Analysis of optimal harvesting of a predator-prey model with Holling type IV functional response

This paper investigates a series of harvesting problems of a harvested predator-prey system with Holling type IV functional response. The bionomic equilibrium, the maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system are studied. It is proved that the MSTY does not exist under the independent harvesting mode, while it may be found with the same predator and prey harvesting efforts mode. By applying the Bang-Bang control and the singular control to the harvesting strategy, the optimal equilibrium state of the discussed system converges faster than that of the system utilizing a single harvesting strategy with the fixed harvesting effort. The MISER 3 software package is adopted to obtain the optimization schemes of two control problems by using the control parameterization method. The findings of our study provide a theoretical basis for biological resource management.     

Human Adaptive Behavior in Common Pool Resource Systems

Overexploitation of common-pool resources, resulting from uncooperative harvest behavior, is a major problem in many social-ecological systems. Feedbacks between user behavior and resource productivity induce non-linear dynamics in the harvest and the resource stock that complicate the understanding and the prediction of the co-evolutionary system. With an adaptive model constrained by data from a behavioral economic experiment, we show that users’ expectations of future pay-offs vary as a result of the previous harvest experience, the time-horizon, and the ability to communicate. In our model, harvest behavior is a trait that adjusts to continuously changing potential returns according to a trade-off between the users’ current harvest and the discounted future productivity of the resource. Given a maximum discount factor, which quantifies the users’ perception of future pay-offs, the temporal dynamics of harvest behavior and ecological resource can be predicted. Our results reveal a non-linear relation between the previous harvest and current discount rates, which is most sensitive around a reference harvest level. While higher than expected returns resulting from cooperative harvesting in the past increase the importance of future resource productivity and foster sustainability, harvests below the reference level lead to a downward spiral of increasing overexploitation and disappointing returns.     

The structure of optimal time- and age-dependent harvesting in the Lotka-McKendrik population model

The paper analyzes optimal harvesting of age-structured populations described by the Lotka-McKendrik model. It is shown that the optimal time- and age-dependent harvesting control involves only one age at natural conditions. This result leads to a new optimization problem with the time-dependent harvesting age as an unknown control. The integral Lotka model is employed to explicitly describe the time-varying age of harvesting. It is proven that in the case of the exponential discounting and infinite horizon the optimal strategy is a stationary solution with a constant harvesting age. A numeric example on optimal forest management illustrates the theoretical findings. Discussion and interpretation of the results are provided.     

东江七种鱼类的生活史类型研究

本文通过渐近体长(L∞)、渐近体重(W∞)、生长系数(K)、初次生殖年龄(Tm)、最大年龄(Tmax)、瞬时自然死亡率(M)和性腺指数(Gl)等7个生态学参数来分析鱼类种群生活史类型。根据r-选择和K-选择的典型特征以及各参数间相互关系的显著性,性腺指数、瞬时死亡率和生长系数是判断东江7种鱼类种群偏向rF)和改变渔业补充年龄(tc)时的产量变化,分析产量变化曲线可知,作为偏向r型的种群,提高捕捞强度不能增加渔业产量,适当的捕捞强度可以取得较高的产量;在低龄阶段提高起捕年龄能增加一定产量,但到达一定年龄后再提高起捕年龄,反而引起产量大幅度下降。只有合理控制捕捞强度和起捕年龄,才能获取最大持续产量。       

