A pioneer validation of a state-space model of vessel trajectories (VMS) with observers’ data

In the context of the expansion of animal tracking and bio-logging, state-space models have been developed with the objective to characterise animals’ trajectories and to understand the factors controlling their behaviour. In the fisheries community, the electronic tagging of vessels commonly designated by Vessel Monitoring Systems (VMS) is developing and provides a new insight for the understanding, the analysis and the modelling of the trajectories of vessels and their prospecting behaviour. VMS data are thus a clue for the proper definition of fishing effort which remains a fundamental parameter of tuna stock assessments. In this context, we used the VMS (recording of hourly positions) of the French tropical tuna purse-seiners operating in the Indian Ocean to characterise three types of movement (states) on the VMS trajectories (stillness, tracking, and cruising). Based on empirical evidences, and on the regular frequency of VMS acquisition, this was achieved by the development of a Bayesian Hidden Markov model for the speeds and turning angles derived from the hourly steps of the trajectories. In a second phase, states were related to activities disentangling stillness into fishing or stop at sea. Finally the quality of the model performances was rigorously quantified thanks to observers’ data. Confronting model prediction and true activities allowed estimating that 10% of the hourly steps were misclassified. The assumptions and model’ choices are discussed, highlighting the fact that VMS data and observers’ data having different time resolutions, the effective use of validating data was troublesome. However, without validation, these analyses remain speculative. The validation part of this work represents an important step for the operational use of state-space models in ecology in the broad sense (predators’ tracking data, e.g. birds or mammals trajectories).     

Optimization of an artificial neural network for identifying fishing set positions from VMS data: An example from the Peruvian anchovy purse seine fishery

The spatial behavior of numerous fishing fleets is nowadays well documented thanks to satellite Vessel Monitoring Systems (VMS). Vessel positions are recorded on a frequent and regular basis which opens promising perspectives for improving fishing effort estimation and management. However, no specific information is provided on whether the vessel is fishing or not. To answer that question, existing works on VMS data usually apply simple criteria (e.g. threshold on speed). Those simple criteria generally focus in detecting true positives (a true fishing set detected as a fishing set); conversely, estimation errors are given no attention. For our case study, the Peruvian anchovy fishery, those criteria overestimate the total number of fishing sets by 182%. To overcome this problem an artificial neural network (ANN) approach is presented here. In order to set both the optimal parameterization and use “rules” for this ANN, we perform an extensive sensitivity analysis on the optimization of (1) the internal structure and training algorithm of the ANN and (2) the “rules” used for choosing both the relative size and the composition of the databases (DBs) used for training and inferring with the ANN. The “optimized” ANN greatly improves the estimates of the number and location of fishing events. For our case study, ANN reduces the total estimation error on the number of fishing sets to 1% (in average) and obtains 76% of true positives. This spatially explicit information on effort, provided with error estimation, should greatly reduce misleading interpretations of catch per unit effort and thus significantly improve the adaptive management of fisheries. While fitted on Peruvian anchovy fishery data, this type of neural network approach has wider potential and could be implemented in any fishery relying on both VMS and at-sea observer data. In order to increase the accuracy of the ANN results, we also suggest some criteria for improving sampling design by at-sea observers and VMS data.     

Effect of variable fishing strategy on fisheries under changing effort and pressure: An agent-based model application

An agent-based model was used to evaluate the response of a two-species fish community to fishing boat exploration strategies, namely: boats following high-yield boats (Cartesian); boats fishing at random sites (stochast-random); and boats fishing at least exploited sites (stochast-pressure). At low fishing pressure, the stochast-random mode yielded a high average catch per boat while sustaining fish biomass. At high fishing pressure, the Cartesian mode was more effective. For the Cartesian strategy, fish biomass exhibited four distinct behaviors with increasing number of boats. In the first phase, the fish biomass dropped with increasing number of boats due to a corresponding rise in biomass extraction. Rapid exploitation occurred in the second phase, when two or more boats occupied the same initial area, that led to the faster abandonment of those sites which then underwent biomass recovery. In the third phase, adding more boats resulted in a fluctuating stock biomass, where the combined effects of initial spatial distribution of boats and rapid localization led to either full stock recovery when boats were eventually confined to a single location due to spillovers, or stock extirpation when the entire area became fully occupied. Beyond the third phase, stock extirpation was assured. In order to break the pattern of localization (bandwagon effect), we introduced stochast-random intruders in a Cartesian-dominated fishery. Adding a single intruder changed the patchy-structured stock biomass pattern of a purely Cartesian fishery to a uniformly explored stock biomass pattern because of the additional spatial information provided by the intruder. Consequently, the average catch per boat increased but at the expense of a disproportionate decline in equilibrium biomass.     

