Extinction and Persistence of Species in Discrete Competitive Systems with a Safe Refuge

AbstractWe analyze a two species discrete competition model in which one species diffuses between two patches, A and B. In this model, two species, species 1 and 2, compete in patch A with species 1 being the sedentary species. Thus, patch B is a safe refuge for species 2. We obtain sufficient conditions for the extinction of species 1. Species 2 is the superior competitor whenever a linear combination of its growth rates always exceeds the growth rate of the sedentary species 1. By using a specific example, we demonstrate that providing a safe refuge does not always make a species a superior competitor. In fact, without diffusion, species 2 drives species 1 to extinction. However, with the addition of diffusion, there is stable coexistence of the two species. If the safe refuge is not suitable for its growth and reproduction, species 2 may go extinct. We obtain sufficient conditions for the extinction of species 2. We also show that a species persists whenever all of its carrying capacities are sufficiently large. This result rules out the possibility of a population becoming arbitrarily close to zero and therefore risking extinction

Population Models in Almost Periodic Environments

We establish the basic theory of almost periodic sequences on Ζ+. Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models

Modelling Wolbachia Infection in a Sex-Structured Mosquito Population Carrying West Nile Virus

Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected mosquito population. Our model incorporates the key effects of Wolbachia infection including cytoplasmic incompatibility and male killing. We also allow the possibility of reduced reproductive output, incomplete maternal transmission, and different mortality rates for uninfected/infected male/female individuals. We study the existence and local stability of equilibria, including the biologically relevant and interesting boundary equilibria. For some biologically relevant parameter regimes there may be multiple coexistence steady states including, very importantly, a coexistence steady state in which Wolbachia infected individuals dominate. We also extend the model to incorporate West Nile virus (WNv) dynamics, using an SEI modelling approach. Recent evidence suggests that a particular strain of Wolbachia infection significantly reduces WNv replication in Aedes aegypti. We model this via increased time spent in the WNv-exposed compartment for Wolbachia infected female mosquitoes. A basic reproduction number R0 is computed for the WNv infection. Our results suggest that, if the mosquito population consists mainly of Wolbachia infected individuals, WNv eradication is likely if WNv replication in Wolbachia infected individuals is sufficiently reduced

Global Stability of Cycles: Lotka-Volterra Competition Model with Stocking

In this article, we prove that in connected metric spaces k - cycles are not globally attracting (where k\u3e2). We apply this result to a two species discrete-time Lotka-Volterra competion model with stocking. In particular, we show that an k-cycle cannot be the ultimate life-history of evolution of all population sizes. This solves Yakubu\u27s conjecture but the question on the structure of the boundary of the basins of attraction of the locally stable n-cycles is still open

The Impact of Working Capital Management on Corporate Performance: Evidence from Listed Non-Financial Firms in Ghana

Working Capital Management (WCM) plays a significant role in the successful operation of businesses due to its significant effect on corporate profitability and liquidity. This study empirically examines the impact of working capital management on the performance of non-financial firms in Ghana. Using secondary data of five listed non-financial firms for the period 2010-2015, the Random effect model was employed to establish the relationship that exists between the various components of working capital management and firm performance and whether these WCM components impact significantly on firm performance. The results show that average payment period and current ratio have a positive relationship with firm performance. Average collection period, inventory turnover, cash conversion cycle, and firm size on the other hand have a negative relationship with firm performance. However, only average collection period, average payment period, cash conversion cycle, and current ratio are found to have a significant impact on firm performance. The study recommends that managers of non-financial firms in Ghana should formulate sound working capital management policies that will enable firms to deal with liquidity challenges and enhance their performance

