Optimal harvesting of fish stocks under a time-varying discount rate

Optimal control theory has been extensively used to determine the optimal harvesting policy for renewable resources such as fish stocks. In such optimisations, it is common to maximise the discounted utility of harvesting over time, employing a constant time discount rate. However, evidence from human and animal behaviour suggests that we have evolved to employ discount rates which fall over time, often referred to as “hyperbolic discounting”. This increases the weight on benefits in the distant future, which may appear to provide greater protection of resources for future generations, but also creates challenges of time-inconsistent plans. This paper examines harvesting plans when the discount rate declines over time. With a declining discount rate, the planner reduces stock levels in the early stages (when the discount rate is high) and intends to compensate by allowing the stock level to recover later (when the discount rate will be lower). Such a plan may be feasible and optimal, provided that the planner remains committed throughout. However, in practice there is a danger that such plans will be re-optimized and adjusted in the future. It is shown that repeatedly restarting the optimization can drive the stock level down to the point where the optimal policy is to harvest the stock to extinction. In short, a key contribution of this paper is to identify the surprising severity of the consequences flowing from incorporating a rather trivial, and widely prevalent, “non-rational” aspect of human behaviour into renewable resource management models. These ideas are related to the collapse of the Peruvian anchovy fishery in the 1970's.     

Effects of market price on the dynamics of a spatial fishery model: Over-exploited fishery/traditional fishery

We present a dynamical model of a spatial fishery describing the time evolution of the fish stock, the fishing effort and the market price of the resource. The market price is fixed by the gap between the supply and the demand. Assuming two time scales, we use “aggregation of variables methods” in order to derive a reduced model governing fish density and fishing effort at a slow time scale. The bifurcation analysis of the reduced model is performed. According to parameters values, three main cases can occur: (i) a stable fishery free equilibrium, (ii) a stable persistent fishery equilibrium and (iii) coexistence of three strictly positive equilibria, two of them being stable separated by a saddle. In this last case, a stable equilibrium corresponds to a traditional fishery with large fish stock, small fishing effort and small market price. The second stable one corresponds to over-exploitation of the resource with small fish stock, large fishing effort and large market price.     

Stock structure analysis of ‘Bombay duck’ (Harpadon nehereus Hamilton, 1822) along the Indian coast using truss network morphometrics

Harpadon nehereus, commonly known as ‘Bombay duck’, is a fish with a discontinuous distribution along the Indian peninsula. The fisheries are dominant on the north‐east and north‐west coast but are absent in commercial landings below 15° north latitude. Heretofore stock assessment studies had not considered the various spawning stock components that replenish this fishery, therefore the present study. Fish samples were collected from four locations: two each from the northeast and the northwest coasts. Twenty‐four morphometric variables were measured using a box‐truss network method. Factor analysis of these variables differentiated the east and the west coast fish populations. Multiple comparisons on the factor scores indicated two independent stocks on the east coast, whereas the fishery on the west coast is replenished by a single stock. The important morphometric traits that accounted for most of the stock variations were related to swimming adaptations of the fish. Future stock assessments can consider the population on the west coast as a single stock when formulating management plans. To harvest the resource in a sustainable manner, the maritime states on the west coast should adopt collaborative efforts towards managing this fishery.     