Threats of illegal,unregulated, and unreported fishing to biodiversity and food security in the Republic of the Congo

Illegal, unregulated, and unreported (IUU) fishing poses a major threat to effective management of marine resources, affecting biodiversity and communities dependent on these coastal resources. Spatiotemporal patterns of industrial fisheries in developing countries are often poorly understood, and global efforts to describe spatial patterns of fishing vessel activity are currently based on automatic identification system (AIS) data. However, AIS is often not a legal requirement on fishing vessels, likely resulting in underestimates of the scale and distribution of legal and illegal fishing activity, which could have significant ramifications for targeted enforcement efforts and the management of fisheries resources. To help address this knowledge gap, we analyzed 3 years of vessel monitoring system (VMS) data in partnership with the national fisheries department in the Republic of the Congo to describe the behavior of national and distant-water industrial fleets operating in these waters. We found that the spatial footprint of the industrial fisheries fleet encompassed over one-quarter of the Exclusive Economic Zone. On average, 73% of fishing activity took place on the continental shelf (waters shallower than 200 m). Our findings highlight that VMS is not acting as a deterrent or being effectively used as a proactive management tool. As much as 33% (13% on average) of fishing effort occurred in prohibited areas set aside to protect biodiversity, including artisanal fisheries resources, and the distant-water fleet responsible for as much as 84% of this illegal activity. Given the growth in industrial and distant-water fleets across the region, as well as low levels of management and enforcement, these findings highlight that there is an urgent need for the global community to help strengthen regional and national capacity to analyze national scale data sets if efforts to combat IUU fishing are to be effective.     

Use of radar detectors to track attendance of albatrosses at fishing vessels

Despite international waters covering over 60% of the world's oceans, understanding of how fisheries in these regions shape ecosystem processes is surprisingly poor. Seabirds forage at fishing vessels, which has potentially deleterious effects for their population, but the extent of overlap and behavior in relation to ships is poorly known. Using novel biologging devices, which detect radar emissions and record the position of boats and seabirds, we measured the true extent of the overlap between seabirds and fishing vessels and generated estimates of the intensity of fishing and distribution of vessels in international waters. During breeding, wandering albatrosses (Diomedea exulans) from the Crozet Islands patrolled an area of over 10 million km² at distances up to 2500 km from the colony. Up to 79.5% of loggers attached to birds detected vessels. The extent of overlap between albatrosses and fisheries has widespread implications for bycatch risk in seabirds and reveals the areas of intense fishing throughout the ocean. We suggest that seabirds equipped with radar detectors are excellent monitors of the presence of vessels in the Southern Ocean and offer a new way to monitor the presence of illegal fisheries and to better understand the impact of fisheries on seabirds.     

Artisanal fishing and coastal conservation in West Africa

Artisanal fishing is an activity which has long occupied an important place on the West African coast. In less than 20 years, the increasingly widespread use of motors in fishing boats and cold storage facilities both on board and on land have enabled fishermen to master the constraints of space and time. Furthermore, globalization has created a demand for new products, thus influencing the behaviour of fishermen and consequently the status of some fish, turtle and marine mammal species. Development policies for artisanal fishing do not adequately reflect the importance of these changes. They tend to use inappropriate scales of reference, be it spatially (national borders take precedence over ecosystems) or temporally (the long-term consequences of development plans are seldom considered). Some international conservation organizations are testing promising new approaches to managing resources more sustainably and restoring degraded ecosystems, and their recent experiences can serve as useful examples to others. It is recommended to grant special rights of access to resident fishermen. In defending ‘their’ resources, they will also protect the ecological functions of the area. Close collaboration with administrations and development assistance agencies is needed to assess consequences of political decisions on the use of resources. The important role of marine protected areas as a tool for fishing management should be better documented and strengthened. These areas should not be considered as isolated units but rather as vital parts of a comprehensive system for improved coastal zone management. Consistent with the ecosystem approach, fishermen and their communities, being the main users of coastal resources, should also play a major role in the design and implementation of any fishing management actions.     