Constant proportion harvest policies: Dynamic implications in the Pacific halibut and Atlantic cod fisheries

a b s t r a c t Overfishing, pollution and other environmental factors have greatly reduced commercially valuable stocks of fish. In a 2006 Science article, a group of ecologists and economists warned that the world may run out of seafood from natural stocks if overfishing continues at current rates. In this paper, we explore the interaction between a constant proportion harvest policy and recruitment dynamics. We examine the discrete-time constant proportion harvest policy discussed in Ang et al. We focus on constant proportion policies (CPPs). CPPs have the potential to stabilize complex overcompensatory stock dynamics, with or without the Allee effect, provided the rates of harvest stay below a threshold. If that threshold is exceeded, CPPs are known to result in the sudden collapse of a fish stock when stock recruitment exhibits the Allee effect. In case studies, we analyze CPPs as they might be applied to Gulf of Alaska Pacific halibut fishery and the Georges Bank Atlantic cod fishery based on harvest rates from 1975 to 2007. The best fit models suggest that, under high fishing mortalities, the halibut fishery is vulnerable to sudden population collapse while the cod fishery is vulnerable to steady decline to zero. The models also suggest that CPP with mean harvesting levels from the last 30 years can be effective at preventing collapse in the halibut fishery, but these same policies would lead to steady decline to zero in the Atlantic cod fishery. We observe that the likelihood of collapse in both fisheries increases with increased stochasticity (for example, weather variability) as predicted by models of global climate change

Toxicity of Bacillus thuringiensis biopesticide produced in shrimp pond sludge as alternative culture medium against Bactrocera dorsalis (Hendel)

Among entomopathogenic bacteria, Bacillus thuringiensis (Bt) has been widely used to replace the conventional chemical pesticides to control insect pets. However, their application is limited due to high production cost through fermentation. In this study, shrimp pond sludge was used as an alternate culture medium for Bt ATCC10792. The sludge was used under three different preparations; (i) without pre-treatment, (ii) with acid treatment (hydrolysed sludge) and (iii) the supernatant obtained after the centrifugation of the hydrolysed sludge. Bacterial growth rate and sporulation were evaluated throughout the fermentation. The highest growth rate and sporulation were observed in hydrolysed sludge with 7.44x106±5.16 CFU/ml and 5.90x106±7.88 CFU/ml, respectively. Bioassay of entomotoxicity test was also carried out on the fruit fly larva, Bactrocera dorsalis (Hendel) and 81.2% mortality was observed. A significant deterioration was observed in larval weight and size. Larval pupation was also reduced in size where treated pupa was 30% smaller than the control and therefore lowering the adult fly emergence rate. Emerged adult fruit fly showed physical deterioration on the morphology (undeveloped, crumpled wings and cranked abdomen) and significantly affecting the survival rate of the flies. This study has proven the potential of shrimp pond sludge to be used as an alternate culture medium for Bt-based biopesticides production

Identification of bioactive compounds produced by bacteria-based biopesticides, Bacillus thuringiensis ATCC 10792 produced in shrimp pond sludge

Biological controls of destructive pest in forest and agriculture sector using bacteria were proven to minimize the problems caused by the usage of chemical insecticides. However, their application is limited due to high production cost through fermentation. In this study, shrimp pond sludge and wastewater were used as an alternate culture medium for bacteria-based biopesticides production. It has been determined by previous part of this study that Bacillus thuringiensis ATCC 10792 in hydrolysed shrimp pond has showed the highest potential to be used as bacteria-based biopestecides based on their high growth rate (7.44x106 ± 5.16 CFU/ml) and sporulation (5.90x106 ± 7.88 CFU/ml). Bioassay of entomotoxicity also showed high mortality rate, disruption on the target insect physically and affect the life cycle of the target insect. Hence, proteomic analysis using SDS-Page and MALDITOF-MS were conducted to identify the bioactive compound that contribute to the toxicity of the bacteria-based biopesticides produced. Separation and identification of the bioactive components produced by the bacteria during the fermentation were done and two types of protein were produced by the bacteria. Superoxide dismustase and spore coat protein were identified to be produced during the fermentation and respectively play an important roles to the toxicity of the bacteria. This study showed the potential of Bt ATCC10792 to be used as biopesticides