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.     

A theory for optimal monitoring of marine reserves

Monitoring of marine reserves has traditionally focused on the task of rejecting the null hypothesis that marine reserves have no impact on the population and community structure of harvested populations. We consider the role of monitoring of marine reserves to gain information needed for management decisions. In particular we use a decision theoretic framework to answer the question: how long should we monitor the recovery of an over‐fished stock to determine the fraction of that stock to reserve? This exposes a natural tension between the cost (in terms of time and money) of additional monitoring, and the benefit of more accurately parameterizing a population model for the stock, that in turn leads to a better decision about the optimal size for the reserve with respect to harvesting. We found that the optimal monitoring time frame is rarely more than 5 years. A higher economic discount rate decreased the optimal monitoring time frame, making the expected benefit of more certainty about parameters in the system negligible compared with the expected gain from earlier exploitation.     

The distribution of the coalescence time and the number of pairwise nucleotide differences in a model of population divergence or speciation with an initial period of gene flow

This paper is concerned with a model of “isolation with an initial period of migration”, where a panmictic ancestral population split into n descendant populations which exchanged migrants symmetrically at a constant rate for a period of time and subsequently became completely isolated. In the limit as the population split occurred an infinitely long time ago, the model becomes an “isolation after migration” model, describing completely isolated descendant populations which arose from a subdivided ancestral population. The probability density function of the coalescence time of a pair of genes and the probability distribution of the number of pairwise nucleotide differences are derived for both models. Whilst these are theoretical results of interest in their own right, they also give an exact analytical expression for the likelihood, for data consisting of the numbers of nucleotide differences between pairs of DNA sequences where each pair is at a different, independent locus. The behaviour of the distribution of the number of pairwise nucleotide differences under these models is illustrated and compared to the corresponding distributions under the “isolation with migration” and “complete isolation” models. It is shown that the distribution of the number of nucleotide differences between a pair of DNA sequences from different descendant populations in the model of “isolation with an initial period of migration” can be quite different from that under the “isolation with migration model”, even if the average migration rate over time (and hence the total number of migrants) is the same in both scenarios. It is also illustrated how the results can be extended to other demographic scenarios that can be described by a combination of isolated panmictic populations and “symmetric island” models.     

Optimal age-dependent sustainable harvesting of natural resource populations: Sustainability value

We studied the optimal age-dependent harvesting of a natural resource population that achieves a maximum income under the constraint of sustainability, i.e. the reproductive adults numbers must exceed a given minimum. The resource species is assumed to be semelparous (a single reproduction over a life). The economic value and natural mortality coefficient can vary with age. The optimal age-dependent harvesting under the sustainability constraint is obtained using Pontryagin’s maximum principle. The constraint of resource sustainability can be treated as an additional term measured in the same units as economic income. Specifically, three terms: (1) current harvesting value, (2) future harvesting value, and (3) sustainability value, are calculated for each age, and the resources should be harvested at the maximum rate when their current harvesting value is greater than the sum of future harvesting value and sustainability value, and should not be harvested otherwise. Numerical analyses of several cases demonstrated that the optimal harvesting schedule depends critically on the natural mortality coefficient and the functional form of the economic value of the resource.     

Seagrass bed patchiness: effects on epifaunal communities in San Diego Bay, USA

Seagrass habitat structure influences epifaunal density, diversity, community composition and survival, but covariation of structural elements at multiple scales (e.g., shoot density or biomass per unit area, patch size, and patch configuration) can confound studies attempting to correlate habitat structure with ecological patterns and processes. In this study, we standardized simulated seagrass shoot density and bed area among artificial seagrass beds in San Diego Bay, California, USA to evaluate the singular effect of seagrass bed configuration (“patchiness”) on the density and diversity of seagrass epifauna. Artificial seagrass beds all were 1 m², but were composed of a single large patch (“continuous” treatment), four smaller patches (“patchy” treatment), or 16 very small patches (“very patchy” treatment). We allowed epifauna to colonize beds for 1 month, and then sampled beds monthly over the next 3 months. Effects of seagrass bed patchiness on total epifaunal density and species-specific densities were highly variable among sampling dates, and there was no general trend for the effects of fragmentation on epifaunal densities to be positive or negative. Epifaunal diversity (measured as Simpson's index of diversity) was highest in very patchy or patchy beds on two out of the three sampling dates. Very patchy beds exhibited the highest dissimilarity in community composition in the first two sampling periods (August and September), but patchy beds exhibited the highest dissimilarity in the third sampling period (October). Our results indicate that seagrass patch configuration affects patterns of epifaunal density, diversity, and community composition in the absence of covarying bed area or structural complexity, and that patchy seagrass beds may be no less valuable as a habitat than are continuous seagrass beds. The spatial pattern employed when harvesting or planting seagrass may influence epifaunal habitat use and should be a key consideration in restoration plans.     

