IMPACT OF FEAR BEHAVIOR ON PREY POPULATION GROWTH PREY-PREDATOR INTERACTION

Experiments on the living environment of vertebrate ecosystems, it has been shown that predators have a massive influence on the demographic growth rate of prey. The proposed fear effect is a mathematical model that affects the reproductive growth rate of prey with the Holling Type I interaction model. Mathematical analysis of the prey-predator model shows that a strong anti-predator response can provide stability for prey-predator interactions. The parameter area taken will be shown for the extinction of the prey population, the balance of population survival, and the balance between the prey birth rate and the predator death rate. Numerical simulations were given to investigate the biological parameters of the population (birth rate, natural mortality of prey, and predators). Another numerical illustration that is seen is the behavior of prey which is less sensitive in considering the risk of predators with the growth rate of prey

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research

STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH APPLICATIONS IN ECOLOGY AND EPIDEMICS

Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and predictions in various areas of life sciences, such as population dynamics, epidemiology, immunology, physiology, and neural networks. The memory or time-delays, in these models, are related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period, and so on. In ordinary differential equations (ODEs), the unknown state and its derivatives are evaluated at the same time instant. In DDEs, however, the evolution of the system at a certain time instant depends on the past history/memory. Introduction of such time-delays in a differential model significantly improves the dynamics of the model and enriches the complexity of the system. Moreover, natural phenomena counter an environmental noise and usually do not follow deterministic laws strictly but oscillate randomly about some average values, so that the population density never attains a fixed value with the advancement of time. Accordingly, stochastic delay differential equations (SDDEs) models play a prominent role in many application areas including biology, epidemiology and population dynamics, mostly because they can offer a more sophisticated insight through physical phenomena than their deterministic counterparts do. The SDDEs can be regarded as a generalization of stochastic differential equations (SDEs) and DDEs.This dissertation, consists of eight Chapters, is concerned with qualitative and quantitative features of deterministic and stochastic delay differential equations with applications in ecology and epidemics. The local and global stabilities of the steady states and Hopf bifurcations with respect of interesting parameters of such models are investigated. The impact of incorporating time-delays and random noise in such class of differential equations for different types of predator-prey systems and infectious diseases is studied. Numerical simulations, using suitable and reliable numerical schemes, are provided to show the effectiveness of the obtained theoretical results.Chapter 1 provides a brief overview about the topic and shows significance of the study. Chapter 2, is devoted to investigate the qualitative behaviours (through local and global stability of the steady states) of DDEs with predator-prey systems in case of hunting cooperation on predators. Chapter 3 deals with the dynamics of DDEs, of multiple time-delays, of two-prey one-predator system, where the growth of both preys populations subject to Allee effects, with a direct competition between the two-prey species having a common predator. A Lyapunov functional is deducted to investigate the global stability of positive interior equilibrium. Chapter 4, studies the dynamics of stochastic DDEs for predator-prey system with hunting cooperation in predators. Existence and uniqueness of global positive solution and stochastically ultimate boundedness are investigated. Some sufficient conditions for persistence and extinction, using Lyapunov functional, are obtained. Chapter 5 is devoted to investigate Stochastic DDEs of three-species predator prey system with cooperation among prey species. Sufficient conditions of existence and uniqueness of an ergodic stationary distribution of the positive solution to the model are established, by constructing a suitable Lyapunov functional. Chapter 6 deals with stochastic epidemic SIRC model with time-delay for spread of COVID-19 among population. The basic reproduction number ℛs0 for the stochastic model which is smaller than ℛ0 of the corresponding deterministic model is deduced. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov functional, and conditions for the extinction of the disease are obtained. In Chapter 7, some numerical schemes for SDDEs are discussed. Convergence and consistency of such schemes are investigated. Chapter 8 summaries the main finding and future directions of research. The main findings, theoretically and numerically, show that time-delays and random noise have a significant impact in the dynamics of ecological and biological systems. They also have an important role in ecological balance and environmental stability of living organisms. A small scale of white noise can promote the survival of population; While large noises can lead to extinction of the population, this would not happen in the deterministic systems without noises. Also, white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can also occur due to the time-delay in the transmission terms

