Dynamics of a harvested cyanobacteria-fish model with modified Holling type Ⅳ functional response

In this paper, considering the aggregation effect and Allee effect of cyanobacteria populations and the harvesting of both cyanobacteria and fish by human beings, a new cyanobacteria-fish model with two harvesting terms and a modified Holling type Ⅳ functional response function is proposed. The main purpose of this paper is to further elucidate the influence of harvesting terms on the dynamic behavior of a cyanobacteria-fish model. Critical conditions for the existence and stability of several interior equilibria are given. The economic equilibria and the maximum sustainable total yield problem are also studied. The model exhibits several bifurcations, such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. It is concluded from a biological perspective that the survival mode of cyanobacteria and fish can be determined by the harvesting terms. Finally, concrete examples of our model are given through numerical simulations to verify and enrich the theoretical results

Repulsive-attractive models for the impact of two predators on prey species varying in anti-predator response

This study considers the dynamical interaction of two predatory carnivores (Lions (Panthera leo) and Spotted Hyaenas (Crocuta crocuta)) and three of their common prey (Buffalo (Syncerus caffer), Warthog (Phacochoerus africanus) and Kudu (Tragelaphus strepsiceros)). The dependence on spatial structure of species’ interaction stimulated the author to formulate reaction-diffusion models to explain the dynamics of predator-prey relationships in ecology. These models were used to predict and explain the effect of threshold populations, predator additional food and prey refuge on the general species’ dynamics. Vital parameters that model additional food to predators, prey refuge and population thresholds were given due attention in the analyses. The stability of a predator-prey model for an ecosystem faced with a prey out-flux which is analogous to and modelled as an Allee effect was investigated. The results highlight the bounds for the conversion efficiency of prey biomass to predator biomass (fertility gain) for which stability of the three species ecosystem model can be attained. Global stability analysis results showed that the prey (warthog) population density should exceed the sum of its carrying capacity and threshold value minus its equilibrium value i.e., W >(Kw + $) −W . This result shows that the warthog’s equilibrium population density is bounded above by population thresholds, i.e., W < (Kw+$). Besides showing the occurrence under parameter space of the so-called paradox of enrichment, early indicators of chaos can also be deduced. In addition, numerical results revealed stable oscillatory behaviour and stable spirals of the species as predator fertility rate, mortality rate and prey threshold were varied. The stabilising effect of prey refuge due to variations in predator fertility and proportion of prey in the refuge was studied. Formulation and analysis of a robust mathematical model for two predators having an overlapping dietary niche were also done. The Beddington-DeAngelis functional and numerical responses which are relevant in addressing the Principle of Competitive Exclusion as species interact were incorporated in the model. The stabilizing effect of additional food in relation to the relative diffusivity D, and wave number k, was investigated. Stability, dissipativity, permanence, persistence and periodicity of the model were studied using the routine and limit cycle perturbation methods. The periodic solutions (b 1 and b 3), which influence the dispersal rate (') of the interacting species, have been shown to be controlled by the wave number. For stability, and in order to overcome predator natural mortality, the nutritional value of predator additional food has been shown to be of high quality that can enhance predator fertility gain. The threshold relationships between various ecosystem parameters and the carrying capacity of the game park for the prey species were also deduced to ensure ecosystem persistence. Besides revealing irregular periodic travelling wave behaviour due to predator interference, numerical results also show oscillatory temporal dynamics resulting from additional food supplements combined with high predation rates

Incorporating neurological and behavioral mechanisms of sociality into predator-prey models

Consumer-resource population models drive progress in predicting and understanding predation. However, they are often built by averaging the foraging outcomes of individuals to estimate per capita functional responses (functions that describe predation rate). Reliance on per-capita functional responses rests on the assumption that that individuals forage independently without affecting each other. Undermining this assumption, extensive behavioral neuroscience research has made clear that facilitative and antagonistic interactions among conspecifics frequently alter foraging through interference competition and persistent neurophysiological changes. For example, repeated social defeats dysregulates rodent hypothalamic signaling, modulating appetite. In behavioral ecology, similar mechanisms are studied under the concept of dominance hierarchies. Neurological and behavioral changes in response to conspecifics undoubtedly play some sort of role in the foraging of populations, but modern predator-prey theory does not explicitly include them. Here we describe how some modern approaches to population modeling might account for this. Further, we propose that spatial predator-prey models can be modified to describe plastic changes in foraging behavior driven by intraspecific interaction, namely individuals switching between patches or plastic strategies to avoid competition. Extensive neurological and behavioral ecology research suggests that interactions among conspecifics help shape populations’ functional responses. Modeling interdependent functional responses woven together by behavioral and neurological mechanisms may thus be indispensable in predicting the outcome of consumer–resource interactions across systems