Tipping points and user-resource system collapse in a simple model of evolutionary dynamics

The growing demand for ecological resources puts pressure on many ecosystems and, in extreme cases, threatens the long-term survival of the associated social–ecological system. The sustainable use of resources helps to avoid the collapse of the system, but requires the balancing of two conflicting aims: the preservation of resource productivity and the provision of satisfactory returns. Although humans can consider expected future pay-offs in decision-making, the inherent variability of ecological resources makes future returns uncertain and complicates the determination of sustainable harvest behaviours. We present here an adaptive model in which human harvest behaviour is linked to a renewable resource with a randomly fluctuating growth rate. In the model, users adjust their harvest behaviour following a trade-off between the potential current harvest and the discounted future productivity of the resource. Our analyses reveal that rising resource variability increases the discount factor required for a sustainable harvest and reduces long-term pay-offs. A high discount factor, indicating certain future returns, makes the user-resource system robust against resource fluctuations albeit at the cost of a lowered maximum total harvest. By considering the user-resource system as a single co-evolving entity, our approach allows for the determination of sustainable harvest strategies in randomly fluctuating environments.     

广义Logistic模型的捕获优化问题

以王寿松所提出的广义Ｌｏｇｉｓｔｉｃ模型为基础,讨论单种群生物资源的捕获优化问题,分析了被开发生物种群的动力学性质。在单位捕获努力量假定下,以最大可持续捕获量为管理目标,确定了线性捕获下的最优捕获策略,得到了最优捕获努力量,最大可持续收获及相应的最优种群水平的显式表达式,包括著名的Ｓｃｈａｅｆｅｒ模型作为特例,推广了相应的结果。     

Discounting and the environment should current impacts be weighted differently than impacts harming future generations?

Background  In Life-Cycle Assessment (LCA), decision makers are often faced with tradeoffs between current and future impacts. One typical example is waste incineration, where immediate emissions to the air from the incineration process have to be weighted against future emissions of slag landfills. Long-term impacts are either completely taken into account or they are entirely disregarded in case of a temporal cut-off. Temporal cutoffs are a special case of discounting. Objective  In this paper, discounting is defined as valuing damages differently at different points of time using a positive or negative discount rate. Apart from temporal cut-offs, discounting has rarely been applied in LCA so far. It is the goal of this paper to discuss the concept of discounting and its applicability in the context of LCA. Methods  For this purpose, we first review the arguments for discounting and its principles in economic sciences. Discounting in economics can be motivated by pure time preference, productivity of capital, diminishing marginal utility of consumption, and uncertainties. The nominal discount rate additionally includes changes in the price level. These arguments and their justification are discussed in the context of environmental impacts harming future generations. Results and Discussion  It is concluded that discounting across generations because of pure time preference contradicts fundamental ethical values and should therefore not be applied in LCA. However, it has to be acknowledged that in practice decision makers often use positive discount rates because of pure time preference — either because they might profit from imposing environmental damage on others instead of themselves or because people in the far future are not of immediate concern to them. Discounting because of the productivity of capital assumes a relationship between monetary values and environmental impact. If such a relationship is accepted, discounting could be applied. However, future generations should be compensated for the environmental damage. It is likely that they would demand a higher compensation if the real per capita income increases. As both the compensation and the discount rate are related to economic growth, the overall discount rate might be close to zero. It is shown that the overall discount rate might even be negative considering that the required compensation could increase (even to infinite) if natural assets remain scarce, whereas the utility of consumption diminishes with increasing income. Uncertainties could justify both positive and negative discount rates. Since the relationship between uncertainties and the magnitude of damage is generally not exponential, we recommend to model changes in the magnitude of damage in scenario analysis instead of considering it in discounting (which requires an exponential function of time in the case of a constant discount rate). We investigated the influence of discounting in a case study of heavy metal emissions from slag landfills. It could be shown that even small discount rates of less than 1 % lead to a significant reduction of the impact score, whereas negative discount rates inflate the results. Conclusions and Recommendations  Discounting is only applicable when temporally differentiated data is available. In some cases, such a temporal differentiation is necessary to take sound decisions, especially when long emission periods are involved. An example is the disposal of nuclear or heavy metal-containing waste. In these cases, the results might completely depend on the discount rate. This paper helps to structure arguments and thus to support the decision about whether or not discounting should be applied in an LCA.     