Partial Differential Equations in Ecology

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots

Spatial and Temporal Variability in the Carrion Insect Community: Using Blow Flies (Family: Calliphoridae) as a Model System to Study Coexistence Mechanisms at Multiple Scales

Resource partitioning can lead to species coexistence. In a field study, temporal and spatial partitioning were examined by testing the effects of season and habitat on the structure of the blow fly community on domestic pig carcasses, Sus scrofa domesticus in southwestern Ontario, Canada. Blow fly communities did not differ between field and forest habitats, however there were seasonal differences. Fall was characterized by having more species and higher levels of species evenness, diversity, and niche overlap than spring and summer. On a finer scale, effects of arrival order were examined in laboratory experiments with three blow fly species: Phormia regina, Lucilia sericata, and the introduced species Chrysomya rufifacies. Arrival order of adults was varied in combinations of two species: L. sericata and P. regina and L. sericata and C. rufifacies . Both positive and negative priority effects were recorded, with species having altered colonization patterns temporally and spatially in response to presence of another species, even at low density (i.e. minimal competition). Blow flies sometimes selected oviposition sites other than the natural orifices predicted by previous studies, such as the neck and cheek regions or between legs. Delays in colonization, particularly for P. regina and C. rufifacies, occurred in response to the absence of heterospecifics. Additional experiments with larvae determined that C. rufifacies and P. regina benefitted from the presence of L. sericata due to predation (for C. rufifacies) or the presence of compound(s) that may aid in the digestion of the resource and increase nutrient availability (for P. regina). In summary, adult and larval experiments indicate that species interactions and differences in arrival order can affect colonization times, the distribution of eggs over a resource, larval interactions and offspring fitness. On a larger scale, temporal partitioning (i.e. seasonal effects) can promote coexistence in blow flies, however, spatial partitioning (i.e. habitat effects) was not evident. This study demonstrates the importance of ADD standardization, emphasizes the need to understand species interactions between native and non-native species, and highlights the need for more ecological studies regarding habitat and seasonal differences within the carrion communit

Sex, friends, and disease: social ecology of elk (Cervus elaphus) with implications for pathogen transmission

Many mammals are social. The most basic social behaviour is when the actions of one conspecific are directed toward another, what we call the ‘dyadic interaction’. Both intrinsic and extrinsic factors may affect an individual’s propensity to interact with other members of a population. I used a social cervid, elk (Cervus elaphus), as a model species to test the importance of intrinsic and extrinsic factors of sociality on dyadic interactions. Dyadic interactions not only form the basis for social structure and information transfer within a population, but are also routes of pathogen transmission. My objective in this thesis was thus twofold: to improve our understanding of sociobiology, but also to gain insight into how sociality may underlie the transmission of communicable wildlife disease. I used a hierarchical, autecological approach from DNA, through individual, dyad, group, subpopulation, and ultimately population to explore the effects of intrinsic factors (e.g., sex and pairwise genetic relatedness) and extrinsic factors (e.g., season, conspecific density, habitat, and elk group size) on sociality. Elk in Riding Mountain National Park (RMNP), Manitoba, Canada, are exposed to the causal agent of bovine tuberculosis (Mycobacterium bovis; TB); however, spatial variation in apparent disease prevalence suggests that TB can only persist in one subpopulation within the Park. Using the natural RMNP system and a captive elk herd that I manipulated, I explored factors that influence interaction rates and durations (as a proxy for pathogen transmission) among elk. Sexual segregation in elk results in seasonal and sex-based differences in interaction rate and duration; with interactions peaking in autumn-winter for both sexes. Female-female dyads interact more frequently than male-male dyads. However, male-male dyads interact for longer durations than do female-female dyads. Interaction rate and duration did not covary with pairwise relatedness. Conspecific density also had sex-specific results for interaction rate and duration. Whereas male-male dyadic interaction rates increase with density, female-female dyads increase until they reach a threshold and subsequently reduce their interaction rates at high density. I observed density dependence in interaction rates in experimental trials and from field data. Furthermore, social networks revealed that social familiarity (i.e., heterogeneity of interactions) can be both frequency- and- density dependent depending on the strength of the relationship (i.e., number of repeat interactions). Density also affected the likelihood that an interaction would occur; however, this was modified by vegetation association used by elk. My results reveal several ecological and evolutionary implications for information transfer and pathogen transmission. In particular, I show that seasonal inter-sex routes of transfer may exist and that transfer is likely to be density-dependent. Finally, I conclude that such transfer is modified by available resources