Fishery policy when considering the future opportunity of harvesting

Free access to a common pool of resource in a country may lead to over-exploitation and sacrifice future opportunities of harvesting. As such, the protection of a common fishery resource is worth investigating. In this paper we develop a two-period model and a multi-period model to analyze the optimal inter-temporal utilization of a finite resource of stock and propose to impose a tax on the harvest rate as an efficient mechanism with an aim at economic sustainability by incorporating the future opportunity of harvesting into the models as a major component of social objectives. The sensitivity analysis of the two-period model shows that (1) labor inputs for harvesting in Period 1 should be reduced, the biomass of fishery stock will increase, but the harvesting in Period 2 should be amplified and the biomass of fishery stock in Period 2 will not be affected if the current generation owns a higher valuation on the future opportunity of harvesting; (2) a higher internal regeneration rate leads to higher harvesting in each period and a higher level of fishery stock in Period 1, but an uncertain level of fishery stock in Period 2; (3) with a higher discount rate the harvesting in Period 1 should increase, but the harvesting in Period 2 should fall and the level of fishery stock in each period will be reduced; (4) a higher fish price in Period 1 leads to higher harvesting in Period 1, but reduced harvesting in Period 2. As a consequence, the level of fishery stock in each period will be reduced; (5) the effect of a change in fish prices in Period 2 on the harvesting and the level of fishery stock in Period 1 is uncertain, but the change in fish prices in Period 2 gives a positive effect on harvesting in Period 2 and a negative effect on the level of fishery stock in Period 2; (6) higher labor wages in Period 1 lead to lower harvesting, but a higher level of fishery stock in Period 1. This encourages an increase in harvesting in Period 2 and leads to a higher level of fishery stock in Period 2; and (7) a change of the labor wage in Period 2 affects the harvesting and the level of fishery stock in Period 1 indecisively, but it gives negative effects on the harvesting in Period 2 and positive effects on the level of fishery stock in Period 2.     

Optimal death strategy of animal populations

Using Pontryagin's maximum principle, the optimal death strategy that maximizes the total reproduction of a population, which has the density dependent growth rate and the weight dependent reproduction, is investigated. As the result, it is shown that the optimal survival curve has a critical age, before which the mortality takes the highest admissible value and after which the lowest. In a population with this optimal death strategy, the change of resource level affects the length of the stage of high mortality. The switching age is explicitly calculated in a special case with a simple growth rate function and a simple weight dependence of reproduction. The average value of mortality or growth coefficient through the prereproductive stages are calculated and compared with the Le Cren's data, where trout was reared in varying resource levels.     

Optimal harvesting strategies for timber and non-timber forest products in tropical ecosystems

Harvesting wild plants for non-timber forest products (NTFPs) can be ecologically sustainable–without long-term consequences to the dynamics of targeted and associated species–but it may not be economically satisfying because it fails to provide enough revenues for local people over time. In several cases, the same species can be harvested for NTFP and also logged for timber. Three decades of studies on the sustainability of NTFP harvest for local people’s livelihood have failed to successfully integrate these socio-economic and ecological factors. We apply optimal control theory to investigate optimal strategies for the combinations of non-lethal (e.g., NTFP) and lethal (e.g., timber) harvest that minimize the cost of harvesting while maximizing the benefits (revenue) that accrue to harvesters and the conservation value of harvested ecosystems. Optimal harvesting strategies include starting with non-lethal NTFP harvest and postponing lethal timber harvesting to begin after a few years. We clearly demonstrate that slow growth species have lower optimal harvesting rates, objective functional values and profits than fast growth species. However, contrary to expectation, the effect of species lifespan on optimal harvesting rates was weak suggesting that life history is a better indicator of species resilience to harvest than lifespan. Overall, lethal or nonlethal harvest rates must be <40 % to ensure optimality. This optimal rate is lower than commonly reported sustainable harvest rates for non-timber forest products.     

Incentives for collecting Gaharu (fungal-infected wood ofaquilaria Spp.; thymelaeaceae) in east Kalimantan

The economic importance of gaharu is assessed in three villages on the Bahau River in north-central Borneo to gain insights about the incentives for harvesting and management of a valuable nontimber forest product. Three indicators of economic value—level and proportion of income, returns to labor, and proportion of gaharu collecting households per village—are used to demonstrate the multiple incentives that NTFP income can generate. The concept of incentive logic is developed as an analytical technique to show how economic values can be linked to incentives for different types of management actions. The article discusses how incentives from gaharu income were most likely linked to the stake local people had in the resource, their preferences about which forest product to harvest, and their willingness to engage in collective action. These incentives contributed to sustainability to the extent they induced actions that reduce threats to the resource. The article suggests that an understanding of the influence of economic incentives on people’s resource management can be improved by recognizing three factors: the multiple incentives created by an income, the logical link of those incentives to a management action, and the influence of other sociocultural and biophysical factors on management.     

