Economics of harvesting age-structured fish populations

A generic age-structured model is developed to derive analytical results on optimal harvesting. Given two age classes, knife-edge selectivity, and no stock-dependent harvesting cost, the steady state is a unique saddle point. Adding harvesting cost does not alter the uniqueness, given that the utility is linear. Under specific conditions such as nonselective gear, optimal harvesting is proved to be a stationary cycle that represents pulse fishing. Optimal steady states are different if age-structured information is ignored and optimization is based on traditional biomass variables. This implies that the existence of optimal sustainable harvesting depends on age-structured information. Given a specific set of conditions such as low interest rate and knife-edge selectivity, optimal harvesting converges toward a unique saddle point independently of the number of age classes.     

Adjusting age and stage distributions for misclassification errors

Ecologists often use samples from the age or stage structure of a population to make inferences about population-level processes and to parameterize matrix models. Typically, researchers make a simplifying assumption that age and stage classes are determined without error, when in fact some level of misclassification often can be expected. If unaccounted for, misclassification will lead to overly optimistic levels of precision and can cause biased estimates of age or stage structure. Although several studies have used information from known-age individuals to quantify errors in age or stage distribution, the problem of estimating the age or stage structure in face of such errors has received comparably little attention. In this paper, we describe a general statistical framework for estimating the true stage distribution of a sample when misclassification rates can be estimated. The estimation process requires auxiliary information on misclassification rates, such as data from individuals of known age. We analyze age-structured harvest records from black bears in Pennsylvania to illustrate how incorporating misclassification errors leads to changes in point estimates and provides a measure of precision.     

Optimal harvesting of a plant-hervibore system: lichen and reindeer in northern Finland

The optimal harvesting policy for a plant-herbivore system consisting of lichen and reindeer in Finnish Lapland is investigated. Using a discrete time model with no age structure it is shown that the optimal procedure to reach target levels for lichen and reindeer involves a possible initial harvest of reindeer and then a sequence of no-harvesting years until the lichen has recovered. After two adjusting harvests the system will settle to an equilibrium. The optimal solution is compared with the fastest possible approach to the target levels. The two solutions coincide if future yields are sufficiently discounted. With a discount factor near one there will be a heavier initial harvest in the optimal solution. It is seen that allowing some harvesting also in the no-harvesting years has no marked effect on the total yield. The target levels for lichen and reindeer are not unique but depend both on discounting and on the length of the planning period.     

Northeast Arctic cod population persistence in the Lofoten-Barents Sea system under fishing.

Population growth, and hence the population's persistence, is affected by several factors such as climate, species interaction, and harvesting pressure. Proper resource management requires an understanding of these factors. We apply techniques based upon age-structured population matrices to analyze estimated stock sizes derived from annual bottom trawl sampling in the winter feeding area of northeast Arctic cod (Gadus morhua L.) from 1981 to 2003. We run generalized additive models to explain population growth rate by different explanatory variables. Cod population growth was found to be positively related to the abundance of capelin (Mallotus villosus Miller), negatively related to the number of cannibalistic cod with a two-year lag, and marginally positively related to the winter North Atlantic Oscillation index (NAO). This model remains true independently from the population status (i.e., fished or non-fished). Capelin abundance is the main variable that to some degree can be adjusted in order to maintain the population size at a given level of cod harvesting. Our results point to the importance of managing conjointly cod and capelin stocks.     

Eradication via destratification: whole-lake mixing to selectively remove rainbow smelt, a cold-water invasive species

Invasive species can have severe effects on aquatic ecosystems. After invasions occur, eradication should be considered whenever the potential loss of ecosystem services outweighs the cost of the eradication method. Here we evaluate the possibility of destratifying Crystal Lake, Wisconsin, USA, to eradicate the invasive fish rainbow smelt (Osmerus mordax). We modeled the effects of three destratification scenarios (non-, low-, and high-mixing) using both physical and biological models. Field observations were used to calibrate the models. Water temperatures estimated from 18 unique DYRESM simulations were used in a bioenergetics model to estimate growth of five age classes of rainbow smelt under normal and destratified conditions. Our simulations indicate that destratification can eliminate optimal rainbow smelt thermal habitat resulting in mortality. Destratified lake temperatures also surpassed several physiological critical temperatures. Bioenergetics simulations predicted a weight loss of 45-55% in yearling and adult rainbow smelt. We found that destratification is potentially effective for eradicating cold-water species in temperate lakes.     

Age,stages, and the role of generation time in matrix models

The earliest matrix models, proposed in the 1940s, consider age classes, and were later proved to be equivalent to the discrete time version of the stable population theory. In this theory and models, besides the asymptotic growth rate, a very important characteristic is the turnover of individuals, measured in various ways by generation time. Models considering stages, on the contrary, do not take into account the age of individuals and seem largely preferable to age-structured models for many populations in which demographic characteristics are related to biological stages (such a seed, rosette, flowering plant, etc.) rather than to age per itself. These two kinds of models can be embedded as particular cases of stage by age models or multistate models. Theses general models can be used to develop a multistate stable population theory with many advantages. This general theory is reviewed with emphasis on general rules for sensitivity analyses in which generation time plays a central role.     

Pigou meets Mirrlees: On the irrelevance of tax distortions for the second-best Pigouvian tax

This paper extends the Mirrlees (1971) model of optimal income redistribution with optimal corrective taxes to internalize consumption externalities. Using general utility structures and exploring both linear and non-linear taxes, it is demonstrated that the optimal second-best tax on an externality-generating good should not be corrected for the marginal cost of public funds, since it equals one in the optimal tax system. In the optimum, distortions of income taxes are equal to marginal redistributional gains. If the government does not have access to a non-distortionary marginal source of finance, the marginal cost of public funds can be either larger or smaller than one depending on subjective preferences for income redistribution. The optimal second-best corrective tax is then either higher or lower than the Pigouvian level. The findings in this paper generalize and amend prior results based on representative-agent models, shedding new light on the weak double-dividend hypothesis, and on the welfare gains of recycling revenue from environmental taxes.     

Demographic Side Effects of Selective Hunting in Ungulates and Carnivores

Abstract:  Selective harvesting regimes are often implemented because age and sex classes contribute differently to population dynamics and hunters show preferences associated with body size and trophy value. We reviewed the literature on how such cropping regimes affect the demography of the remaining population (here termed demographic side effects ). First, we examined the implications of removing a large proportion of a specific age or sex class. Such harvesting strategies often bias the population sex ratio toward females and reduce the mean age of males, which may consequently delay birth dates, reduce birth synchrony, delay body mass development, and alter offspring sex ratios. Second, we reviewed the side effects associated with the selective removal of relatively few specific individuals, often large trophy males. Such selective harvesting can destabilize social structures and the dominance hierarchy and may cause loss of social knowledge, sexually selected infanticide, habitat changes among reproductive females, and changes in offspring sex ratio. A common feature of many of the reported mechanisms is that they ultimately depress recruitment and in some extreme cases even cause total reproductive collapse. These effects could act additively and destabilize the dynamics of populations, thus having a stronger effect on population growth rate than first anticipated. Although more experimental than observational studies reported demographic side effects, we argue that this may reflect the quite subtle mechanisms involved, which are unlikely to be detected in observational studies without rigorous monitoring regimes. We call for more detailed studies of hunted populations with marked individuals that address how the expression of these effects varies across mating systems, habitats, and with population density. Theoretical models investigating how strongly these effects influence population growth rates are also required.     

Cannibalism in an age-structured predator–prey system

The effect of cannibalism on an age-structured predator–prey system is studied. Three stable equilibrium states are found. Using a Hopf bifurcation analysis, it is found that the non washout steady state looses its stability as the cannibalism attack rate increases past a bifurcation point S_c. The dependence of the bifurcation point on the other parameters in the model is found. It is shown that the trajectory of the solution spirals in for attack rates S<S_c and exhibits limit cycle behavior for S>S_c.     

Optimization model for a wolf-ungulate system

Public outcries against predator control create a need to devise management policies that optimally balance the cost (managerial and environmental) of predator control against the benefit of ungulate harvesting. To address this problem, an optimization procedure utilizing stochastic dynamic programming is described. Through this approach, optimal feedback strategies for a wolf-ungulate system in Alaska are estimated. The dynamic predator-prey model used in the analysis is based on parameter estimates from data collected over an eight-year period in Denali (Mt. McKinley) National Park. Stability analysis of the system revealed that stability properties depend on predator search efficiency. The effects of random fluctuations in winter severity and alternative objective functions are considered in the estimation of optimal feedback strategies. Optimal moose harvesting strategies appear to be dependent on wolf control costs. If no wolf control cost is assessed, optimal moose harvest is independent of wolf density. Optimal wolf control strategies are completely insensitive to moose density. The strategies are compared to current and simplified management policies.     

Ecological and economic considerations on fishing and rearing of Tapes phillipinarum in the lagoon of Venice

A population dynamic model for Tapes philippinarum has been developed, using experimental data for the estimation of mortality, and literature information for recruitment. The population dynamic model has been coupled to a eco-physiological model of T. philippinarum previously developed, in order to simulate the evolution of individual size and number of individuals in each age class.The resulting age-size class model has been used to analyse the implication of different scenarios of fishing/harvesting of the bivalve in the lagoons of the Northern Adriatic Sea, where fishery and aquaculture represent important economic activities.Ten years long simulations have been performed, in which initial density, harvesting efficiency, minimum harvested size, were varied. Comparisons between the different strategies are made in term of total yields and bio-economic income. The model gives suggestions on the optimal fishing effort, in case of fishery, and on optimal seeding size and seeding moment, in case of aquaculture.A discussion of model results provides indications on harvesting policies which are appropriate from ecological-economical point of view. The final result is that economically more profitable strategies coincide with ecologically more conservative policies.     

Evaluation of pay-for-release conservation incentives for unintentionally caught threatened species

In the developing world, the exploitation of threatened species jeopardizes their permanence in the wild. Because not all captures are intentional, for instance when capture methods have low selectivity, pressure on these species may be lessened by releasing living incidentally caught animals. However, it is often unrealistic to expect people to voluntarily do so because it means foregoing the benefits of resource extraction. Financial incentives for such animal release may foster conservation objectives. Reducing human–animal conflicts, protecting natural habitat, and conserving nests of threatened species are examples of conservation benefits that can be built on financial reward systems. However, incentives aiming to protect unintentionally captured threatened species are scarce. We considered pay for release, a type of ecosystem-service payment designed to foster the release of incidentally captured threatened species. We aimed to determine the best conditions to implement this scheme, its potential benefits (e.g., incentivizing the release of threatened species), and pitfalls and priority research needs (e.g., required conditions for pay for release to work) to show that its global applicability is possible. Given that approaches solely based on education and law enforcement may be ineffective under some circumstances, we argue that pay for release can protect incidentally captured endangered species if used under conditions conducive for its success. When local participants’ intrinsic motivation for conservation is weak, but the release of incidentally live-caught animals into their habitats is readily achievable, pay-for-release schemes could jump start urgently needed conservation efforts against indiscriminate animal harvesting.     

Optimal escapement levels in stochastic and deterministic harvesting models

A constant-escapement feedback policy is shown to be optimal in maximizing expected discounted net revenue from an animal resource whose dynamics are described by a stochastic stock-recruitment model, provided that unit harvesting costs satisfy certain conditions. The optimal escapement in this model is compared with that in the corresponding deterministic model and it is shown how the way in which unit harvesting costs vary with population abundance can be important in determining the relative sizes of the optimal escapements. In most cases, the optimal stochastic escapement is no less than the optimal deterministic escapement.     

Modeling the Effects of Trophy Selection and Environmental Disturbance on a Simulated Population of African Lions

Abstract:  Tanzania is a premier destination for trophy hunting of African lions (Panthera leo) and is home to the most extensive long-term study of unhunted lions. Thus, it provides a unique opportunity to apply data from a long-term field study to a conservation dilemma: How can a trophy-hunted species whose reproductive success is closely tied to social stability be harvested sustainably? We used an individually based, spatially explicit, stochastic model, parameterized with nearly 40 years of behavioral and demographic data on lions in the Serengeti, to examine the separate effects of trophy selection and environmental disturbance on the viability of a simulated lion population in response to annual harvesting. Female population size was sensitive to the harvesting of young males (≥3 years), whereas hunting represented a relatively trivial threat to population viability when the harvest was restricted to mature males (≥6 years). Overall model performance was robust to environmental disturbance and to errors in age assessment based on nose coloration as an index used to age potential trophies. Introducing an environmental disturbance did not eliminate the capacity to maintain a viable breeding population when harvesting only older males, and initially depleted populations recovered within 15–25 years after the disturbance to levels comparable to hunted populations that did not experience a catastrophic event. These results are consistent with empirical observations of lion resilience to environmental stochasticity .     

Mathematical modelling for conservation and management of gorgonians corals: youngs and olds,could they coexist?

Gorgonian corals are long-lived, slow-growing marine species dominating Mediterranean rocky bottoms. Endowed with complex morphologies they give a structure to the whole community, moreover, being efficient suspension feeders, they play a key role in plankton-benthos energy flow and CO₂${\text{CO}}_2$ storage. Thus, the structure and the development of benthic, hard bottom communities are linked to gorgonian survival. The red coral Corallium rubrum (L. 1758) is a precious gorgonian endemic to the Mediterranean Sea. Harvested and traded world-wide since ancient times red coral is a clear example of overexploited marine resource. This species is structured into self-seeding, genetically differentiated populations, some of which, living in the shallower part of the species bathymetric distribution, was recently affected by anomalous mortality events linked to global climate change. The co-occurrence of overharvesting and mass mortality could dramatically affect such populations. Demographic population models, widely applied by conservation biologists to check population viability and to project population trends over time are fundamental to foster survival of such populations matching harvesting to population growth rates. Therefore we set out a dynamic model of a genetically differentiated red coral population living in shallow waters. This population is characterised by small/young, crowded colonies and high recruitment rate. On the basis of the size–age structure determined for this population, a static life-history table, in which survival and reproduction coefficients of the different size–age classes were reported, has been set out. Demographic data were included in a non-linear, discrete, age-structured dynamic model, based on a Leslie-Lewis transition matrix. Our field data indicate that the recruits-to-larvae ratio is actually density-dependent. Such dependence, positive for low and negative for high density values, was included into the model and the effect of colonies of different size–age classes on recruits-to-larvae ratio was considered to be proportional to the number of polyps they have. We applied such model to simulate the trends of the studied population under different increases of survival and life-span. As some populations of gorgonians actually show the dominance of sparse, big/old colonies and low recruitment rate, while others are characterised by crowded, small/young colonies and high recruitment rate, we simulated the shift from the former to the latter structure increasing survival and life-span. Our results suggest that a dramatic mortality increase of bigger–older colonies (due, in the case of red coral to overfishing) could have determined the population structure we found.     

