Predator-prey models with cannibalism in prey

Cannibalism in the predator-prey model is the study to show the interaction between prey and predator where the presence of cannibalism exists in both species in real life. Moreover, cannibalism is ubiquitous in natural communities and also among researchers who are interested in mathematical ecology. The predator-prey model system is modelled using ordinary differential equations to describe the dynamic behaviour of the systems. This study introduces the stage-structured models where the adult and juvenile prey species are considered. The purpose of the study is to analyse the effect of the stage-structured of prey cannibalism on the stability based on the concept of Lotka-Volterra in the predator-prey model. Thus, in this study, there are two cases are considered: prey cannibalism in the predator-prey model with predation on adult prey and model with predation on juvenile prey. The objectives of this research are (i) to formulate the concept of Lotka-Volterra in a predator-prey model, (ii) to analyse prey cannibalism in predator-prey model with predation on adult prey, (iii) to analyse the predator-prey in prey cannibalism with predation on juvenile prey, and (iv) to analyse the effect of stage-structured predator-prey model with cannibalism in prey on stability. In analysing the models, the stability of the equilibrium point is obtained and described by using the properties of the eigenvalues and the Routh-Hurwitz Criteria. Last but not least, numerical examples and graph analysis are given to illustrate the stability of equilibrium points

Balanced exploitation and coexistence of interacting, size-structured, fish species

This paper examines some effects of exploitation on a simple ecosystem containing two interacting fish species, with life histories similar to mackerel (Scomber scombrus) and cod (Gadus morhua), using a dynamic, size-spectrum model. Such models internalize body growth and mortality from predation, allowing bookkeeping of biomass at a detailed level of individual predation and growth and enabling scaling up to the mass balance of the ecosystem. Exploitation set independently for each species with knife-edge, size-at-entry fishing can lead to collapse of cod. Exploitation to achieve a fixed ratio of yield to productivity across species can also lead to collapse of cod. However, harvesting balanced to the overall productivity of species in the exploited ecosystem exerts a strong force countering such collapse. If balancing across species is applied to a fishery with knife-edge selection, size distributions are truncated, changing the structure of the system and reducing its resilience to perturbations. If balancing is applied on the basis of productivity at each body size as well as across species, there is less disruption to size-structure, resilience is increased, and substantially greater biomass yields are possible. We note an identity between the body size at which productivity is maximized and the age at which cohort biomass is maximized. In our numerical results based on detailed bookkeeping of biomass, cohort biomass reaches its maximum at body masse

Modeling the ecology and evolution of communities: A review of past achievements, current efforts, and future promises

Background: The complexity and dynamical nature of community interactions make modeling a useful tool for understanding how communities develop over time and how they respond to external perturbations. Large community-evolution models (LCEMs) are particularly promising, since they can address both ecological and evolutionary questions, and can give rise to richly structured and diverse model communities. Questions: Which types of models have been used to study community structure and what are their key features and limitations? How do adaptations and/or invasions affect community formation? Which mechanisms promote diverse and table communities? What are the implications of LCEMs for management and conservation? What are the key challenges for future research? Models considered: Static models of community structure, demographic community models, and small and large community- evolution models. Conclusions: LCEMs encompass a variety of modeled traits and interactions, demographic dynamics, and evolutionary dynamics. They are able to reproduce empirical community structures. Already, they have generated new insights, such as the dual role of competition, which limits diversity through competitive exclusion, yet facilitates diversity through speciation. Other critical factors determining eventual community structure are the shape of trade-off functions, inclusion of adaptive foraging, and energy availability. A particularly interesting feature of LCEMs is that these models not only help to contrast outcomes of community formation via species assembly with those of community formation via gradual evolution and speciation, but that they can furthermore unify the underlying invasion processes and evolutionary processes into a single framework

Elucidating Complex Animal Interactions in the Modern World: Determining the occurrence and effects of intraguild predation within food webs

