Calculating effective growth rate from a random Leslie model: Application to incidental mortality analysis

• Published in: Ecological modelling Vol. 251; pp. 312 - 322
• Main Authors: CACERES, Manuel O, CACERES-SAEZ, Iris
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 24.02.2013; Elsevier
• Subjects: age structure; algorithms; Animal and plant ecology; Animal, plant and microbial ecology; anthropogenic activities; Biological and medical sciences; bycatch; Cetacean population dynamics; Demecology; Effective growth rate; evolution; Fundamental and applied biological sciences. Psychology; General aspects; General aspects. Techniques; Harbor porpoise; Mammalia; Methods and techniques (sampling, tagging, trapping, modelling...); mortality; Phocoena phocoena; pollution; population growth; population size; Random Leslie matrix; threatened species; Uncertainty; Vertebrates: general zoology, morphology, phylogeny, systematics, cytogenetics, geographical distribution; viability; Cetacean population dynamics; Uncertainty; Random Leslie matrix; Effective growth rate; Harbor porpoise; Growth rate; Mortality; Phocoena phocoena; Vertebrata; Mammalia; Population dynamics; Models; Cetacea
• DOI: 10.1016/j.ecolmodel.2012.12.021
• ISSN: 0304-3800

[Display omitted] ► We present an algorithm to tackle random survival models in a Leslie matrix dynamics. ► We exemplify the method using a random incidental mortality population growth model. ► We define an effective growth rate taking into account the time evolution of an age structured population. ► A mathematical approach has been presented to calculate, by random perturbation, the growth of the mean-value vector population dynamics. Demographic models are commonly used to study cetacean population dynamics and are characterized by a wide range of age classes. The primary building blocks are age-specific survival or mortality and birth rates, which can be combined using a Leslie matrix protocol to provide estimates of maximum possible rates of increase for population size. In this context, specific mortality data are valuable for modeling the viability of threatened species. Depletion of prey, pollution, and other anthropogenic disturbances are believed to have contributed to the decline of populations, but the evidence is less conclusive for these factors than for bycatch. In an attempt to estimate a population growth rate that incorporates uncertainties in vital parameters, we apply a random Leslie analysis to calculate effective growth rate for the time-dependent mean-value population. Here we provide the algorithm to implement it for a general 13×13 random survival model. An effective growth rate can be characterized by studying the time evolution of the mean-value population vector state (in an age-structured description). We show that the asymptotic behavior of the mean-value vector state, which characterizes the population growth rate when the model has random vital parameters, exhibits a value that is below previously expected potential estimations. We demonstrate the procedure using bibliographic revision data of the harbor porpoise (Phocoena phocoena) in Canadian waters, subjected to incidental mortality.