Analysis of sedimentation at the fishing harbor entrance: case study of El-Burullus,Egypt

Sedimentation in artificial ports and harbors is a common issue throughout the world. Based on an assessment of the coastal fishing harbors in Egypt, the El-Burullus fishing harbor has been found to suffer severely from siltation. Sediment deposits are concentrated at the harbor entrance, which threatens navigation through this area. Although the harbor authority has constructed a perpendicular extension on the main breakwater to mitigate these siltation issues, fishing boats are still suffering from the siltation at the harbor entrance. Dredging is required every year to maintain continuity of navigation through the harbor; the cost of dredging is a critical element which impacts the economic feasibility of the harbor. Therefore, the need to investigate new solutions for the siltation issue is critical. In this study, a two-dimensional calibrated and validated model using the Coastal Modeling System package is used to understand the coastal processes within the study area. It is also used to investigate the effects of the proposed breakwater extension on the siltation at the harbor outlet. Field data such as hydrographic surveys, waves, tides, and lake outlet discharge data were collected and included in the model. The results obtained for the current breakwater conditions confirmed the claims of the fishermen that the sedimentation problem still occurs at the entrance. Thus, five possible solutions to mitigate the problem were proposed and simulated considering the following parameters: sediment deposition rate to the west of the main breakwater, the erosion rate in front of the seawall in the eastern part of the harbor, and the morphological changes within the El-Burullus lake outlet. According to the simulation results, reducing the length of the upper edge of the middle jetty by 90 m improves the stability of the harbor entrance. Alternatively, replacing the perpendicular extension by an inclined extension of 60 m in length and shortening the middle jetty by 60 m reduces the accretion and erosion rates around the harbor which promotes the long-term stability for the coastal area in addition to favorable conditions to the El-Burullus harbor entrance.     

Sardine (Sardina pilchardus) stress reactions to purse seine fishing

Observations from the purse seine fishery off northern Portugal are used to describe the early dynamics of sardine (Sardina pilchardus) stress reactions and identify likely stressors during the commercial fishing operation. Sardine blood and muscle were sampled from the onset of fishing (school identification and encircling) to the end of fish transfer onboard (90–120 min later). The evolution of haematocrit, haemoglobin, cortisol, glucose, ionic concentrations, ATP and its catabolites were modelled using linear mixed models as a function of time spent in the net, biological (sex, reproductive state and condition) and operational variables (catch, light level and phase of fishing operation). Significant linear trends with time were detected for most stress variables and mean concentrations after 2 h in the net were similar to literature values corresponding to acute stress reactions for teleosts. Biological variables were rarely significant and explained a small proportion of variation, while operational variables were never significant. For each stress variable, levels varied considerably between trips but the temporal evolution was common across trips. Random trip effects were uncorrelated among most biochemical variables, suggesting that distinct factors affected each stress variable during the sampled trips. However, the linear trend with time spent in the net observed for most stress variables indicates that the duration of the fishing operation is an important stressor in purse seine fishing due to the progressive water volume restriction, crowding and manipulation associated to the fishing method.     

An individual-based stochastic hazard model of eastern king prawn (Melicertus plebejus) migration with spatially and temporally varying fishing effort