Individual and social discounting in a viscous population

Social discounting in economics involves applying a diminishing weight to community-wide benefits or costs into the future. It impacts on public policy decisions involving future positive or negative effects, but there is no consensus on the correct basis for determining the social discount rate. This study presents an evolutionary biological framework for social discounting. How an organism should value future benefits to its local community is governed by the extent to which members of the community in the future are likely to be its kin. Trade-offs between immediate and delayed benefits to an individual or to its community are analysed for a modelled patch-structured iteroparous population with limited dispersal. It is shown that the social discount rate is generally lower than the individual (private) discount rate. The difference in the two rates is most pronounced, in ratio terms, when the dispersal level is low and the hazard rate for patch destruction is much smaller than the individual mortality rate. When decisions involve enforced collective action rather than individuals acting independently, social investment increases but the social discount rate remains the same.     

Inventory rationing for a system with heterogeneous customer classes

Many retailers find it useful to partition customers into multiple classes based on certain characteristics. We consider the case in which customers are primarily distinguished by whether they are willing to wait for backordered demand. A firm that faces demand from customers that are differentiated in this way may want to adopt an inventory management policy that takes advantage of this differentiation. We propose doing so by imposing a critical level (CL) policy: when inventory is at or below the critical level demand from those customers that are willing to wait is backordered, while demand from customers unwilling to wait will still be served as long as there is any inventory available. This policy reserves inventory for possible future demands from impatient customers by having other, patient, customers wait. We model a system that operates a continuous review replenishment policy, in which a base stock policy is used for replenishments. Demands as well as lead times are stochastic. We develop an exact and efficient procedure to determine the average infinite horizon performance of a given CL policy. Leveraging this procedure we develop an efficient algorithm to determine the optimal CL policy parameters. Then, in a numerical study we compare the cost of the optimal CL policy to the globally optimal state-dependent policy along with two alternative, more naïve, policies. The CL policy is slightly over 2 % from optimal, whereas the alternative policies are 7 and 27 % from optimal. We also study the sensitivity of our policy to the coefficient of variation of the lead time distribution, and find that the optimal CL policy is fairly insensitive, which is not the case for the globally optimal policy.     

The behaviour of the common hamster (Cricetus cricetus) under zoo conditions

Studies on the behaviour of the common hamster are very rare and fragmentary. From August till the middle of September 2005 we observed behaviour of six individuals of the common hamster (one female and five juveniles: three males and two females) and from the second part of September till October 2005 we observed behaviour of two juvenile males after they were separated from the group. The “Focal animal sampling” was used as an observation method, and the total time of observation amounted to 75 hours. During our observation 7707 bouts of behaviour were recorded. Both social and non-social behaviour were categorised. The number of the non-social behaviour prevailed significantly over the number of the social behaviour (n=496; 6.4%). The most frequent observed non-social behaviour was: head rearing (n=2019; 28%). Among interindividual interactions “escape” (45.4%; n=225) and “vocalisation” (15.7%; n=78) were noticed most frequently. Play-fighting, direct identification, following and hugging were the only aspects of the social behaviour characteristic of the young.The behaviour repertoire of the common hamster seems to be similar to the behaviour of the golden hamster (Mesocricetus auratus).     

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.     

Bio-economics of a renewable resource in a seasonally varying environment

In this paper we study the bio-economics of a renewable resource with governing dynamics described by two distinct growth functions (viz., logistic and Gompertz growth functions) in a seasonally varying environment. Seasonality is introduced into the system by taking the involved ecological parameters to be periodic. In this work, we establish a procedure to obtain the optimal path and compute the optimal effort policy which maximizes the net revenue to the harvester for a fairly general optimal control problem and apply this procedure to the considered models to derive some important conclusions. These problems are solved on the infinite horizon. We find that, for both the models, the optimal harvest policy and the corresponding optimal path are periodic after a finite time. We also obtain optimal solution, a suboptimal harvesting policy and the corresponding suboptimal approach path to reach this optimal solution. The key results are illustrated using numerical simulations and we compare the revenues to the harvester along the optimal and suboptimal paths. The general procedure developed in this work, for obtaining the optimal effort policy and the optimal path, has wider applicability.     

Duration of courtship effort as a costly signal

We consider a male and a female in a courtship encounter over continuous time. Both parties pay participation costs per unit time. The game ends when either one or other of the parties quits or the female accepts the male as a mate. We assume that there is a binary variable which determines whether the male is a “good” or “bad” type from the female's point of view, according to either his condition or his willingness to care for the young after mating. This variable is not directly observable by the female, but has fitness consequences for her: she gets a positive fitness payoff from mating with a “good” male but a negative fitness payoff from mating with a “bad” male. We assume also that a “good” male has a higher ratio of fitness benefit from mating to fitness cost per unit time of courtship than a “bad” male. We show that, under suitable assumptions, there are evolutionarily stable equilibrium behaviours in which time-extended courtship takes place. A “good” male is willing to court for longer than a “bad” male; in this way the duration of a male's courtship signals his type, and acts as a costly handicap. By not being willing to mate immediately the female achieves a degree of screening because the posterior probability that the male is “good”, conditional on his not having quit the game, increases with the duration of courtship.     