Working with,not against,coral-reef fisheries

The fisheries policies of some Pacific island nations are more appropriate to the biology of their resources than are some of the fisheries policies of more industrialized countries. Exclusive local ownership of natural resources in Palau encourages adjustive management on biologically relevant scales of time and space and promotes responsibility by reducing the tragedy of the commons. The presence of large individuals in fish populations and adequate size of spawning aggregations are more efficient and meaningful cues for timely management than are surveys of abundance or biomass. Taking fish from populations more than halfway to their carrying capacity is working favorably with the fishery because removing fish potentially increases resource stability by negative feedback between stock size and population production. Taking the same amount of fish from a population below half its carrying capacity is working against the fishery, making the population unstable, because reducing the reproductive stock potentially accelerates reduction of the population production by positive feedback. Reef fish are consumed locally, while Palauan laws ban the export of reef resources. This is consistent with the high gross primary production with little excess net production from undisturbed coral-reef ecosystems. The relatively rapid growth rates, short life spans, reliable recruitment and wide-ranging movements of open-ocean fishes such as scombrids make them much more productive than coral-reef fishes. The greater fisheries yield per square kilometer in the open ocean multiplied by well over a thousand times the area of the exclusive economic zone than that of Palau’s coral reefs should encourage Palauans to keep reef fishes for subsistence and to feed tourists open-ocean fishes. Fisheries having only artisanal means should be encouraged to increase the yield and sustainability by moving away from coral reefs to bulk harvesting of nearshore pelagics.     

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

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. (2009) and then expand the framework to include stock-recruitment functions that are compensatory and overcompensatory, both with and without the Allee effect.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.     

Interspecific Resource Competition Effects on Fisheries Revenue

In many fisheries multiple species are simultaneously caught while stock assessments and fishing quota are defined at species level. Yet species caught together often share habitat and resources, resulting in interspecific resource competition. The consequences of resource competition on population dynamics and revenue of simultaneously harvested species has received little attention due to the historical single stock approach in fisheries management. Here we present the results of a modelling study on the interaction between resource competition of sole (Solea solea) and slaice (Pleuronectus platessa) and simultaneous harvesting of these species, using a stage-structured population model. Three resources were included of which one is shared with a varied competition intensity. We find that plaice is the better competitor of the two species and adult plaice are more abundant than adult sole. When competition is high sole population biomass increases with increasing fishing effort prior to plaice extinction. As a result of this increase in the sole population, the revenue of the stocks combined as function of effort becomes bimodal with increasing resource competition. When considering a single stock quota for sole, its recovery with increasing effort may result in even more fishing effort that would drive the plaice population to extinction. When sole and plaice compete for resources the highest revenue is obtained at effort levels at which plaice is extinct. Ignoring resource competition promotes overfishing due to increasing stock of one species prior to extinction of the other species. Consequently, efforts to mitigate the decline in one species will not be effective if increased stock in the other species leads to increased quota. If a species is to be protected against extinction, management should not only be directed at this one species, but all species that compete with it for resource as well.     

A bioeconomic model of a fishery with saturated catch and variable price: Stabilizing effect of marine reserves on fishery dynamics

In this paper, we study a mathematical bio-economic model of a fishery with varying price. The three dimensional model describes the time evolution of the resource, the fishing effort and the price. The model is original because it considers a nonlinear harvesting function assumed to depend upon stock size and fishing effort with a saturation effect with respect to the resource as well as a price equation depending on demand and supply which is in addition proportional to price. Assuming that the price varies at a fast time scale, we are able to use ”aggregation of variables methods” in order to reduce the model in a two dimensional model at a slow time scale. This aggregated (reduced) model is analyzed. Several numerical simulations of the model are performed to substantiate our analytical findings. The existence of nonlinear harvesting makes the dynamics of the model more complicated, including multiple equilibria, bi-stability and limit cycle. Such large amplitude cycle variations are not desirable because they generate periods of overfishing at periods of very low activity. We then study the effects of marine reserves on the dynamics of the fishery, showing that for an adequate number of small reserves, limit cycle oscillations are switched off.     