尖头塘鳢(Eleotris oxycephala Temmiuck et Schlegel)的年龄、生长和生活史类型的研究

本文采用胸鳍第二支鳍骨为研究东江尖头塘鳢的年龄鉴定材料。胸鳍第二支鳍骨(远侧部)长的骨(R)与体长(L)的关系L=10.6565 54.3848R。用von Bertalanffy生长方程可表达体长、体重与年龄的关系:L=298.6(1-e~(-0.2313(t 0.3028))];W_t=577.4(1-e~(-0.2313(t 0.3028))]~3。根据r-选择和K-选择的典型特征以及渐近体长(L_∞)、渐近体重(W_∞)、生长系数(K)、瞬时自然死亡率(M)、初次生殖年龄(T_m)、最大年龄(T_(max))和性腺指数(GI)等7个生态学参数值,可以判断尖头塘鳢偏向r-选择。应用平衡产量模式计算改变瞬时捕捞死亡率(F)和渔业补充年龄(t_c)时的产量变化,同样证实尖头塘鳢生活史偏向r-选择。作为渔业管理对策,尖头塘鳢的捕捞年龄可定为2—3龄,以2龄为主,这样既能保护资源,又能获得较好的经济效益。     

Harvesting in a resource dependent age structured Leslie type population model

We analyse the effect of harvesting in a resource dependent age structured population model, deriving the conditions for the existence of a stable steady state as a function of fertility coefficients, harvesting mortality and carrying capacity of the resources. Under the effect of proportional harvest, we give a sufficient condition for a population to extinguish, and we show that the magnitude of proportional harvest depends on the resources available to the population. We show that the harvesting yield can be periodic, quasi-periodic or chaotic, depending on the dynamics of the harvested population. For populations with large fertility numbers, small harvesting mortality leads to abrupt extinction, but larger harvesting mortality leads to controlled population numbers by avoiding over consumption of resources. Harvesting can be a strategy in order to stabilise periodic or quasi-periodic oscillations in the number of individuals of a population.     

An assessment of the maximum sustainable yield of ivory from African elephant populations.

A general, logistic population model is used to explore the dynamics of harvested elephant populations. The model includes two features peculiar to elephant populations and the harvesting of ivory. First, because of the shape of the growth curve of tusks with age, the conversion factor that relates the number of elephants killed to the ivory yield in weight is not constant, but a function of the population size. Second, tusks from animals that die from natural causes can be retrieved and included in the total yield of ivory. The implications of the relationship between tusk size and age of an animal on the maximum sustainable yield in terms of ivory tonnage and in terms of the number of tusks are explored. The nonequilibrium implications of the tusk growth curve on the population dynamics under different harvesting strategies are also investigated. Results indicate that the maximum sustainable yield is achieved at very low harvest rates with population levels close to the pristine equilibrium. When tusks from animals that die of natural causes are included in the harvest, the maximum yield may, depending on the mortality and recruitment parameters, occur when there is no direct harvest.     

Sustainable harvesting of wild seaweed resources

Abstract

Macroalgae have played an important role in coastal communities for centuries. In the past, they have been harvested and gathered from shorelines around the world for traditional uses such as food, animal feed and a crude fertilizer (marine manure). Today, seaweeds are used in a multitude of applications with expanding global industries based on hydrocolloids, cosmetics and food supplements, and also as a potential biofuel source. However, of the approximately 10?000 algal species reported to exist, only a small number are commercially utilized. While representing only a small fraction of total global seaweed production, harvesting and gathering ‘wild’ seaweeds has had, and continues to have, an integral role in many coastal societies, often being intrinsically linked to the cultural identity of those coastal communities. Today, 32 countries actively harvest seaweeds from wild stocks, with over 800?000 t harvested annually from natural beds. It is vitally important that seaweeds are utilized sustainably and that natural resources are effectively managed by coastal communities with vested interests around the world. As the popularity of seaweeds increases and the use of less traditional species with novel applications comes to the fore, it is critically important to make certain that the sustainability of the resource is ensured given the increased pressures of harvesting. Issues exist regarding ownership of the resource and its over-exploitation, and the implementation of environmentally damaging harvesting techniques must be avoided. Resource scientists, managers, conservationists, governments, and other stakeholders need to be proactive in the sustainable management of these vulnerable, yet valuable, resources.     

