Analysis of lethal and sublethal impacts of environmental disasters on sperm whales using stochastic modeling

Azmy S Ackleh,Baoling Ma,Hal Caswell,Tingting Tang,Natalia Sidorovskaia,Amy Veprauskas,Ross A Chiquet

doi:10.1007/s10646-017-1813-4

Abstract

Mathematical models are essential for combining data from multiple sources to quantify population endpoints. This is especially true for species, such as marine mammals, for which data on vital rates are difficult to obtain. Since the effects of an environmental disaster are not fixed, we develop time-varying (nonautonomous) matrix population models that account for the eventual recovery of the environment to the pre-disaster state. We use these models to investigate how lethal and sublethal impacts (in the form of reductions in the survival and fecundity, respectively) affect the population’s recovery process. We explore two scenarios of the environmental recovery process and include the effect of demographic stochasticity. Our results provide insights into the relationship between the magnitude of the disaster, the duration of the disaster, and the probability that the population recovers to pre-disaster levels or a biologically relevant threshold level. To illustrate this modeling methodology, we provide an application to a sperm whale population. This application was motivated by the 2010 Deepwater Horizon oil rig explosion in the Gulf of Mexico that has impacted a wide variety of species populations including oysters, fish, corals, and whales.

Highlights

A disturbance, natural or anthropogenic, that causes a sufficiently great reduction in the vital rates will cause a growing population to decline
The eventual impact of an environmental disaster, such as the Deepwater Horizon (DWH) oil spill, on a population depends on the recovery of the environment to pre-event conditions, how the environmental recovery affects the vital rates, and how the changes in vital rates translate into population growth
We use stochastic analysis to analyze the population recovery process during environmental recovery from a perturbation. Though we present this analysis using the sperm whale model described by model (1)–(2) and the environmental recovery processes given by Eq (3), this analysis is general enough to be applied to other population models and recovery functions

Summary

Introduction

A disturbance, natural or anthropogenic, that causes a sufficiently great reduction in the vital rates will cause a growing population to decline. The environmental recovery process appears in the matrix population model in the form of a time course of reductions in survival rates or fecundity These reductions are assumed to represent the lethal and sublethal impacts of a disturbance, respectively. The eventual impact of an environmental disaster, such as the DWH oil spill, on a population depends on the recovery of the environment to pre-event conditions (or, as close as it may come to recovery), how the environmental recovery affects the vital rates, and how the changes in vital rates translate into population growth To analyze this process, the parameters in the projection matrix that describes the population become functions of time, depending on the scenario for environmental recovery. The recovery time is more sensitive to ε0 when TCritical is large This means that when lethal effects impact the population for a long time period, a small change in the proportional reduction on survival rates results in a large change in the population dynamics. This corresponds to the well known pattern for other long-lived species (Heppell et al 2000)

Discussion

Findings

Compliance with ethical standards