Baoling Ma

Assessing the Deepwater Horizon oil spill impact on marine mammal population through acoustics: Endangered sperm whales

Long-term monitoring of endangered species abundance based on acoustic recordings has not yet been pursued. This paper reports the first attempt to use multi-year passive acoustic data to study the impact of the Deepwater Horizon oil spill on the population of endangered sperm whales. Prior to the spill the Littoral Acoustic Demonstration Center (LADC) collected acoustic recordings near the spill site in 2007. These baseline data now provide a unique opportunity to better understand how the oil spill affected marine mammals in the Gulf of Mexico. In September 2010, LADC redeployed recording buoys at previously used locations 9, 25, and 50 miles away from the incident site. A statistical methodology that provides point and interval estimates of the abundance of the sperm whale population at the two nearest sites is presented. A comparison of the 2007 and the 2010 recordings shows a decrease in acoustic activity and abundance of sperm whales at the 9-mile site by a factor of 2, whereas acoustic activity and abundance at the 25-mile site has clearly increased. This indicates that some sperm whales may have relocated farther away from the spill. Follow-up experiments will be important for understanding long-term impact.

A Second-Order High-Resolution Scheme for a Juvenile-Adult Model of Amphibians

In this article we consider a juvenile-adult population model of amphibians in which juveniles are structured by age and adults are structured by size. We develop a second-order explicit high-resolution scheme to approximate the solution of the model. Convergence of the finite difference approximation to the unique weak solution with bounded total variation is proved. Numerical examples demonstrate the high-resolution property and the achievement of the designed accuracy for the scheme. The scheme is then applied to understand the dynamics of an urban amphibian population.

A second-order high resolution finite difference scheme for a structured erythropoiesis model subject to malaria infection.

We develop a second-order high-resolution finite difference scheme to approximate the solution of a mathematical model describing the within-host dynamics of malaria infection. The model consists of two nonlinear partial differential equations coupled with three nonlinear ordinary differential equations. Convergence of the numerical method to the unique weak solution with bounded total variation is proved. Numerical simulations demonstrating the achievement of the designed accuracy are presented.

Finite difference approximations for a size-structured population model with distributed states in the recruitment

We consider a size-structured population model where individuals may be recruited into the population at different sizes. First- and second-order finite difference schemes are developed to approximate the solution of the model. The convergence of the approximations to a unique weak solution is proved. We then show that as the distribution of the new recruits become concentrated at the smallest size, the weak solution of the distributed states-at-birth model converges to the weak solution of the classical Gurtin–McCamy-type size-structured model in the weak* topology. Numerical simulations are provided to demonstrate the achievement of the desired accuracy of the two methods for smooth solutions as well as the superior performance of the second-order method in resolving solution-discontinuities. Finally, we provide an example where supercritical Hopf-bifurcation occurs in the limiting single state-at-birth model and we apply the second-order numerical scheme to show that such bifurcation also occurs in the distributed model.

Persistence and global stability in a selection–mutation size-structured model

We analyse a selection–mutation size-structured model with n ecotypes competing for common resources. Uniform persistence and robust uniform persistence are established, when the selection–mutation matrix Γ is irreducible, i.e. individuals of one ecotype may contribute directly or indirectly to individuals of other ecotypes. Similar results are also presented for a particular reducible form of Γ. In the case of pure selection in which the offspring of one ecotype belong to the same ecotype, i.e. Γ=I, the identity matrix, we prove that the boundary equilibrium that describes competitive exclusion, with the fittest being the winner ecotype, is globally asymptotically stable. We show that small perturbations of the pure selection matrix lead to the existence of globally asymptotically stable interior equilibria. For the case when the selection–mutation matrix is reducible, we present and discuss the outcome of a series of numerical simulations.

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

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.

Modeling as a complementary tool to acoustic data for understanding the impact of environmental disasters on marine mammals

This study is focused on how environmental disasters, such as the Deepwater Horizon oil rig explosion in 2010, affect the dynamics of marine mammal populations, particularly sperm whales and beaked whales, in the Northern Gulf of Mexico. We briefly describe how modeling techniques are used to estimate densities of marine mammals using passive acoustic data. We then develop a matrix model to examine the possible long-term effects of a disaster. We consider cases in which the effects of a disturbance result in reductions in either survival (lethal impacts) or fecundity (sublethal impacts). This model, combined with demographic stochasticity, allows us to study the long-term recovery process following an environmental disaster. In particular, recovery probabilities and recovery times of the population are computed, and formulas are derived to compute the sensitivity of the recovery time to changes in properties of the population or the environmental disturbance. We then extend the modeling methodology to con...

Environmental Acoustic Recording System (EARS) in the Gulf of Mexico

The Littoral Acoustic Demonstration Center (LADC) was formed in early 2001 to utilize Environmental Acoustic Recording System (EARS) buoys developed by the Naval Oceanographic Office (NAVOCEANO) which has provided technical guidance and support to LADC. The purpose of LADC is to make environmental measurements, which is not part of the mission of NAVOCEANO. This chapter describes the Gulf of Mexico marine mammal measurements and related data analysis of LADC. LADC has also used the buoys to characterize the three-dimensional acoustic field of a seismic airgun array and to analyze the noise due to nearby storms. LADC is a consortium of scientists from universities and the U.S. Navy. The following institutions are or have been represented: initially, the University of New Orleans, the University of Southern Mississippi, and the Naval Research Laboratory-Stennis Space Center; and then the University of Louisiana at Lafayette, the Applied Research Laboratories at the University of Texas at Austin, and Oregon State University. The scientists are listed in the first section of the chapter. A technical overview of EARS technology is given in Sect. 6.2. The current Generation 2 EARS buoys can record four channels of up to 25 kHz each or one channel up to 96 kHz.

Passive Acoustic Monitoring of the Environmental Impact of Oil Exploration on Marine Mammals in the Gulf of Mexico

The Gulf of Mexico is a region densely populated by marine mammals that must adapt to living in a highly active industrial environment. This paper presents a new approach to quantifying the anthropogenic impact on the marine mammal population. The results for sperm and beaked whales of a case study of regional population dynamics trends after the Deepwater Horizon oil spill, derived from passive acoustic-monitoring data gathered before and after the spill in the vicinity of the accident, are presented.

Parameter Estimation in a Size-Structured Population Model with Distributed States-at-Birth

A least-squares method is developed for estimating parameters in a size-structured population model with distributed states-at-birth from field data. First and second order finite difference schemes for approximating the nonlinear-nonlocal partial differential equation model are utilized in the least-squares problem. Convergence results for the computed parameters are established. Numerical results demonstrating the efficiency of the technique are provided.