Animal interactions structure food webs with stability being contingent on the presence and strength of multi-species interactions. Intraguild predation (IGP) is a complex interaction that can impact species at the individual, population and community levels, ultimately determining the strength, direction and linearity of trophic cascades and species abundance across trophic levels. IGP occurs among a minimum of three species; a predator (IGpredator) that kills and consumes a prey (IGprey) with which it competes for a common resource. Through a systematic literature search, I determined traditional to modern approaches to measure the occurrence and effect of IGP and then identified the research effort afforded to the different implication levels and IGP effects characterized by Polis et al. (1989). I highlighted IGP effects that require focused attention and provided recommendations on methods that could be used to address knowledge gaps. To understand the role of IGP in higher order predators, I focused on the large shark assemblage given their largely unknown role in top down control and limited IGP studies to date. The large shark assemblage exhibits high phenotypic plasticity that results in varied functional roles (e.g. secondary vs. tertiary piscivores) suggesting complex IGP interactions occur. Stable isotope analysis (SIA) provides an approach to reconstruct consumer diet to examine IGP, however, a detailed understanding of tissue preparation techniques is first required to ensure accurate interpretation of results. Elasmobranch liver is a useful high turnover tissue for IGP studies, but it contains high lipid levels and is expected to retain urea and TMAO for osmotic balance which can bias isotopic values. I found that deionized water washing for urea and TMAO removal was not required as δ15N values were not modified following treatment. Residual lipid within lipid extracted liver samples, however, required the development of C:N thresholds to derive ecologically relevant liver isotopic values. A preliminary comparison between muscle and liver tissue highlighted the value of liver for understanding short vs. long term movements and its application for IGP studies. The occurrence, class and consistency of IGP among large sharks was examined using published stomach content data and prey contributions from stable isotope mixing models. IGP was present among all sharks with the strength and class varying by species, ontogeny and over time (i.e. daily vs. annually). Understanding shark functional roles within marine food webs can improve management practices through the lens of multi-species interactions; targeted conservation on shark species involved in moderate levels of IGP with high connectance among species may enhance food web stability

Stability of steady states of meta-food webs on discrete spatial networks

The concept of a food web is deceivingly simple. A simple map of interaction links between species. Nor is a spatially discrete network a particular daunting construct. Yet, even after almost a century of research there are still many unanswered questions about food webs and their spatial extensions, meta- food webs, and the perhaps most urgent one is, in the words of “father of modern ecology” (Slack, 2010), George Evelyn Hutchinson: “Why are there so many kinds of animals?” (Hutchinson, 1959) It has yet to be satisfyingly understood how complex food webs remain relatively stable and robust. The overwhelming complexity of real species relations and the difficulty for biologists and ecologists in gathering both precise and extensive field data makes it nearly impossible to faithfully recreate all nuances of actual food webs. This makes the topic particular appealing to the physicist who delights in abstracting problems to reveal underlying principles. The central focus of this thesis is thus to provide additional tools and insights to the topic of stability in meta-food webs. The generalized modelling method is particularly suited to this task as it is built around the idea of normalization to steady states which can be analysed concerning their stability. We offer an introduction to this method by examining the most simple food web possible consisting of a single predator and a single prey species. This provides a look at the fundamental terms and possibilities of the generalized modelling approach and gives some basic trends for the stability of food webs that are surprisingly sturdy in their applicability, e.g. the notion that large exponents for the primary production of biomass are destabilizing. We then add a spatial factor with a second patch so that we are dealing with a meta-food web. The food webs on each patch are homogeneous and we focus on the effect of migration between the two patches. Dispersal is overall destabilizing but can become less destabilizing for adaptive migration in certain parameter ranges. We also ask the question what dynamics occur during the transition from a stable to an unstable system which leads us to the phenomena that fall under the umbrella term of bifurcation. These simple systems show the full range of bifurcations including simple pattern building. From there we increase the complexity by incorporating heterogeneous food webs on each of the patches. This asymmetry allows for a wider range of behaviour at the point of bifurcation and now the additional element of synchrony between patches and species has to be taken into account. The ratio of oscillatory behaviour in case of perturbation increases and the oscillations becomes more anti- phasic compared to the homogeneous food webs; indicators of a higher robustness. The impact on linear stability cannot be easily predicted. We then extend the meta-food web from two patches and two species to many species on spatially distributed networks of patches though only with homogeneous local food webs. We show the analogy between reaction-diffusion systems on continuous space and on networks and how this can be applied to meta-food webs. Exploiting the inherent structure we can formulate a master stability function that allows for a separation of topological influences and those that stem from food web dynamics. Meta- communities become in general less stable for larger food webs and can be stable or unstable depending on the spatial configuration. They show primarily oscillatory and most likely rather localized responses to disturbances which are arguments for the robustness of the meta-communities. Finally, we summarize the results from the different sections. The steady states of food webs on spatial networks become less and less stable for increasing complexity but at the same time show signs of increasing robustness