Resource conflicts between humans and the African wild dog (Lycaon pictus)

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg in fulfilment of the requirements for the degree of Master of Science, 2017The African wild dog (Lycaon pictus) is one of South Africa’s most endangered carnivores. The species has suffered massive range shrinkages in the past few decades and population numbers have dropped significantly. Along with other factors responsible for its decline, one of the most notable threats to the African wild dog is conflict with humans. These carnivores are often persecuted by farmers for their alleged depredation of livestock and captive-bred game species, although doubt exists as to whether wild dogs are the avid depredators as suggested. My research therefore aimed to investigate the conflict between people and African wild dog, focussing on livestock depredation. Due to heterogeneous farming landscapes, the history and location of protected areas and the endangered status of the African wild dog, South Africa provides many opportunities to study this particular type of human-carnivore conflict. Firstly, I conducted a meta-analysis of human-carnivore conflict using published literature about African wild dog depredation of livestock and game and compared these to other African carnivores as well as non-African carnivores. Results indicated that African wild dog were less avid depredators than other African species such as lion (Panthera leo) and spotted hyena (Crocuta crocuta). Also evident was that high carnivore and livestock densities, coupled with poor communities with poor livestock husbandry practices, make people and carnivores in developing regions more vulnerable to human-carnivore conflicts. Secondly, I assessed actual African wild dog occurrence in relation to the location of farms, livestock density and several other anthropogenic and natural landscape features. This was achieved using GPS data from four collared African wild dog individuals from packs residing in the northeastern part of South Africa and resource selection functions. Results from these analyses suggested that, whilst African wild dog may occur in close proximity to farms, they established home ranges in areas of low livestock density and few farms, indicating predictive avoidance of areas where mortality may occur. Major roads were highlighted as a vulnerability for the African wild dog, whilst nature reserves and vegetation were also important predictors of wild dog occurrence. Other anthropogenic and natural landscape features varied in importance in determining wild dog occurrence. Knowledge about how the African wild dog selects its resources will enable us to identify vulnerabilities for these carnivores as well as areas where they are likely to occur, aiding in conservation planning. Though African wild dog have historically been reported to kill livestock such goats and cattle, my study seems to indicate that these carnivores are not avid stock-killers. Given the precarious survival status of the African wild dog and the food security needs of people in a developing region strongly suggests the need for cooperation of farmers and the education of communities to aid the recovery of this uniquely African carnivore.XL201

When is bigger better? The effects of group size on the evolution of helping behaviours: Effects of group size on evolution of helping

Understanding the evolution of sociality in humans and other species requires understanding how selection on social behaviour varies with group size. However, the effects of group size are frequently obscured in the theoretical literature, which often makes assumptions that are at odds with empirical findings. In particular, mechanisms are suggested as supporting large-scale cooperation when they would in fact rapidly become ineffective with increasing group size. Here we review the literature on the evolution of helping behaviours (cooperation and altruism), and frame it using a simple synthetic model that allows us to delineate how the three main components of the selection pressure on helping must vary with increasing group size. The first component is the marginal benefit of helping to group members, which determines both directfitness benefits to the actor and indirect fitness benefits to recipients. While this is often assumed to be independent of group size, marginal benefits are in practice likely to be maximal at intermediate group sizes for many types of collective action problems, and will eventually become very small in large groups due to the law of decreasing returns. The second component is the response of social partners on the past play of an actor, which underlies conditional behaviour under repeated social interactions. We argue that under realistic conditions on the transmission of information in a population, this response on past play decreases rapidly with increasing group size so that reciprocity alone (whether direct, indirect, or generalised) cannot sustain cooperation in very large groups. The final component is the relatedness between actor and recipient, which, according to the rules of inheritance, again decreases rapidly with increasing group size. These results explain why helping behaviours in very large social groups are limited to cases where the number of reproducing individuals is small, as in social insects, or where there are social institutions that can promote (possibly through sanctioning) large-scale cooperation, as in human societies. Finally, we discuss how individually devisedinstitutions can foster the transition from small-scale to large-scale cooperative groups in human evolution

The Importance of Keeping the Big Ones: Harvest Slot Limits and Marine Protected Areas for the Management of the Caribbean Spiny Lobster