Prehistoric versus modern Baltic Sea cod fisheries: selectivity across the millennia

Combining Stone Age and modern data provides unique insights for management, extending beyond contemporary problems and shifting baselines. Using fish chronometric parts, we compared demographic characteristics of exploited cod populations from the Neolithic Period (4500 BP) to the modern highly exploited fishery in the central Baltic Sea. We found that Neolithic cod were larger (mean 56.4 cm, 95% confidence interval (CI)+/-0.9) than modern fish (weighted mean length in catch =49.5+/-0.2 cm in 1995, 48.2+/-0.2 cm in 2003), and older (mean ages=4.7+/-0.11, 3.1+/-0.02 and 3.6+/-0.02 years for Neolithic, 1995, and 2003 fisheries, respectively). Fishery-independent surveys in 1995 and 2003 show that mean sizes in the stock are 16-17 cm smaller than reflected in the fishery, and mean ages approximately 1-1.5 years younger. Modelled von Bertalanffy growth and back-calculated lengths indicated that Neolithic cod grew to smaller asymptotic lengths, but were larger at younger ages, implying rapid early growth. Very small Neolithic cod were absent and large individuals were rare as in modern times. This could be owing to selective harvests, the absence of small and large fish in the area or a combination. Comparing modern and prehistoric times, fishery selection is evident, but apparently not as great as in the North Atlantic proper.     

The Dynamics of a Fish Stock Exploited in Two Fishing Zones

This work presents a specific stock-effort dynamical model. The stocks correspond to two populations of fish moving and growing between two fishery zones. They are harvested by two different fleets. The effort represents the number of fishing boats of the two fleets that operate in the two fishing zones. The bioeconomical model is a set of four ODE's governing the fishing efforts and the stocks in the two fishing areas. Furthermore, the migration of the fish between the two patches is assumed to be faster than the growth of the harvested stock. The displacement of the fleets is also faster than the variation in the number of fishing boats resulting from the investment of the fishing income. So, there are two time scales: a fast one corresponding to the migration between the two patches, and a slow time scale corresponding to growth. We use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model for the total fishing effort and fish stock of the two fishing zones. The mathematical analysis of the model is shown. Under some conditions, we obtain a stable equilibrium, which is a desired situation, as it leads to a sustainable harvesting equilibrium, keeping the stock at exploitable densities.     

劳动力转移和森林管护水平对森林碳密度的影响——基于福建253个村的实证研究

森林生态系统具有重要的固碳功能,有效的森林管理是提升碳密度的重要方式。随着农村劳动力转移,森林管护水平也随之变化,进而可能影响森林碳密度。为了厘清劳动力转移和森林管护水平对森林碳密度的作用机理,以提升森林碳密度。利用福建5县（区）253个村1999年与2009年的林业二类调查数据和入村调研数据,采用转换因子连续函数法评价了森林碳密度,再运用层次回归模型分析了劳动转移对森林碳密度的影响,并检验了森林管护水平对二者的中介作用。结果表明：（1）10年间森林碳密度普遍提升,但区域差异明显;空间上森林碳密度呈由南向北递增,提升率呈由南向北递减。（2）劳动力转移对森林碳密度有显著促进作用,而森林管护水平对森林碳密度有显著削弱作用,并对劳动力转移与森林碳密度之间的关系具有显著中介效应。（3）劳动力特征、采伐方式及森林自然禀赋等因素,主要通过生计依赖、生境状况和生物量对森林碳密度产生显著影响。据此提出：适当减少对森林的人为干扰,丰富林农生计来源,转变林业经营目标,科学采伐成熟和过熟林,保护天然起源林,丰富人工林树种等政策建议。     