Optimal exploitation of a fishery employing a non-linear harvesting function

A harvesting function is developed to described the rate of removal of fish from a fish population. The function incorporates the effects of both the handling or processing time of the catch and the competition, between boats in the fleet, for the fish.We will assume that the growth rate of the fish population can be modelled with a concave, dome shaped growth curve. With this assumption, it has been shown that if the rate of harvesting the fish is linearly related to both effort (which can be thought of as some measure of the number of boats in the fleet) and the population size, then the population will tend towards a single equilibrium level which is globally stable. This paper shows that the saturation effects due to the handling time may generate two equilibrium levels (one stable, one unstable) rather than a single globally stable equilibrium. The results of competition between boats are economically undesirable because of the decrease in efficiency. However, this competition may be beneficial to the exploited fish population.Using the harvesting model derived earlier, the steady state or long term optimal harvesting policies as well as the transition paths to these states are developed. The only constraint is on the maximum allowable effort which is effectively an upper limitation on the fleet size or number of man-hours of fishing.     

Monitoring and estimating the flow conditions and fish presence probability under various flow conditions at reach scale using genetic algorithms and kriging methods

The combination of current velocity and water depth influences stream flow conditions, and fish activities prefer particular flow conditions. This study develops a novel optimal flow classification method for identifying types of stream flow based on the current velocity and the water depth using a genetic algorithm. It is applied to the Datuan stream in northern Taiwan. Fish were sampled and their habitat investigated at the study site during the spring, summer, fall and winter of 2008-2009. The current velocity, water depth and maps of the presence probability of fish were estimated by ordinary and indicator kriging. The optimal classification results were compared with the classification results obtained using the Froude number and empirical methods. The flow classification results demonstrate that the proposed optimal flow classification method that considers depth-velocity and optimally identified criteria for classifying flow types, yields a current velocity and water depth of 0.32 (m/s) and 0.29 (m), respectively, and classifies the flow conditions in the study area as pool, run, riffle and slack. The variography results of the current velocity and the water depth data reveal that seasonal flows are not spatially stationary among seasons in the study area. Kriging methods and a two-dimensional hydrodynamic model (River 2D) with empirical and optimal flow classification methods are more effective than the Froude number method in classifying flow conditions in the study area. The flow condition classifications and probability maps were generated by River 2D, ordinary kriging and indicator kriging, to quantify the flow conditions preferred by Sicyopterus japonicus in the study area. However, the proposed optimal classification method with kriging and River 2D is an effective alternative method for mapping flow conditions and determining the relationship between flow and the presence probability of target fish in support of stream restoration.     

Restoring Natural Resources with Destination-Driven Costs

Economics typically assumes that injured natural resources are restored along a fixed path of increasing marginal costs. By contrast, many restoration efforts—such as cleaning a contaminated aquifer or replacing the sand on an oil-tarnished beach—are characterized bydestination-driven costs, which depend mainly on final quality, not the prerestoration quality. Given the resulting nonconvexities in cost, the optimal level of restoration may be a discontinuous and nonmonotonic function of post-injury quality. Regulatory rules should reflect these patterns, as should liability rules, since restoration plans and costs determine the expected cost of putting a resource at risk.     

Optimal management of renewable resources with growing demand and stock externalities

In an equilibrium framework, optimal management of renewable resources in the presence of growing demand or externalities leads to steady states that differ from those characterized by rate of interest equals rate of change in growth plus rate of change in prices. Measures to reach an optimum with externalities other than direct controls are found to be critically mediated by the costs of harvesting.     

Intertemporal environmental management with a storable pollutant

A model is developed which allows decisions on generation and emission of an environmental pollutant to be separated in time. After deducing and discussing the necessary conditions for the socially optimal time pattern of generation and emission the possibility of using pollution taxation to motivate this optimal solution is investigated. The principle finding is that there exists no time pattern of fixed per-unit pollution taxes that will result in optimality. In particular, this demonstrates the failure of that pattern of fixed per-unit taxes which reflects the optimal marginal social cost of emission at each point in time.