This paper describes an individual-based stochastic model of eastern king prawn migration along the eastern Australian coast. Migration is treated as one-dimensional diffusion with drift. Capture of a prawn is seen as a failure event driven by movement through a spatially and temporally variable fishing mortality hazard. This hazard is combined with a uniform natural mortality hazard. We use a Monte Carlo method to estimate parameters by comparing expected numbers of tag-returns predicted from the model with previously published tag-release data. As the previous study used a discrete compartmental model, with compartments corresponding to zones of constant fishing effort, we used the same zones and fishing effort in our comparison. The marginal distribution of yield in each zone per single recruit is determined, providing more information compared with the deterministic approach to yield-per-recruit. Using our model we also derive the constant fishing mortality rate equivalent to a spatially variable fishing mortality rate in its impact on the proportion of prawns surviving the migration to reach spawning grounds. Determination of this proportion could contribute significantly to a sustainability assessment of the fishery. It is demonstrated using the AIC that better fits to the data of the previous study and greater parsimony are obtained using our model than were found in the deterministic compartmental analysis of that study. This improvement results from the ability of our model to account separately for average speed of movement and average dispersal rate, whereas in the previous deterministic compartmental model, movement is governed by just one parameter. Our individual-based model includes a parameter that explicitly accounts for dispersal of prawns in migration, so it can distinguish between speed effects and dispersal effects in the data. It also models both types of mortality as processes distinct from those of movement. This enables it to better separate movement and mortality effects compared to the compartmental approach, in which movement and mortality are treated as similar departure processes from a compartment. This separation reduces confounding of movement and mortality effects when parameters are estimated.     

Which forcing factors fit? Using ecosystem models to investigate the relative influence of fishing and changes in primary productivity on the dynamics of marine ecosystems

Fishing mortality and primary production (or proxy for) were used to drive the dynamics of fish assemblages in 9 trophodynamic models of contrasting marine ecosystems. Historical trends in abundance were reconstructed by fitting model predictions to observations from stock assessments and fisheries independent survey data. The model fitting exercise derives values for otherwise unknown parameters that specify the relative strength of trophic interactions and, in some instances, a time series anomaly for changes in primary production. We measured how much better or worse were model predictions when bottom-up forcing by primary production were added to top-down forcing by fishing. Searching for cross system patterns, the relative contribution of fishing and changes in primary production, mediated through trophic interactions, are evaluated for the ecosystems as a whole and for selected similar species in different ecosystems. The analysis provides a simple qualitative way to explain which forcing factors have most influence on modeled dynamics. Both fishing and primary production forcing were required to obtain the best model fits to data. Fishing effects more strongly influenced 6 of 9 of the ecosystems, but primary production was more often found to be the main factor influencing the selected pelagic and demersal fish stock trends. Examination of sensitivity to ecological and model parameters suggests that the results are the product of complex food-web interactions rather than simple deterministic responses of the models.     

Reconstructing historical marine ecosystems using food web models: Northern British Columbia from Pre-European contact to present

Mass-balance trophic models (Ecopath with Ecosim) are developed for the marine ecosystem of northern British Columbia (BC) for the historical periods 1750, 1900, 1950 and 2000 AD. Time series data are compiled for catch, fishing mortality and biomass using fisheries statistics and literature values. Using the assembled dataset, dynamics of the 1950-based simulations are fitted to agree with observations over 50 years to 2000 through the manipulation of trophic flow parameters and the addition of climate factors: a primary production anomaly and herring recruitment anomaly. The predicted climate anomalies reflect documented environmental series, most strongly sea surface temperature and the Pacific Decadal Oscillation index. The best-fit predator–prey interaction parameters indicate mixed trophic control of the ecosystem. Trophic flow parameters from the fitted 1950 model are transferred to the other historical periods assuming stationarity in density-dependent foraging tactics. The 1900 model exhibited an improved fit to data using this approach, which suggests that the pattern of trophic control may have remained constant over much of the last century. The 1950 model is driven forward 50 years using climate and historical fishing drivers. The resulting ecosystem is compared to the 2000 model, and the dynamics of these models are compared in a predictive forecast to 2050. The models suggest similar restoration trajectories after a hypothetical release from fishing.     

Using hidden Markov chains and empirical Bayes change-point estimation for transect data

Consider a lattice of locations in one dimension at which data are observed. We model the data as a random hierarchical process. The hidden process is assumed to have a (prior) distribution that is derived from a two-state Markov chain. The states correspond to the mean values (high and low) of the observed data. Conditional on the states, the observations are modelled, for example, as independent Gaussian random variables with identical variances. In this model, there are four free parameters: the Gaussian variance, the high and low mean values, and the transition probability in the Markov chain. A parametric empirical Bayes approach requires estimation of these four parameters from the marginal (unconditional) distribution of the data and we use the EM-algorithm to do this. From the posterior of the hidden process, we use simulated annealing to find the maximum a posteriori (MAP) estimate. Using a Gibbs sampler, we also obtain the maximum marginal posterior probability (MMPP) estimate of the hidden process. We use these methods to determine where change-points occur in spatial transects through grassland vegetation, a problem of considerable interest to plant ecologists.     