Sustainable forestry: A model of the effects of nitrogen removals in wood harvesting and fire on the nitrogen balance of regrowth eucalypt stands

Abstract Sustainable forest use is an integral part of Australia's recently adopted National Forest Policy; consequently, there is an urgent need for quantitative, ecologically based measures of sustainability. One process that may affect ecosystem sustainability is the removal of nutrients through forest harvesting and fire. This paper presents a model-based analysis of the combined consequences of harvesting and fire management practices for the nitrogen (N) budgets of managed forest ecosystems. The model, called N-BAL, evaluates the balance between N removals due to harvesting and fire (prescribed and regeneration burns), and N inputs (both natural and as added fertilizer), and leads to a criterion for the maintenance of site N reserves. That criterion can be used to estimate the accretion (or depletion) of site N over a single forest rotation, or to predict sustainable stem productivity for given N inputs and management practices. The analysis is applied to managed stands of karri (Eucalyptus diversicolor F. Muell.) in southwestern Australia to investigate whether natural N inputs are sufficient to maintain site N capital under current harvesting and fire practices. Model predictions for stands harvested at age 100 years with slash burns and regular prescribed burns range from a rotation-averaged depletion rate of 22 kg ha^?1 year^?1 to an annual accretion of 14 kg ha^?1 year^?1, depending on assumed N inputs and fire frequency and intensity. The mean annual N balance is highly sensitive to rates of natural N inputs, fire intensity and inter-fire period, and less sensitive to rotation length. These results are tentative and highlight the need for further research to improve estimates of several key model parameters and relationships.     

State-dependent life-history equations

Matrix population models provide a natural tool to analyse state-dependent life-history strategies. Reproductive value and the intrinsic rate of natural increase under a strategy, and the optimal life-history strategy can all be easily characterised using projection matrices. The resultant formulae, however, are not directly comparable with the corresponding formulae for age structured populations such as Lotka's equations and Fisher's formula for reproductive value. This is because formulae involving projection matrices lose track of what happens to an individual over its lifetime and are only concerned with expected numbers of descendants one time step in the future. In contrast the usual age-dependent formulae explicitly followed a single individual through from birth to death.In this paper I show how the state-dependent formulae can be rewritten to be directly comparable with the standard age-structured formulae. Although the formulae are intuitively obvious the decomposition into current and future reproductive success differs from that previously given and is, I suggest, a more natural definition. The derivation of appropriate equations for optimal life-histories relies on results from dynamic programming theory; and is much more general and easier than previous derivations.The value of rewriting projection matrix results in terms of the lifetime of an individual organism is illustrated by an example in which the optimal plastic response to an environment is derived.     

Effects of harvesting on spatial and temporal diversity of carbon stocks in a boreal forest landscape

Carbon stocks in managed forests of Ontario, Canada, and in harvested wood products originated from these forests were estimated for 2010–2100. Simulations included four future forest harvesting scenarios based on historical harvesting levels (low, average, high, and maximum available) and a no‐harvest scenario. In four harvesting scenarios, forest carbon stocks in Ontario's managed forest were estimated to range from 6202 to 6227 Mt C (millions of tons of carbon) in 2010, and from 6121 to 6428 Mt C by 2100. Inclusion of carbon stored in harvested wood products in use and in landfills changed the projected range in 2100 to 6710–6742 Mt C. For the no‐harvest scenario, forest carbon stocks were projected to change from 6246 Mt C in 2010 to 6680 Mt C in 2100. Spatial variation in projected forest carbon stocks was strongly related to changes in forest age (r = 0.603), but had weak correlation with harvesting rates. For all managed forests in Ontario combined, projected carbon stocks in combined forest and harvested wood products converged to within 2% difference by 2100. The results suggest that harvesting in the boreal forest, if applied within limits of sustainable forest management, will eventually have a relatively small effect on long‐term combined forest and wood products carbon stocks. However, there was a large time lag to approach carbon equality, with more than 90 years with a net reduction in stored carbon in harvested forests plus wood products compared to nonharvested boreal forest which also has low rates of natural disturbance. The eventual near equivalency of carbon stocks in nonharvested forest and forest that is harvested and protected from natural disturbance reflects both the accumulation of carbon in harvested wood products and the relatively young age at which boreal forest stands undergo natural succession in the absence of disturbance.     