Darwin's apes and “savages”

Since his visit to Tierra del Fuego in the 1830s, Darwin had been fascinated by the “savages” that succeeded in surviving on such a “broken beach”, and because they were certainly similar in behaviour to our ancestors. However, he was also fascinated by baboons’ behaviour, according to Brehm's accounts: hamadryas baboons showed a strong altruism to the point of risking their own lives in order to save their infants from attack by dogs. In 1871, he mentions he would rather have descended from brave baboons than from “savages”, considered egoistic. We study the two sources of these ideas and try to show how Darwin's comparative reflections on apes and “savages” made him the first evolutionist anthropologist.     

Time discounting and the body mass index: Evidence from the Netherlands

In many Western countries, the relative weight of people -- measured by the body mass index (BMI) -- has increased substantially in recent years, leading to an increasing incidence of overweight and related health problems. As with many forms of risky behavior, it is plausible that overweight is related to the individual discount rate. Increases in credit card debts, the rise in gambling and the development of a more hedonic life style, suggest that the average discount rate has increased over time. An increase in time discounting may be a contributing factor in the rise in BMI. Applying a large set of indicators for the individual discount rate from a Dutch survey, this paper analyzes whether changes in time discounting can account for differences in body mass between individuals at a given point in time and whether changes in the average individual discount rate can explain the remarkable increase in BMI experienced in recent years in the Netherlands. We find some evidence for a link between time discounting and differences in BMI between people, but this relationship depends strongly on the choice of the proxy for the discount rate. Giving our hypothesis the best chance, we analyze the development of the time discounting proxies that are most strongly related to BMI. We find no evidence for a change of these proxies over time. Our main conclusion therefore is that overweight might be related to the way people discount future health benefits, but the increase in BMI is more likely explained by shifts in other parameters that determine the intertemporal decisions regarding the trade-off of current and future health and satisfaction.     

Optimal harvesting with exponential growth in an environment with random disasters and bonanzas

The optimal discounted present value of an exploited population under constant effort harvesting in an environment with random disasters and bonanzas is investigated. The deterministic component of growth is density independent (also called Malthusian or exponential). The disasters and bonanzas are random, occurring at the times of events of a Poisson process. The density independent properties of the model and the constant effort open loop policy lead to an exact solution for the expected present value. The optimal expected present value is compared with those in deterministic models with and without deterministic type jumps. Both deterministic and random jumps can have a significant influence on the optimal present value. However, the effort to achieve the optimal is not sensitive to variations in the total jump frequency or in the discount rate. The average random jump model is much easier to apply than the deterministic jump model. Bonanzas can have much more of an effect on the present value than disasters given similar jump rates.     

Prevention of avian influenza epidemic: what policy should we choose?

Human-to-human transmission of the avian influenza has been extremely rarely reported, and is considered as limited, inefficient and unsustained. However, experts warn an occurrence of “mutant avian influenza”, which can easily spread among humans, because the avian influenza is already endemic, in particular in Asian poultry, and it is evolving in domestic and wild birds, pigs and humans. Outbreak of such mutant avian influenza in the human world may have devastating consequences, which are comparable with these for the 1918 “Spanish influenza”. In this paper we develop a mathematical model for the spread of the mutant avian influenza, and explore the effectivity of the prevention policies, namely the elimination policy which increases the effective additional death rate of the infected birds and the quarantine policy which reduces the number of infective contacts.     

Optimal control for pandemic influenza: The role of limited antiviral treatment and isolation

The implementation of optimal control strategies involving antiviral treatment and/or isolation measures can reduce significantly the number of clinical cases of influenza. Pandemic-level control measures must be carefully assessed specially in resource-limited situations. A model for the transmission dynamics of influenza is used to evaluate the impact of isolation and/or antiviral drug delivery measures during an influenza pandemic. Five pre-selected control strategies involving antiviral treatment and isolation are tested under the “unlimited” resource assumption followed by an exploration of the impact of these “optimal” policies when resources are limited in the context of a 1918-type influenza pandemic scenario. The implementation of antiviral treatment at the start of a pandemic tends to reduce the magnitude of epidemic peaks, spreading the maximal impact of an outbreak over an extended window in time. Hence, the controls’ timing and intensity can reduce the pressures placed on the health care infrastructure by a pandemic reducing the stress put on the system during epidemic peaks. The role of isolation strategies is highlighted in this study particularly when access to antiviral resources is limited.     

污染环境中可再生资源的最优收获问题

探讨了污染环境下双种群的最优收获问题．利用Pontryagin极大值原理得到一种最优分配方案——处理资源种群体内毒素的努力度与收获资源种群的努力度的分配方案,使经营者的经济收入达到最大,同时也得到次最优均衡解。