Population dynamical behavior of Lotka-Volterra system under regime switching

In this paper, we investigate a Lotka-Volterra system under regime switching dx(t) = diag(x1(t); : : : ; xn(t))[(b(r(t)) + A(r(t))x(t))dt + (r(t))dB(t)]; where B(t) is a standard Brownian motion. The aim here is to find out what happens under regime switching. We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence and extinction. We find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the Markov chain. The limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients. Finally, the main results are illustrated by several examples

ii Control of chaotic population dynamics

Ecological and economic consideration

The Role of Plasticity in Bumble Bee Responses to Environmental Variability

An aim of contemporary biology is elucidating the causes and consequences of phenotypic plasticity. Here, I approach this aim by exploring the eco-evolutionary dynamics of phenotypic plasticity and environmental variability in bumble bees (Apidae: Bombus), a congeneric clade of eusocial pollinating insects. Throughout their evolution, bumble bees have encountered spatiotemporal variability imposed by dynamic floral environments. Today, bumble bees additionally encounter spatiotemporal variability imposed by anthropogenic environmental change. In this dissertation, I explore how phenotypic plasticity affects how successfully bumble bees respond to environmental variability imposed by anthropogenic global change (Chapters 1 and 2) and their floral resources (Chapters 3 and 4). I focus on two notably plastic traits that have ecologically consequential implications: body size plasticity and behavioral plasticity. Using a combination of phenotypic, molecular, and modeling approaches - with data spanning field populations, biological collections, and laboratory colonies - the results of this work suggest that body size plasticity and behavioral plasticity are integral to the success of bumble bees in variable environments. I find that intraspecific trait variation is key to understanding population responses to environmental variability. Specifically, I find evidence that greater worker body size plasticity enables bumble bees to more successfully contend with anthropogenic environmental change (Chapters 1 and 2) and that behavioral variation is induced by floral variability (Chapters 3 and 4). Overall, this dissertation reveals that bumble bees respond to environmental variability in myriad ways and that these responses manifest at the individual-, colony-, and population-levels of biological organization. In addition to helping elucidate the eco-evolutionary dynamics of phenotypic plasticity and environmental variability, this work suggests that understanding the relationship between plasticity and bumble bee success in variable environments is integral to conserving these ecologically consequential pollinators

Predicting the spatial distribution of an invasive plant species and modeling tolerance to herbivory using Lythrum salicaria L. as a model system

Understanding the ecological factors behind the landscape-level distribution of invasive species is a rapidly growing area of research with strong applied implications. In a major part of my thesis, which comprises chapters 2 &3, the focus is on spatial pattern analyses and predictive modeling of an invasive wetland plant: Purple Loosestrife (Lythrum salicaria L.). More specifically, the first part of my thesis (i.e. chapter 2) considers a novel hierarchical approach, wherein the spatial distribution of loosestrife in a human-modified landscape was found to be the consequence of three key hierarchical factors: wetland habitat availability, disturbance prone surrounding land-use conditions around the wetland habitat, and propagule pressure. In chapter 3, the spatial factors and ecological processes characterized in chapter 2 were put-together and several logistic and autologistic regression models were developed to predict locations of loosestrife occurrences. Incorporating propagule pressure as an autocovariate was found to be crucial in making accurate predictions of loosestrife invasion risk. However, in the absence of propagule pressure, the surrounding land-use model highlighted the role of anthropogenic edges in defining the invasibility of wetland habitats. From an applied perspective, the model based risk maps assist conservationists and land managers in predicting and checking the spatial spread of invasive loosestrife. In the fourth and last research chapter of my thesis, a mathematical model is developed to explore herbivore tolerance in perennials with long-term belowground storage. The inspiration behind this model is loosestrife, an invasive perennial, and its biocontrol insect herbivores. More specifically, a discrete time model was built to explore the role of belowground allocation of biomass in a perennial plant with distinct growing season and under regular seasonal defoliation by herbivores. The model addresses the role of two co-occurring traits like utilization of stored reserves for early-season growth and post-herbivory regrowth and consequent tolerance potential. The model results highlighted that belowground biomass allocation plays a critical role as it allows the plant to persist despite severe periodic defoliation by herbivores. The model findings also indicated that when highly efficient early-season use of stored reserves is coupled with high belowground biomass allocation potential the plant biomass and herbivore population can show sustained cycles. From the perspective of invasive perennials, the model suggests that brief periods of intense seasonal herbivory is incapable of extirpating the invasive plant population as long as the latter can efficiently allocate biomass belowground

Species And Habitat Interactions Of The Gopher Tortoise: A Keystone Species?

Species-species and species-habitat interactions have been demonstrated to be important in influencing diversity across a variety of ecosystems. Despite generalities in the importance of these interactions, appropriate mechanisms to explain them are absent in many systems. In sandhill systems of the southeast U.S., gopher tortoises have been hypothesized to be a crucial species in the maintenance of diversity and function. However, the mechanisms and magnitude in which they influence their communities and habitats have rarely been empirically quantified. I examined how habitat structure influences tortoise abandonment of burrows and how tortoise densities influence nonvolant vertebrate community diversity. Tortoise burrow abandonment is directly influenced by canopy closure, with each percent increase in canopy cover relating to a ~2% increase in the probability of burrow abandonment. In addition, tortoise burrow density was positively correlated with diversity and evenness, but not species richness. This influence was directly proportional to burrow density, supporting a dominance role for this species and rejecting the commonly asserted keystone species mechanism. I also quantified the influence of tortoises in influencing diversity relative to other environmental and habitat variables. Through this research, I have demonstrated that disturbance and habitat structure are important, but diversity responds most to density of burrows in the habitat. These findings demonstrate the intricate relationships interacting to maintaining diversity in sandhill systems. In particular, habitat change leading to declines of gopher tortoises may have drastic negative impacts on vertebrate species diversity

