Abstract:

A discrete time matrix mathematical model was developed to study the population-level effects of a time-varying environmental disaster. A two chain Markov model includes parameters for stochastic growth rate, magnitude of impact of the environmental disaster, average duration of the impact, and average time between disasters. This model can be used to examine the sensitivity and elasticity of the growth rate with respect to the environmental parameters. Related dataset is available under GRIIDC UDI R4.x261.000:0016. This dataset supports the publication: Veprauskas, A., Ackleh, A. S., & Tang, T. (2018). Examining the effect of reoccurring disturbances on population persistence with application to marine mammals. Journal of Theoretical Biology, 455, 109–117. doi:10.1016/j.jtbi.2018.07.011

Suggested Citation:

Azmy Ackleh, Amy Veprauskas. 2018. Discrete mathematical model to study population extinction under various conditions of environmental disaster. Distributed by: GRIIDC, Harte Research Institute, Texas A&M University–Corpus Christi. doi:10.7266/N71R6P4N

Publications:

Veprauskas, A., Ackleh, A. S., & Tang, T. (2018). Examining the effect of reoccurring disturbances on population persistence with application to marine mammals. Journal of Theoretical Biology, 455, 109–117. doi:10.1016/j.jtbi.2018.07.011

Purpose:

This model can be used to examine the sensitivity and elasticity of the growth rate with respect to the environmental parameters, and was initially compiled to model sperm whale population levels after the Deepwater Horizon oil spill.

Data Parameters and Units:

numerical_stochastic_growth_rate.m: This code calculates the numerical stochastic growth rate. growth_rate_and_error_over_epsilon_eqn2_6.m: This code calculates Tuljapurkar’s approximation for the stochastic growth rate and its error. growth_rate_and_error_over_epsilon_eqn3_1.m: This code calculates the approximation given in equation (1) for the stochastic growth rate and its error. extinction_multiple_epsilons.m: gives the difference between the probability of quasi-extinction for the case of multiple possible reduction values and the probability of quasi-extinction for the case of a single reduction value. probability_extinction_1and2_events.m: gives the probability of quasi-extinction. A readme file with instructions about the model and codes has been provided with this dataset.

Individual Files: