Optimal impulsive harvesting on non-autonomous Beverton–Holt difference equations

Optimal impulsive control in periodic ecosystem

Foresters often claim that the goal of good forest policy is to have a sustained forest yield, or even a maximum sustainable yield. They also claim that people wish to save a few extra trees for their children. This bequest motive is not modelled in the standard approach to the optimal rotation problem. In this paper, we present a standard version of an overlapping generation model augmented with a simple tree technology. We show in particular that the market equilibrium can be dynamically inefficient, and that a bequest motive in terms of trees can correct for the overaccumulation of capital that causes the inefficiency. The bequest motive also enables us to account for a harvesting intensity varying with age (young people typically cut more than elderly people) in spite of a perfect capital market.

The population dynamics of Rastrelliger kanagurta from the northwestern coastal waters of Sri Lanka were studied based on the length frequency data collected from October 1993 to September 1994. The resource is mainly exploited by gillnets and beach seines. The length frequency distributions ofRastreIliger kanagurta for the two gear types were similar with two prominent peaks at 13.5-15.5 cm and 20.524.5 cm (total length) length ranges. In addition, smaller individuals with total lengths varying from 7.5-10.5 cm were also observed among the beach seine catches.Population parameters were estimated using the FiSAT software package. The asymptotic length, growth constant and the growth performance index were estimated to be 28.0 cm (total length), 1.5 year -1 and 3.07 respectively. The estimated value for the natural mortality coefficient using the Pauly's empirical formula was 2.37 year-1. The fishing mortality coefficient for the combined fishery was estimated at 2.62 year-1 while the estimated values for the total mortality coefficient and the exploitation rates were 4.99 year-1 and 0.53 respectively. The recruitment was continuous with two peaks per year.The length based Thompson and Bell model was used in the bio­economic prediction. Of the possible scenarios, increasing the gillnet effort while maintaining that of the beach seines at the present level appeared to be the most realistic in accordance with the existing social and legal framework. The maximum sustainable yield and maximum sustainable economic yield for the combined fishery were estimated at 207 MT and 200 MT respectively. As the corresponding effort levels were 3 and 1.6 times the present effort, it is reasonable to conclude that the stocks are not over­exploited at present.

Ricker's stock-recruitment equation, including the multivariate ENSO index (MEI) as an environmental variable, was fitted to data of the Pacific sardine (Sardinops sagax caerulea) fishery from Magdalena Bay, Baja California Sur, Mexico. The equation was then incorporated into an age-structured, bioeconomic model. Uncertainty was incorporated by using environmental fluctuations; seven-year projections, equivalent to one sardine generation, were computed. Five management options were considered in the projections: open access, effort at maximum sustainable economic yield (fMSE), catch at maximum sustainable yield (CMSY), equivalent effort level applied in the year 2004 (f2004), and an arbitrary catch quota of 40000 tons (CQ40000). Projection results were summarised by the indicator Net Present Value (NPV) of the fishery for the modelled period. The strategies that involved some regulation in the effort level (fMSE and f2004) yielded the largest NPV. On the other hand, the strategies that involved regulation of the catch predicted—in addition to a lower NPV—a substantial increase in the effort to achieve the desired catch level. This study is the first bioeconomic approach for a sardine fishery management plan in this region.

Harvesting induced stability and instability in a tri-trophic food chain

In this paper, we consider a stochastic Gilpin-Ayala model under regime switching. Obtain the optimal harvesting effort and the maximum sustained yield by investigating the condition of average boundness of the system, and the ergodicity of the Markov chain. Also, through an example, we have proved our conclusion.

In this paper, we consider an autonomous model with impulsive harvest. We investigate the impulsive harvest policies for constant effort harvest and proportional harvest. For different harvest effort function, it is shown that there exists an unique impulsive periodic solution which is semi-stable or globally asymptotically stable. For the latter, the optimal harvest effort that maximizes the sustainable yield per unit time is determined.