中国“三大经济模式”的可持续发展——以真实发展指标对6个典型城市的可持续性评估为例

“珠江模式”、“温州模式”、“苏南模式”的发源地是中国经济发展的前沿地带,评估其可持续发展情况对中国经济的下一步发展具有重要的指导意义.本文采用真实发展指标(GPI),评估了1995—2012年中国“三大经济模式”下广州、深圳、温州、苏州、无锡、常州6个典型城市的可持续发展情况.结果表明: 研究期间,6个城市的GDP呈指数型增长,但GPI在1995—2005年间并无增长,2005年以后才开始上升,GPI与GDP的差距越来越大;“珠江模式”虽然经济增长迅猛,但经济、社会、环境损耗突出,实现其可持续发展必须解决分配不均、交通拥堵、环境污染等问题;“温州模式”人均GPI后期与其他城市拉开差距,发展后劲不足,贫富差距突出,社会账户水平较低且增长缓慢,发展方式亟待转型;“苏南模式”虽然资源消耗较为突出,但各类损耗处于中等水平,经济增长迅猛,社会账户水平稳步提高,GPI所反映出的真实发展水平也较高,相对具有可持续发展潜力.“三大经济模式”应持续关注可持续发展的经济、环境与社会三大方面,而“珠江模式”、“温州模式”应更积极地寻求发展转型.     

Adaptive changes in harvested populations: plasticity and evolution of age and size at maturation

We investigate harvest-induced adaptive changes in age and size at maturation by modelling both plastic variation and evolutionary trajectories. Harvesting mature individuals displaces the reaction norm for age and size at maturation toward older ages and larger sizes and rotates it clockwise, whereas harvesting immature individuals has the reverse qualitative effect. If both immature and mature individuals are harvested, the net effect has approximately the same trend as when harvesting immature individuals only. This stems from the sensitivity of the evolutionary response, which depends on the maturity state of harvested individuals, but also on the type of harvest mortality (negatively or positively density dependent, density independent) and the value of three life-history parameters (natural mortality, growth rate and the trade-off between growth and reproduction). Evolutionary changes in the maturation reaction norm have strong repercussions for the mean size and the density of harvested individuals that, in most cases, result in the reduction of biomass--a response that population dynamical models would overlook. These results highlight the importance of accounting for evolutionary trends in the long-term management of exploited living resources and give qualitative insights into how to minimize the detrimental consequences of harvest-induced evolutionary changes in maturation reaction norms.     

The economic value and sustainable harvest of plants and animals from the tropical forest: Assumptions,hypotheses, and methods

Recent studies of non-timber products from tropical rain forests have emphasized the economic value of these products and the sustainability of present harvests. Many of these studies rely upon a set of untested assumptions about the effects of harvesting upon the forest and the economic value of non-timber forest products in both the marketplace and in the daily life of rural people. These assumptions were formulated as a series of hypotheses during the workshop held in the Regional Community Forestry Training Center, Kesetsart University, Bangkok, in May 1992. The six hypotheses developed by workshop participants will be used to guide future research. As the hypotheses are tested, the data will be used to create a more realistic assessment of the sustainability and economic value of extraction of non-timber products from tropical forests.     

The effect of optimal harvesting on the dynamics of size and genetic composition of a two-age population

The effect of optimal stationary harvesting at a constant harvest rate on the dynamics of a two-age population is considered. It has been shown analytically that harvesting a fixed rate of the population size of only one age cohort is optimal. As has been observed, the maximum of revenue function is unattainable in the case of concurrent harvesting of both age cohorts. It has been demonstrated that the direction of natural selection does not explicitly change when unselectively harvesting individuals; however, the adaptive genetic diversity of an unharvested population can be lost due to harvesting.     

Optimization of harvesting age in an integral age-dependent model of population dynamics

The paper deals with optimal control in a linear integral age-dependent model of population dynamics. A problem for maximizing the harvesting return on a finite time horizon is formulated and analyzed. The optimal controls are the harvesting age and the rate of population removal by harvesting. The gradient and necessary condition for an extremum are derived. A qualitative analysis of the problem is provided. The model shows the presence of a zero-investment period. A preliminary asymptotic analysis indicates possible turnpike properties of the optimal harvesting age. Biological interpretation of all results is provided.