Invasive elodea threatens remote ecosystem services in Alaska: a spatially-explicit bioeconomic risk analysis

Thesis (Ph.D.) University of Alaska Fairbanks, 2017This dissertation links human and ecological systems research to analyze resource management decisions for elodea, Alaska's first submerged aquatic invasive plant. The plant likely made it to Alaska through the aquarium trade. It was first discovered in urban parts of the state but is being introduced to remote water bodies by floatplanes and other pathways. Once introduced, elodea changes freshwater systems in ways that can threaten salmon and make floatplane destinations inaccessible. The analysis integrates multiple social and ecological data to estimate the potential future economic loss associated with its introduction to salmon fisheries and floatplane pilots. For estimating the effects on commercial sockeye fisheries, multiple methods of expert elicitation are used to quantify and validate expert opinion about elodea's ecological effects on salmon. These effects are believed to most likely be negative, but can in some instances be positive. Combined with market-based economic valuation, the approach accounts for the full range of potential ecological and economic effects. For analyzing the lost trip values to floatplane pilots, the analysis uses contingent valuation to estimate recreation demand for landing spots. A spatially-explicit model consisting of seven regions simulates elodea's spread across Alaska and its erratic population dynamics. This simulation model accounts for the change in region-specific colonization rates as elodea populations are eradicated. The most probable economic loss to commercial fisheries and recreational floatplane pilots is $97 million per year, with a 5$456 million annually. The analysis describes how loss varies among stakeholders and regions, with more than half of statewide loss accruing to commercial sockeye salmon fisheries in Bristol Bay. Upfront management of all existing invasions is found to be the optimal management strategy for minimizing long-term loss. Even though the range of future economic loss is large, the certainty of long-term damage favors investments to eradicate current invasions and prevent new arrivals. The study serves as a step toward risk management aimed at protecting productive ecosystems of national and global significance.General introduction -- Chapter 1. Quantifying Expert Knowledge Using a Discrete Choice Model: Persistence of Salmonids in Habitat Invaded by Elodea -- Chapter 2. Aquatic Invasive Species Change Ecosystem Services from the World's Largest Sockeye Salmon Fisheries in Alaska -- Chapter 3. Aquatic Invasive Plants Alter Recreation Access for Alaska's Floatplane Pilots: an Application of Stated Geographic Preferences to Economic Valuation -- Chapter 4. Aquatic Invasive Species from Urban Source Lakes Threaten Remote Ecosystem Services in Alaska: Linking Floatplane Pathway Dynamics with Bioeconomic Risk Analysis -- General Conclusion -- References -- Appendix

The Study of Growth and Performance in Local Chicken Breeds and Varieties: A Review of Methods and Scientific Transference

A review of the scientific advances in the study of the growth and performance in native chicken breeds and varieties over the past 20 years was performed. Understanding the growth patterns of native breeds can only be achieved if the constraints characterizing these populations are considered and treated accordingly. Contextually, the determination of researchers to use the same research methods and study designs applied in international commercial poultry populations conditions the accuracy of the model, variability capturing ability, and the observational or predictive performance when the data of the local population are fitted. Highly skewed sex ratios favouring females, an inappropriate census imbalance compensation and a lack of population structure render models that are regularly deemed effective as invalid to issue solid and sound conclusions. The wider the breed diversity is in a country, the higher the scientific attention paid to these populations. A detailed discussion of the most appropriate models and underlying reasons for their suitability and the reasons preventing the use of others in these populations is provided. Furthermore, the factors conditioning the scientific reception and impact of related publications used to transfer these results to the broad scientific public were evaluated to serve as guidance for the maximization of the success and dissemination of local breed information

E pluribus unum: what individual whales can tell us about enigmatic species distribution and social organization

Large whales have historically been difficult to study and many aspects of their ecology remain unknown especially at the long -term population level. The ability to identify individual whales based on natural markings provides the opportunity to track individuals over time and space; this data may offer more insight into the ecology of whales than previously imagined. This study demonstrates use of photo-identification data to model both social structure and habitat selection, minimizing the need for invasive research and greatly increasing the sample size used in such endeavors. A conditional logistic model is written for a 20-year sightings dataset on humpback whales collected by Allied Whale research trips and on the Bar Harbor Whale Watch Company vessels, examining choice of individuals over a given landscape and incorporating the cost of movement. Habitat choices are represented by static and remotely sensed variables including bathymetry, distance from shore, and sea surface temperature. Results show significant active decisions of whales to move towards specific hotspots ~23km offshore of intermediate depth. These models are validated by systematic boat surveys conducted during two field seasons. Sightings data are also applied to social networking analyses. Association indices are calculated for each dyad of whales and preferred association is tested for through a valid Markov chain of permutations. Network structure is delineated through optimal modularity clustering producing visualizations of communities. Significant preferred companionship is seen between 94 dyads and individuals are separated into nine communities. Community structure is not entirely stable and shifts over time. Lastly, movement behavior and social structure between the whales in the northern Gulf of Maine are compared to that of the whales in the southern Gulf of Maine. The analyses listed above are run on a 26-year dataset provided by Provincetown Center for Coastal Studies on humpback whales on Stellwagen Bank. Differences are seen between northern and southern whales in use of habitat and degree of sociality. Whales in the southern aggregation are more gregarious, but have a lesser degree of long-term community structure. By applying new analytic tools to long-term observations, this research provides insights into humpback whale social behavior and ecology that should inform marine management strategies in the region