Azmy S. Ackleh

Giant panda (Ailuropoda melanoleuca) population dynamics and bamboo (subfamily Bambusoideae) life history: a structured population approach to examining carrying capacity when the prey are semelparous

The giant panda, Ailuropoda melanoleuca, is a highly specialized Ursid whose diet consists almost entirely of various species of bamboo. Bamboo (Bambusoideae) is a grass subfamily whose species often exhibit synchronous semelparity. Synchronous semelparity can create local drops in carrying capacity for the panda. We modeled the interaction of pandas and their bamboo food resources with an age structured panda population model linked to a natural history model of bamboo biomass dynamics based on literature values of bamboo biomass, and giant panda life history dynamics. This paper reports the results of our examination of the interaction between pandas and their bamboo food resource and its implications for panda conservation. In the model all panda populations were well below the carrying capacity of the habitat. The giant panda populations growth was most sensitive to changes in birth rates and removal of reproductive aged individuals. Periodic starvation that has been documented in conjunction with bamboo die-offs is probably related to the inability to move to other areas within the region where bamboo is still available. Based on the results of this model, giant panda conservation should concentrate on keeping breeding individuals in the wild, keep corridors to different bamboo species open to pandas, and to concentrate research on bamboo life history.

A finite difference approximation for a coupled system of nonlinear size-structured populations

Abstract : We study a quasilinear nonlocal hyperbolic initial-boundary value problem that models the evolution of N size-structured subpopulations competing for common resources. We develop an implicit finite difference scheme to approximate the solution of this model. The convergence of this approximation to a unique bounded variation weak solution is obtained. The numerical results for a special case of this model suggest that when subpopulations are closed under reproduction, one subpopulation survives and the others go to extinction. Moreover, in the case of open reproduction, survival of more than one population is possible.

Invasion, disturbance, and competition: modeling the fate of coastal plant populations.

Wetland habitats are besieged by biotic and abiotic disturbances such as invasive species, hurricanes, habitat fragmentation, and salinization. Predicting how these factors will alter local population dynamics and community structure is a monumental challenge. By examining ecologically similar congeners, such as Iris hexagona and I. pseudacorus (which reproduce clonally and sexually and tolerate a wide range of environmental conditions), one can identify life-history traits that are most influential to population growth and viability. We combined empirical data and stage-structured matrix models to investigate the demographic responses of native (I. hexagona) and invasive (I. pseudacorus) plant populations to hurricanes and salinity stress in freshwater and brackish wetlands. In our models I. hexagona and I. pseudacorus responded differently to salinity stress, and species coexistence was rare. In 82% of computer simulations of freshwater marsh, invasive iris populations excluded the native species within 50 years, whereas native populations excluded the invasive species in 99% of the simulations in brackish marsh. The occurrence of hurricanes allowed the species to coexist, and species persistence was determined by the length of time it took the ecosystem to recover. Rapid recovery (2 years) favored the invasive species, whereas gradual recovery (30 years) favored the native species. Little is known about the effects of hurricanes on competitive interactions between native and invasive plant species in marsh ecosystems. Our models contribute new insight into the relationship between environmental disturbance and invasion and demonstrate how influential abiotic factors such as climate change will be in determining interspecific interactions.

SURVIVAL OF THE FITTEST IN A GENERALIZED LOGISTIC MODEL

In this paper we discuss the asymptotic behavior of a logistic model with distributed growth and mortality rates. In particular, we prove that the entire population becomes concentrated within the subpopulation with highest growth to mortality ratio, and converges to the equilibrium defined by this ratio. Finally, we present a numerical example illustrating the theoretical results.

Parameter estimation in a structured algal coagulation-fragmentation model

Coagulation of phytoplankton is a fundamental mechanism for vertical ux of carbon in the ocean. This process is dependent on parameters that are not available from experimental data, such as the encounter rate of particles, the contact eeciency of unlike particles and the probability of sticking upon contact. Fragmentation, the breakup of large particles into two smaller ones has been observed in the ocean, but very little modeling eeort for incorporating this process in the dynamics of phytoplankton has been attempted. In this paper we incorporate fragmentation process into a nonlinear hyperbolic equation that describes the evolution of a size struc-tured algal population with the aggregation model. We examine through numerical simulation the eeect of fragmentation on the dynamics of phyto-plankton. We present convergence theory for estimating parameters in this model using nonlinear least squares t. The least square method is then tested numerically in ideal cases where the data is the model output with some added noise.

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 NONAUTONOMOUS JUVENILE-ADULT MODEL: WELL-POSEDNESS AND LONG-TIME BEHAVIOR VIA A COMPARISON PRINCIPLE ∗

A nonautonomous nonlinear continuous juvenile-adult model where juveniles and adults depend on different resources is developed. It is assumed that juveniles are structured by age, while adults are structured by size. Existence-uniqueness results are proved using the monotone method based on a comparison principle established in this paper. Conditions on the model parameters that lead to extinction or persistence of the population are obtained via the upper-lower solution technique.

Classical and Modern Numerical Analysis: Theory, Methods and Practice

Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis. The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB code will be available on the CRC Press website to illustrate various concepts.

Population Estimates of Hyla cinerea (Schneider) (Green Tree Frog) in an Urban Environment

Abstract Hyla cinerea (Green Treefrog) is a common wetlands species in the southeastern US. To better understand its population dynamics, we followed a relatively isolated population of Green Treefrogs from June 2004 through October 2004 at a federal office complex in Lafayette, LA. Weekly, Green Treefrogs were caught, measured, marked with VIE tags, and released. The data were used to estimate population size. The time frame was split into two periods: before and after August 17, 2004. Before August 17, 2004, the average estimated population size was 143, and after August 24, 2005, this value jumped to 446, an increase possibly due to tadpoles metamorphosing into adults.

Existence-uniqueness and long time behavior for a class of nonlocal nonlinear parabolic evolution equations

We establish existence and uniqueness of solutions for a general class of nonlocal nonlinear evolution equations. An application of this theory to a class of nonlinear reaction-diffusion problems that arise in population dynamics is presented. Furthermore, conditions on the initial population density for this class of problems that result in finite time extinction or persistence of the population is discussed. Numerical evidence corroborating our theoretical results is given.