Maximum Sustainable Yield

Using surplus production model packages of ASPIC (a stock-production model incorporating covariates) and CEDA (Catch effort data analysis), we analyzed the catch and effort data of Sillago sihama fishery in Pakistan. ASPIC estimates the parameters of MSY (maximum sustainable yield), F msy (fishing mortality), q (catchability coefficient), K (carrying capacity or unexploited biomass) and B1/K (maximum sustainable yield over initial biomass). The estimated non-bootstrapped value of MSY based on logistic was 598 t and that based on the Fox model was 415 t, which showed that the Fox model estimation was more conservative than that with the logistic model. The R 2 with the logistic model (0.702) is larger than that with the Fox model (0.541), which indicates a better fit. The coefficient of variation (cv) of the estimated MSY was about 0.3, except for a larger value 88.87 and a smaller value of 0.173. In contrast to the ASPIC results, the R 2 with the Fox model (0.651–0.692) was larger than that with the Schaefer model (0.435–0.567), indicating a better fit. The key parameters of CEDA are: MSY, K, q, and r (intrinsic growth), and the three error assumptions in using the models are normal, log normal and gamma. Parameter estimates from the Schaefer and Pella-Tomlinson models were similar. The MSY estimations from the above two models were 398 t, 549 t and 398 t for normal, log-normal and gamma error distributions, respectively. The MSY estimates from the Fox model were 381 t, 366 t and 366 t for the above three error assumptions, respectively. The Fox model estimates were smaller than those for the Schaefer and the Pella-Tomlinson models. In the light of the MSY estimations of 415 t from ASPIC for the Fox model and 381 t from CEDA for the Fox model, MSY for S. sihama is about 400 t. As the catch in 2003 was 401 t, we would suggest the fishery should be kept at the current level. Production models used here depend on the assumption that CPUE (catch per unit effort) data used in the study can reliably quantify temporal variability in population abundance, hence the modeling results would be wrong if such an assumption is not met. Because the reliability of this CPUE data in indexing fish population abundance is unknown, we should be cautious with the interpretation and use of the derived population and management parameters.

Forest soil carbon and nitrogen cycles under biomass harvest: Stability, transient response, and feedback

Pretty good yield (PGY) is a sustainable fish yield corresponding to obtaining no less than a specified large percentage of the maximum sustainable yield (MSY). We investigated 19 European fish stocks to test the hypothesis that the 95% PGY yield range is inherently precautionary with respect to impairing recruitment. An FMSY range was calculated for each stock as the range of fishing mortalities (F) that lead to an average catch of at least 95% of MSY in long-term simulations. Further, a precautionary reference point for each stock (FP.05) was defined as the F resulting in a 5% probability of the spawning-stock biomass falling below an agreed biomass limit below which recruitment is impaired (Blim) in long-term simulations. For the majority of the stocks analysed, the upper bound of the FMSY range exceeded the estimated FP.05. However, larger fish species had higher precautionary limits to fishing mortality, and species with larger asymptotic length were less likely to have FMSY ranges impairing recruitment. Our study shows that fishing at FMSY generally is precautionary with respect to impairing recruitment for highly exploited teleost species in northern European waters, whereas the upper part of the range providing 95% of MSY is not necessarily precautionary for small- and medium-sized teleosts.

This study compares the harvest capacity of Taiwan's offshore fishing fleet to sustainable yields of offshore fisheries and evaluates different legislative strategies designed to reduce the fishing fleet. Aggregate offshore fisheries' stock changes and harvest functions are specified and estimated. Results show that the stock has been declining since 1973. Based on dynamic simulations, this study shows that neither the program to restrict the building of new vessels nor a combination of this program with the vessel retirement and buy back program is sufficient to avoid the downward trend in harvests and the deteriorating state of stocks. While reducing fishing effort to the maximum sustainable yield (MSY) level might suffice as an initial vessel reduction measure, attaining MSY within 5 to 10 years seems preferable over a one-year approach. The long-run economic situation would be further improved by an additional reduction of fishing effort to the optimal yield (OY) level.

Attaining maximum sustained yield (MSY) is a central goal in U.S. fisheries management. To attain MSY, fishing mortality is maintained at FMSY and biomass at BMSY. Replacing FMSY and BMSY by “proxies” for FMSY and BMSY is commonplace. However, these proxies are not equivalent to FMSY and BMSY. The lack of equivalency is an important issue with regard to whether MSY is attained or whether biomass production is wasted. In this paper we study the magnitude of the equivalency. We compare FMSY/BMSY (calculated using the ASPIC toolbox) with the proxy estimates, F40%/B40%, published in GARM III. Our calculations confirm that in general the FMSY/BMSY calculations differ from the GARM III proxy estimates. The proxy estimates generally indicate that the stocks are overfished and are at relatively low biomasses, while the ASPIC estimates generally reflect the opposite: the stocks are not overfished and are at relatively high levels of abundance. In comparing the two approaches, the ASPIC estimates appeared favorable over the proxy estimates because 1) the ASPIC estimates involve only a few parameters in contrast to the many parameters estimated in the proxy approach, 2) “real variance” estimates for the proxy are not available so that it is difficult to evaluate the statistical adequacy of the proxy approach relative to the ASPIC approach, and 3) the proxy approach is based on many components (e.g., growth, stock and recruitment, etc.) that are subject to considerable uncertainty.

In this paper, the optimization problem of harvesting for a stochastic predator-prey model with S-type distributed time delays (which contain both discrete time delays and continuously distributed time delays) is studied by using ergodic method. Sufficient and necessary conditions for the existence of optimal harvesting strategy are obtained. Moreover, the optimal harvesting effort (OHE, for short) and the maximum of expectation of sustainable yield (MESY, for short) are given. Some numerical simulations are introduced to illustrate our main results.

A family of general production curves for exploited populations