Recent evolution of fishery and land reclamation in Curonian and Lesina lagoons

The evolution of fishery and land reclamation in Lesina (Italy) and Curonian (Lithuania/Russia) lagoons was analysed as an example of recent trends in European coastal lagoons. Social and political changes were considered, addressing resource exploitation and inherent impacts on ecosystems. In both lagoons, the mismanagement of the fish stock led to the depletion of fish resources and to the decline of commercial fishery. In parallel, vast wetland fringes were reclaimed and turned into intensively managed farmland, with a marked loss of aquatic–terrestrial ecotones. In the last decades, the annual fish yield fell to less than 40 kg ha⁻¹ in the Lesina lagoon, where the fishermen dwindled to 40 units, mostly pensioners rounding off their income. Recently, in the Curonian lagoon, more than 100 small private fishing enterprises were licensed to fish. Overall, the landed catches were difficult to monitor, which resulted in a substantial uncontrolled landing of fish (up to 60% of the fish yield). Under these conditions, the sustainable exploitation of lagoons and their resources can be achieved through an integrated management of watershed and lagoons. The restoration of ecotones, marshes and floodplains and the preservation of semi-natural agricultural ecosystems have to be considered as priorities. Examples of such approach are provided by pilot programs, aiming at the commercial exploitation of the reed belts along the Curonian lagoon fringes. Reed harvesting would increase the acreage of important migration corridors and spawning habitats for fish, also providing an additional income to the local communities. Guest editors: A. Razinkovas, Z. R. Gasiūnaitė, J. M. Zaldivar and P. Viaroli European Lagoons and their Watersheds: Function and Biodiversity     

Recruitment prediction for Pacific herring (Clupea pallasi) on the west coast of Vancouver Island, Canada

The accurate prediction of recruitment to the fishery is a very important tool within the management structure of any fish stock being exploited. In the case of the Pacific herring, Clupea pallasi, fishery in Canada, a forecast of the abundance of each herring stock is particularly important for formulating an annual catch quota. The sustainable management of the fishery and the resource is based in part on accurate recruitment forecasting because Pacific herring are short-lived and so the recruitment contributes a significant part of the total spawning run targeted by the fishery each year. Several factors are believed be important in determining the success of recruitment besides spawners biomass. Since herrings are “r” strategists, conditions related to the egg, the planktonic, or even the juvenile stage might determine the future level of recruitment. Recently a formula that defines conditions for a semi-quantitative level of recruitment forecast was elaborated using genetic algorithms and current study attempts to improve on this model. Using salinity in two quarterly periods during the planktonic and pre-recruit stages, temperature and spawning biomass for the west coast of Vancouver Island stock, classification rules that define recruitment in 3 different levels (low, medium and high) were developed with a genetic algorithm, setting low and high boundaries for each condition. A 75% success in classifying recruitment was obtained. The model was shown to be particularly effective at predicting when the recruitment would be low, which could be important from the perspective of the Precautionary Approach and the sustainable management of this stock.     

Detecting and managing fisheries-induced evolution

Exploitation of fish populations can induce evolutionary responses in life histories. For example, fisheries targeting large individuals are expected to select for early maturation at smaller sizes, leading to reduced fecundity and thus also reduced fisheries yield. These predicted phenotypic shifts have been observed in several fish stocks, but disentangling the environmental and genetic causes behind them has proved difficult. Here, we review recent studies investigating phenotypic shifts in exploited populations and strategies for minimizing fisheries-induced evolution. Responses to selective harvesting will depend on species-specific life-history traits, and on community-level and environmental processes. Therefore, the detection of fisheries-induced evolution and successful fish stock management requires routine population monitoring, and a good understanding of genetics, relevant ecological processes and changing environmental conditions.     

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。       

The role of marine reserves in achieving sustainable fisheries

Many fishery management tools currently in use have conservation value. They are designed to maintain stocks of commercially important species above target levels. However, their limitations are evident from continuing declines in fish stocks throughout the world. We make the case that to reverse fishery declines, safeguard marine life and sustain ecosystem processes, extensive marine reserves that are off limits to fishing must become part of the management strategy. Marine reserves should be incorporated into modern fishery management because they can achieve many things that conventional tools cannot. Only complete and permanent protection from fishing can protect the most sensitive habitats and vulnerable species. Only reserves will allow the development of natural, extended age structures of target species, maintain their genetic variability and prevent deleterious evolutionary change from the effects of fishing. Species with natural age structures will sustain higher rates of reproduction and will be more resilient to environmental variability. Higher stock levels maintained by reserves will provide insurance against management failure, including risk-prone quota setting, provided the broader conservation role of reserves is firmly established and legislatively protected. Fishery management measures outside protected areas are necessary to complement the protection offered by marine reserves, but cannot substitute for it.     

