Elsevier

Ecological Informatics

Volume 1, Issue 2, April 2006, Pages 189-193
Ecological Informatics

Full Length Article
Monte Carlo modeling of the effect of extreme events on the extinction dynamics of faunal species with 2-stage life cycles

https://doi.org/10.1016/j.ecoinf.2006.02.001Get rights and content

Abstract

Our paper computationally explores the extinction dynamics of an animal species effected by a sudden spike in mortality due to an extreme event. In our study, the animal species has a 2-stage life cycle and is endowed with a high survival probability under normal circumstances. Our proposed approach does not involve any restraining assumptions concerning environmental variables or predator–prey relationships. Rather it is based on the simple premise that if observed on an year-to-year basis, the population size will be noted to either have gone up or come down as compared to last year. The conceptualization is borrowed from the theory of asset pricing in stochastic finance. The survival probability (λ) is set at unity i.e. the model assumes that all young members of the population mature into adults capable of reproduction. As we bias our model heavily in favor of survival, the chance of the population size increasing over time is much higher than it suffering a decline, if no extreme events occur. One of the critical parameters in our simulation model is the shock size i.e. the number of immediate mortalities that may be caused by an extreme event. We run our model for two pre-selected fecundity levels denoted as “high” and “low”. Under each of the two fecundity levels one hundred independent simulation runs are conducted over a time period of ten stages (i.e. five generations) and the relevant descriptive statistics are reported for the terminal (i.e. the fifth) generation. Shock sizes are varied until at least one scenario of total extinction is observed in the simulation output. Any extinctions occurring in t0 are treated as “trivial cases” and not counted. Our results indicate that an extreme event with a minimum shock size exceeding 2 / 3 the size of the pristine population can potentially drive animal species with 2-stage life cycles to extinction for both “low” and “high” fecundity levels.

Section snippets

Background and research objective

The primal problem which proponents of population viability analysis (PVA) initially set out to solve concerned the minimum size of population of a species that is required for it to have a reasonable probability of survival over a reasonable length of time (Morris and Doak, 2002). However, animal species with no clearly observed threat to either their population size or fecundity may nevertheless become threatened with extinction within a relatively short period of time as result of a sudden,

Conceptual framework

In our present model the survival probability is purposely assigned a value of unity. This loads our model heavily in favor of survival i.e. we endow the species with a property that all the young can mature into reproductive adults with a hundred percent certainty. We do this to isolate the effect of the shock size (i.e. the number of immediate mortalities) of an extreme event on the extinction dynamics of the species. Setting λ = 1 virtually rules out natural extinction of the species.

We

Model building

It is assumed that the initial population consists of one hundred immature young. That is, in t0, there are Y0 = 100 immature young and A0 = 0 mature adults. In the next year i.e. t1, there will be A1 = 100 mature adults (assuming λ = 1) and these will in turn become a new breed of immature young produce f(At) before themselves dying out by end of the year.

On lines of a derivative asset pricing problem we perceive that Yt+1 = f(At) can either go up or come down at each sample point (year); similar to the

Analysis of simulation results and future research directions

One hundred independent simulation runs are conducted under each of the two fecundity levels and sample means and standard deviations are reported for the terminal Y values. Summarized graphical results of the simulation are given in the Appendix. All the outputs show high negative skewness and high kurtosis. The negative skewness is of course engineered by the nature of the simulation process itself; in order to reflect the element of “unpleasant surprise” associated with an extreme event. The

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