Elements of fishing community resilience to climate change in the coastal zone of Bangladesh

Resilience has been conceptualized in various ways by anthropologists, ecologists, systems scientists and engineers; the boundaries of resilience are subjective and context dependent. Consequently, choosing the standards and metrics for assessing resilience remains key challenges for policy makers. In this study, using multicriteria evaluation of 40 basic criteria of human, physical, financial, natural and social assets, we have identified several elements, such as experienced fishermen, natural abundance of hilsa (Tenualosa ilisha), ability to assert decision on fish selling, nets and boats ownership, social harmony and capacity of buying food as essential livelihood assets for the fishermen at Hatiya Island, Bangladesh. These assets may enhance the relative resilience of the fishing community of the island to climate change by as much as 20–40%. The results of this study will improve our understanding of the elements that lead to resilience at the community level.     

Mercury bioaccumulation and trophic transfer in sympatric snapper species from the Gulf of Mexico.

Consumption of marine fish is a major route of toxic methyl mercury (MeHg) exposure to ocean apex predators and human populations. Here we explore the influence of trophic structure on total mercury (Hg) accumulation in red snapper (RS, Lutjanus campechanus) and gray snapper (GS, Lutjanus griseus) from the coastal Louisiana region of the Gulf of Mexico, west of the Mississippi River. The objectives of this investigation were to: (1) determine the effectiveness of the use of offshore recreational fishing charter boats and marinas as sources of fish samples and (2) compare species differences in Hg bioaccumulation, trophic position, and carbon sources. Our data show that length-normalized Hg concentrations (> or = 97% as MeHg in tissue of both species) were 230% greater in GS in comparison to RS collected from the same general area. Stable C and N isotope signatures (delta15N and delta13C) indicate that GS occupy a slightly higher trophic position (approximately 30% of one trophic position higher) on the Gulf food web in comparison to RS and that GS appear to incorporate higher trophic positioned prey, continually and at smaller sizes. Mercury was strongly correlated with combined delta15N and delta13C in pooled species data, arguing that most of the substantial difference in Hg bioaccumulation between RS and GS can be explained by modest differences in their trophic position and, to a lesser degree, carbon sources, which had low variation and high overlap among species. These observations demonstrate that even minor to moderate differences in trophic position and food habits in sympatric species can create relatively large differences in bioaccumulation regimes and underscores the importance of quantitative characterization of trophic structure in marine MeHg bioaccumulation studies.     

Management and exploitation dynamics of small-scale fisheries in the Bay of Biafra: An integrative analysis of purse seine fishing activity

For many decades, fisheries research has focused on stock assessment and the impact of the fishery effort on resources. Although this knowledge remains necessary, a more integrated analysis of the joint dynamics of resource and operational activities is needed to provide more useful advice for the management of fishery systems. Since 1994 a new approach to fishery science has been carried out for Cameroonian small-scale fisheries, the aim being the incorporation into fishery science of research on fishery management, fishing processes and fishermen's behaviour. This paper presents a more systemic data approach which combines biological parameters and operational factor analyses with the goal of sustainable development. From two years of data collected on the purse seine fishing units operating in the Bay of Biafra (2002 and 2003), a set of three correspondence analyses is applied: (1) to the length frequency distribution of Ethmalosa fimbriata, (2) to the number of visits per fishing ground, and (3) to the species appearance frequency in the landings. These three analyses were plotted per month-year period. The results are presented in the form of an annual exploitation cycle, linking fishing grounds, the main species caught, and corresponding fishing period.     

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.     