色林错渔业生产的现状与可持续利用的对策

色林错裸鲤（Gymnocypris selincuoensis)是藏北色林错湖泊中惟一的一种鱼类。本文介绍了色林错渔业的开发利用情况,并对色林错裸鲤最小捕捞年龄、捕捞强度、最小网目以及最佳年捕捞产量进行了探讨。从可持续发展的角度,我们认为对色林错鱼类资源的利用必须以保证现有湖泊生态系统的稳定为核心,在满足维持一个足够数量及年龄结构的繁殖群体的基础上,以获得最佳持续经济利益为目标。以往强调甚至采用的最大持续产量理论在高原极端环境条件下并不能作为鱼类资源利用的追求目标或确定渔产量的标准,而只能作为对其捕捞强度的参考。总的允许渔获量应当根据最适捕捞死亡率F0．2来确定。本文最后提出了色林错湖泊鱼类资源可持续利用的8条具体措施。     

Evolutionary regime shifts in age and size at maturation of exploited fish stocks

Worldwide declines of fish stocks raise concerns about deleterious consequences of harvesting for stock abundances and individual life histories, and call for appropriate recovery strategies. Fishes in exploited stocks mature earlier at either larger or smaller sizes due to both genetic and plastic responses. The latter occur commonly when reduced competition for food leads to faster growth. Using a size-structured consumer-resource model, which accounts for both genetic and plastic responses, we show that fisheries-induced evolutionary changes in individual life history and stock properties can easily become irreversible. As a result of annual spawning, early maturation at small sizes and late maturation at large sizes can become alternative, evolutionarily and ecologically stable states under otherwise identical environmental conditions. Exploitation of late-maturing populations can then induce an evolutionary regime shift to smaller maturation sizes associated with stepwise, 1-year decreases in age at first reproduction. Complete and early fishing moratoria slowly reverse this process, but belated or partial closure of fisheries may accelerate or even instigate further evolution to smaller sizes at maturation. We suggest that stepwise decreases in maturation age can be used as early warnings of upcoming evolutionary changes, and should inspire timely restrictions of fisheries.     

Modelling the effect of Nile perch predation and harvesting on fisheries dynamics of Lake Victoria

We used a mathematical model to predict and explain the effect of harvesting combined with predation by the Nile perch on Nile tilapia. The model incorporates three developmental stages of each species. The findings show that uncontrolled human exploitation of the stock leads to loss of fish biodiversity in the lake. The results of the study also show that increasing harvesting rate of the mature Nile perch leads to stable stationary states of the system. However, increasing predation rates by Nile perch lead to unstable equilibria.     

An analysis of genetic stock identification on a small geographical scale using microsatellite markers,and its application in the management of a mixed‐stock fishery for Atlantic salmon Salmo salar in Ireland

A genetic stock identification (GSI) study was undertaken in a fishery for Atlantic salmon Salmo salar to determine the effects of restrictive fishery management measures on the stock composition of the fishery, and if accurate and precise stock composition estimates could be achieved on the small geographical scale where this fishery operates, using a suite of only seven microsatellite loci. The stock composition of the Foyle fishery was shown to comprise almost exclusively of Foyle origin fish in the 3 years after restrictive measures were introduced in 2007, compared to 85% the year before. This showed that the restrictive measures resulted in the Foyle fishery being transformed from a mixed‐stock fishery to an almost exclusively single‐stock fishery, and showed how GSI studies can guide and evaluate management decisions to successfully manage these fisheries. Highly accurate and precise stock composition estimates were achieved in this study, using both cBAYES and ONCOR genetic software packages. This suggests accurate and precise stock composition is possible even on small geographical scales.