1974;Kot and Schaffer, 1984;Lauwerier and Metz, 1986). Models of this kind are very easy to handle and can give rise to spectacular dynamics, in particular when the map is non-invertible as in the famous case of seasonally breeding organisms with nonoverlapping generations (May, 1974).…”

Section: Introductionmentioning

confidence: 99%

Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities

Rinaldi

Muratori

Kuznetsov

1993

Bulletin of Mathematical Biology

139

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ForewordThis paper presents the analysis of a periodically fbrced second order nonlinear dynamical system describing predator-prey communities. Six different seasonality mechanisms are identified and compared in terms of bifurcation diagrams. The analysis is carried out by means of an interactive package which detects Hopf, flip and fold bifurcations curves as well as codimension two bifurcation points. The results are in agreement with the general theory of periodically perturbed Hopf bifurcations. This work shows that complex environmental issues can be highlighted by suitably combining basic results of nonlinear system theory and powerful numerical techniques. Moreover, the two classical routes to chaos, namely, torus destruction and cascade of period doublings, are numerically detected. Since in the case of constant parameters the model cannot have multiple attractors, catastrophes, and chaos, the results support the conjecture that seasons can very easily give rise to complex population dynamics.

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“…Although traditional population models often ignore seasonality [5,6], theoretical and empirical work suggest that seasonality can have important consequences for the dynamics of populations, e.g. by either stabilizing or destabilizing population fluctuation [3,[7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Carry-over effects, sequential density dependence and the dynamics of populations in a seasonal environment

2013

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Most animal populations have distinct breeding and non-breeding periods, yet the implications of seasonality on population dynamics are not well understood. Here, we introduce an experimental model system to study the population dynamics of two important consequences of seasonality: sequential density dependence and carry-over effects (COEs). Using a replicated seasonal population of Drosophila, we placed individuals at four densities in the non-breeding season and then, among those that survived, placed them to breed at three different densities. We show that COEs arising from variation in non-breeding density negatively impacts individual performance by reducing per capita breeding output by 29 -77%, implying that non-lethal COEs can have a strong influence on population abundance. We then parametrized a bi-seasonal population model from the experimental results, and show that both sequential density dependence and COEs can stabilize long-term population dynamics and that COEs can reduce population size at low intrinsic rates of growth. Our results have important implications for predicting the successful colonization of new habitats, and for understanding the long-term persistence of seasonal populations in a wide range of taxa, including migratory organisms.

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The effects of seasonality on discrete models of population growth

Cited by 83 publications

References 25 publications

Seasonal Compensation of Predation and Harvesting

Seasonal Compensation of Predation and Harvesting

Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities

Carry-over effects, sequential density dependence and the dynamics of populations in a seasonal environment

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