Abstract:

This dataset utilizes a two-state Markov chain discrete-time matrix model (R4.x261.000:0017) to describe the response of the population to reoccurring disturbances. Three parameters are used to describe the magnitude of impact of a disturbance, the average duration of impact of a disturbance, and the average time between disturbances, then the stochastic growth rate is approximated. This dataset uses an example population of sperm whales in the northern Gulf of Mexico and the application of the model formulation to determine how an oil spill and its parameters will affect population growth. This dataset is in support of 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. Dataset for: Examining the effect of reoccurring disturbances on population persistence with application to marine mammals. Distributed by: GRIIDC, Harte Research Institute, Texas A&M University–Corpus Christi. doi:10.7266/N75H7DVZ

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 dataset describes the three environmental parameters and approximates the population level growth rate of a sperm whale population after a single or multiple disturbances, in this case oil spills.

Data Parameters and Units:

Growth_rate_and_error_over_epsilon.xlsx: (Sheet1) epsilon (0), the stochastic growth rate calculated using equation (3.1) (Columns B-D) or through numerical simulation (Columns E-G) assuming that the time between disturbances is 40 years and the length of effect of a disturbance is 20 years (columns B, E), 40 years (columns C, F), 80 years (columns D, G). Confidence intervals for the numerical growth rate assuming that the time between disturbances is 40 years and the length of effect of a disturbance are 20 years (columns H, I), 40 years (columns J, K), 80 years (columns L, M). (Sheet2) Epsilon (0), the stochastic growth rate calculated using equation (2.6) (Columns B-D) assuming that the time between disturbances is 40 years and the length of effect of a disturbance is 20 years (columns B), 40 years (columns C), 80 years (columns D). Probability_of_extinction_1and2_events.xlsx: epsilon (0), length of effect of a disturbance (row 1), a matrix whose entries give the probability of extinction for the corresponding epsilon (0) and length of effect of a disturbance (column) when one disturbance occurs every 100 years (sheet 1) or two disturbances occur every 100 years (sheet 2). Compare_extinction_for_mulitple_epsilons.xlsx: epsilon (0), length of effect of a disturbance (row1), matrix whose entries give the probability of extinction for the multiple epsilon case minus the probability of extinction for the single epsilon case for the corresponding epsilon and length of effect of a disturbance when one disturbance occurs every 100 years and the variance in the multiple epsilon cases is approximately 20% of the mean (Sheet 1), one disturbance occurs every 100 years and the variance in the multiple epsilon cases is approximately 30% of the mean (sheet 2), two disturbances occur every 100 years and the variance in the multiple epsilon cases is approximately 20% of the mean (sheet 3), two disturbances occur every 100 years and the variance in the multiple epsilon cases is approximately 30% of the mean (sheet 4).

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