Efficient Markov chain Monte Carlo sampling for hierarchical hidden Markov models

Traditional Markov chain Monte Carlo (MCMC) sampling of hidden Markov models (HMMs) involves latent states underlying an imperfect observation process, and generates posterior samples for top-level parameters concurrently with nuisance latent variables. When potentially many HMMs are embedded within a hierarchical model, this can result in prohibitively long MCMC runtimes. We study combinations of existing methods, which are shown to vastly improve computational efficiency for these hierarchical models while maintaining the modeling flexibility provided by embedded HMMs. The methods include discrete filtering of the HMM likelihood to remove latent states, reduced data representations, and a novel procedure for dynamic block sampling of posterior dimensions. The first two methods have been used in isolation in existing application-specific software, but are not generally available for incorporation in arbitrary model structures. Using the NIMBLE package for R, we develop and test combined computational approaches using three examples from ecological capture–recapture, although our methods are generally applicable to any embedded discrete HMMs. These combinations provide several orders of magnitude improvement in MCMC sampling efficiency, defined as the rate of generating effectively independent posterior samples. In addition to being computationally significant for this class of hierarchical models, this result underscores the potential for vast improvements to MCMC sampling efficiency which can result from combinations of known algorithms.     

The application of a multiple-recapture technique for the study of some aspects of dynamics of large fish populations

The multiple-recapture technique can be used to study some aspects of the dynamics of large fish populations, if a part of the fishing fleet is considered as experimental fishing boats by appointing obserers to release tagged fish which are captured, while untagged fish captured are retained. The tagged and untagged populations are assumed to have different properties such as catchability and survival rates. The fish are sampled during a number of sampling surveys with equal duration and no intervening time intervals between them. It is assumed that fish suffer from mortalities during sampling surveys. The parameters of untagged populations can be estimated with the help of the readily estimated parameters of tagged fish (Rafail, 1972), the relationship between the parameters of tagged and untagged populations, and the numbers of untagged fish captured during the sampling surveys. The estimates are free from Types A and B tagging errors.     

Effects of near‐future ocean acidification,fishing, and marine protection on a temperate coastal ecosystem

Understanding ecosystem responses to global and local anthropogenic impacts is paramount to predicting future ecosystem states. We used an ecosystem modeling approach to investigate the independent and cumulative effects of fishing, marine protection, and ocean acidification on a coastal ecosystem. To quantify the effects of ocean acidification at the ecosystem level, we used information from the peer‐reviewed literature on the effects of ocean acidification. Using an Ecopath with Ecosim ecosystem model for the Wellington south coast, including the Taputeranga Marine Reserve (MR), New Zealand, we predicted ecosystem responses under 4 scenarios: ocean acidification + fishing; ocean acidification + MR (no fishing); no ocean acidification + fishing; no ocean acidification + MR for the year 2050. Fishing had a larger effect on trophic group biomasses and trophic structure than ocean acidification, whereas the effects of ocean acidification were only large in the absence of fishing. Mortality by fishing had large, negative effects on trophic group biomasses. These effects were similar regardless of the presence of ocean acidification. Ocean acidification was predicted to indirectly benefit certain species in the MR scenario. This was because lobster (Jasus edwardsii) only recovered to 58% of the MR biomass in the ocean acidification + MR scenario, a situation that benefited the trophic groups lobsters prey on. Most trophic groups responded antagonistically to the interactive effects of ocean acidification and marine protection (46%; reduced response); however, many groups responded synergistically (33%; amplified response). Conservation and fisheries management strategies need to account for the reduced recovery potential of some exploited species under ocean acidification, nonadditive interactions of multiple factors, and indirect responses of species to ocean acidification caused by declines in calcareous predators.     

Optimum size limit for a fishery with a limited fishing season

In the management of a fishery with many year-classes, a standard objective is to maximize the biomass yield. If the fishing effort is fixed, this objective can be attained by prescribing an optimum size limit. This implies that only fish which are larger than the optimum size limit should be caught. The theory for computing the optimum size limit when fishing is carried out continuously is well established. In contrast the theory for computing the optimum size limit when the fishing season is limited to the same period in each year has not been developed in spite of the fact that many fisheries are exploited in this manner. A fishing season may be limited because the weather or the migration patterns of the fish population permits fishing only during a certain period in the year. A fishing season may also be limited because it is necessary to reduce the fishing mortality in order to conserve the fish population.A theory for computing the optimum size limit when the fishing season is limited is developed in this paper. It is applied to a hypothetical fishery. The data for this example comes from the North Sea plaice fishery. It is found that for a given fishing effort the optimum size limit is 44.5 cm if fishing is carried out continuously, 41.3 cm if fishing is limited to 6 months in a year and 28.7 cm if fishing is limited to a period of one tenth of a year in each year.