Fishing typically removes the oldest and/or largest individuals from populations undermining stability and reproductive success. Traditional fisheries management tools fail to protect these oldest and/or largest individuals, but two less conventional tools: marine protected areas (MPAs), and harvest slot limits have the potential to do so. Here I tested the possible use of these tools for the Caribbean spiny lobster, Panulirus argus, an iconic and economically valued species. After decades of intense fishing, the largest lobsters have largely been wiped out. The loss of the largest lobsters is significant as large lobsters have considerably greater reproductive potential than their smaller counterparts. I had four main objectives (1) developing a technique for directly ageing P. argus using banding in the gastric ossicles, (2) examining the possibility of reproductive senescence as it relates to body size in P. argus, (3) modeling the potential use of harvest slot limits and MPAs using a two-sex stage-structured matrix model, and (4) assessing the possible ecological consequences in terms of interactions with prey-species, of increasing the abundance and size of P. argus through a series of cafeteria trials. This work provides some necessary background information to support using MPAs and harvest slot limits in the management of P. argus in the Caribbean - calls for which has grown appreciably in recent years. Direct ageing of P. argus using bands in the gastric ossicles proved successful as it was possible to validate the ages of wild caught lobsters with lobsters of known age. The success of this technique opens up the potential for age based stock assessment and consideration of the relationship between size, age and reproduction. Lobsters were not found to exhibit reproductive senescence and for several of the metrics tested there was a positive relationship with parental size, confirming the biological value of retaining the largest lobsters in populations. The modeling demonstrated clearly the potential for MPAs and slot limits combined to increase the sizes and densities of P. argus in the marine environment, while the cafeteria trials demonstrated that larger lobsters did not have any appreciable preference for species of high ecological value

Environmental Impact Statement

Introduction Gray wolves (Canis lupus) are thriving and expanding in number and distribution in Montana. This is because of natural emigration from Canada and a successful federal effort that reintroduced wolves into Yellowstone National Park (YNP) and the wilderness areas of central Idaho. There are probably more wild wolves in Montana now than at any time in the past 70 years. Since 1974, the U.S. Fish and Wildlife Service (USFWS) has managed wolves in Montana, under the authority of the Endangered Species Act (ESA). The biological recovery goal for the northern Rockies wolf population is a total of 30 or more breeding pairs for three years in the states of Montana, Idaho, and Wyoming, with breeding pair being defined as a male and a female that raised at least two pups to December 31. The biological requirements for recovery were met at the end of 2002. But before USFWS will propose to delist, federal managers must be confident that a secure, viable population of gray wolves will persist if the protections of the ESA are removed. To provide that assurance, Montana, Idaho, and Wyoming must develop conservation and management plans and adopt other regulatory mechanisms in state law. Upon review and approval of the state plans, USFWS will propose to delist the gray wolf. Upon delisting, management authority for wolves will return to the state governments where wolves reside. Purpose and Need for the Proposed Action USFWS has managed wolves in Montana as endangered or as experimental, nonessential under the authority of ESA. In March 2003 USFWS down listed wolves in the Northwest Montana Recovery Area as threatened. Montana Fish, Wildlife & Parks (FWP) proposes to prepare and adopt a wolf conservation and management plan so that management authority can be transferred to the State of Montana because the biological recovery goal has been met. If Idaho, Wyoming and Montana do not develop and adopt conservation and management plans, which in combination must assure the long-term security of wolves in the northern Rockies, USFWS will not delist the gray wolf. In that case, wolves in Montana will continue to be managed by the federal government. USFWS anticipates the delisting process could begin in 2003 or 2004, if wolf management plans are completed by the three states and pass independent scientific peer review. The State of Montana would adopt a wolf conservation and management plan prior to USFWS’s proposal to delist wolves, but the plan would not be implemented until USFWS officially transfers legal authority to the state. Under Montana statute, FWP is the agency charged with conservation and management of resident wildlife. FWP recognizes the gray wolf as a native species and is committed to recovery of the species within Montana. The purpose of the plan is to manage wolves consistent with Montana’s own state laws, policies, rules, and regulations. FWP intends to implement positive conservation and management strategies to make sure that all federal requirements are met, recovery is complete, and that wolves are integrated as a valuable part of Montana’s wildlife heritage. FWP also recognizes that the long-term future of wolves in Montana depends on carefully balancing the complex biological, social, economic, and political aspects of wolf management. FWP will consider the wide spectrum of interests in designing and implementing a flexible program that is responsive and addresses the challenges faced by people directly affected by wolves