The ecology of jaguars (panthera onca) in a human-influenced landscape

Despite intense persecution over the last century, the jaguar (Panthera onca) has sustained a wide geographic distribution, perhaps due to its elusive nature and rather flexible ecology. This study investigated jaguar ecology under anthropogenic pressures in Belize, Central America. A suite of methods including camera-trap surveys, diet analysis, discussions with local stakeholders, and population simulations were used to study a population of jaguars spanning the boundary of a protected forest. Camera-trap data combined with capture-recapture population models are increasingly used to estimate the density of mammals such as jaguars with individually identifiable coat patterns. A review of current methods highlighted problems associated with estimating the sizes of lowdensity populations. Simulations to assess the robustness of the method found that camera failure can negatively or positively bias the abundance estimate, depending on the particular nature of capture histories. The most commonly used model estimator in the literature was nevertheless robust to failures of up to 10% of trap-occasions. Pooling trap-occasions reduced the effect of camera failure. Sub-sampling data from large-scale surveys indicated a threshold survey area of ~170 km2, below which estimates of density were inflated and unreliable. For surveys exceeding this threshold size, jaguar density varied across the landscape from the protected forest to the human-influenced lands such that <30% contiguous forest precipitated reduction. Reduced densities with distance from contiguous forest and proximity to human habitation may result principally from direct conflicts with people. The influence of anthropogenic factors on the coexistence of jaguars and pumas (Puma concolor) was investigated by comparing their habitat use and feeding ecology. Diet was analysed from the largest sample to date of scats from one area identified to species. Jaguars and pumas made similar use of the secondary rainforest, despite differences in diet. Although both cats relied heavily on one species of small prey (5-10 kg), for jaguars this was the nine-banded armadillo (Dasypus novemcinctus) while for pumas it was the paca (Agouti paca). Both cats took some larger prey, mainly white-lipped peccaries (Dictolyes pecari) by jaguars and red brocket deer (Mazama americana) by pumas. Energetics models indicated that reproduction may be limited for either species if large prey are unavailable for females with dependents. Outside the forest block, jaguars rarely ate large wild prey species; instead, a diet of smaller wild prey was supplemented with large domestic stock. Pumas were scarce outside the protected forest, possibly reflecting a reluctance to utilise domestic species near human developments and competition with humans for their preferred prey of paca and deer, which are also prized regionally as game species. Human-induced mortality of jaguars outside the protected forest was mainly associated with livestock predation. Both sexes were equally active on pastures and were persecuted at a similar rate. Many of those killed were young individuals in good body condition, suggesting high turnover rates augmented by immigration. Population simulations indicated that the observed levels of human-induced mortality could be maintained only with immigration from the protected forest. Without natal dispersers (2-4 year olds) immigrating in, the hunted population had zero probability of persisting beyond 20 years. Simulations indicated that the jaguar populations inhabiting the two main protected forest blocks in Belize could persist in isolation and maintain low levels of emigration to the unprotected population. However the probability of all three populations persisting for 100 years fell to ~50% if the migration of natal dispersers from the protected to unprotected population exceeded ~12% per year

Invasive Species in Forests and Rangelands of the United States

This open access book describes the serious threat of invasive species to native ecosystems. Invasive species have caused and will continue to cause enormous ecological and economic damage with ever increasing world trade. This multi-disciplinary book, written by over 100 national experts, presents the latest research on a wide range of natural science and social science fields that explore the ecology, impacts, and practical tools for management of invasive species. It covers species of all taxonomic groups from insects and pathogens, to plants, vertebrates, and aquatic organisms that impact a diversity of habitats in forests, rangelands and grasslands of the United States. It is well-illustrated, provides summaries of the most important invasive species and issues impacting all regions of the country, and includes a comprehensive primary reference list for each topic. This scientific synthesis provides the cultural, economic, scientific and social context for addressing environmental challenges posed by invasive species and will be a valuable resource for scholars, policy makers, natural resource managers and practitioners