Jan E. Beyer

Reconsidering the Consequences of Selective Fisheries

Balanced fishing across a range of species, stocks, and sizes could mitigate adverse effects and address food security better than increased selectivity. Concern about the impact of fishing on ecosystems and fisheries production is increasing (1, 2). Strategies to reduce these impacts while addressing the growing need for food security (3) include increasing selectivity (1, 2): capturing species, sexes, and sizes in proportions that differ from their occurrence in the ecosystem. Increasing evidence suggests that more selective fishing neither maximizes production nor minimizes impacts (4–7). Balanced harvesting would more effectively mitigate adverse ecological effects of fishing while supporting sustainable fisheries. This strategy, which challenges present management paradigms, distributes a moderate mortality from fishing across the widest possible range of species, stocks, and sizes in an ecosystem, in proportion to their natural productivity (8), so that the relative size and species composition is maintained.

A stochastic model of larval fish growth

As the first step of gaining insight into the importance of starvation as a regulatory mechanism of mortality in the very early life of individual fish species this paper describes a stochastic dynamic model of growth and mortality of winter flounder larvae (Pseudopleuronectes americanus) reared in the laboratory under experimental conditions. The basis of the model is a Markov process with continuous weight-states operating on a day-to-day basis. A minimum growth curve is applied as an absorbing barrier to describe mortality due to starvation. Exact computation principles and Monte Carlo simulation techniques are applied to compute model characteristics, individual fish larval histories, survival probabilities and the weight probability distributions of live larvae. The results seem to be in fair agreement with larval behavior and the rates of growth and mortality observed in the laboratory.

Vertical migration and dispersion of sprat (Sprattus sprattus) and herring (Clupea harengus) schools at dusk in the Baltic Sea

In populations of herring (Clupea harengus) or sprat (Sprattus sprattus), one typically observes a pattern of schools forming at dawn and dispersing at dusk, usually combined with vertical migration. This behaviour influences interactions with other species; hence a better understanding of the processes could contribute to deeper insight into ecosystem dynamics. This paper reports field measurements of the dispersal at dusk and examines two hypotheses through statistical modelling: that the vertical migration and the dissolution of schools is determined by decrease in light intensity, and that the dissolution of schools can be modelled by diffusion, i.e. active repulsion is not required. The field measurements were obtained during 3 days in March at one location in the Baltic Sea and included continuous hydroacoustical monitoring, trawl samples, and hydrographical CTD data. Echogram patterns were analysed using the school detection module in Echoview ® and local light intensities were calculated using a model for surface illuminance. The data and the analysis support that schools migrate upwards during dusk, possibly trying to remain aggregated by keeping the local light intensities above a critical threshold, that schools initiate their dissolution when ambient light intensity drops below this critical threshold, and that fish subsequently swim in an uncorrelated random walk pattern.

How optimal life history changes with the community size-spectrum

This paper derives optimal life histories for fishes or other animals in relation to the size spectrum of the ecological community in which they are both predators and prey. Assuming log-linear size-spectra and well known scaling laws for feeding and mortality, we first construct the energetics of the individual. From these we find, using dynamic programming, the optimal allocation of energy between growth and reproduction as well as the trade-off between offspring size and numbers. Optimal strategies were found to be strongly dependent on size spectrum slope. For steep size spectra (numbers declining rapidly with size), determinate growth was optimal and allocation to somatic growth increased rapidly with increasing slope. However, restricting reproduction to a fixed mating season changed optimal allocations to give indeterminate growth approximating a von Bertalanffy trajectory. The optimal offspring size was as small as possible given other restrictions such as newborn starvation mortality. For shallow size spectra, finite optimal maturity size required a decline in fitness for large size or age. All the results are compared with observed size spectra of fish communities to show their consistency and relevance.

Life-history constraints on the success of the many small eggs reproductive strategy

The reproductive strategy of most fishes is to produce a large number of tiny eggs, leading to a huge difference between egg size and asymptotic body size. The viability of this strategy is examined by calculating the life-time reproductive success R(0) as a function of the asymptotic body size. A simple criterion for the optimality of producing small eggs is found, depending on the rate of predation relative to the specific rate of consumption. Secondly it is shown that the success of the reproductive strategy is increasing with asymptotic body size. Finally the existence of both upper and lower limits on the allowed asymptotic sizes is demonstrated. A metabolic upper limit to asymptotic body size for all higher animals is derived.

Stochastic stomach theory of fish: an introduction

Abstract Fish stomach dynamics is discussed and introduced analytically by a simple individually-based stomach model for total stomach content. The predator encounters food (meals) in a Poisson process, starting to search for a new meal when the stomach is empty. Basic equations for the frequency distributions of stomach content are derived for general classes of meal-size distributions and rate models of gastric evacuation. Probability characteristics in steady-state of empty and non-empty stomachs are evaluated from first principles with particular attention to the square root rate model of gastric evacuation. The average rate of food consumption and the functional response are derived from simple renewal theory and from obtaining the average of the gastric evacuation rates. Effects of meal size biased stomach sampling are introduced. As a primer on modelling the stomach content of piscivorous fish, the model is discussed in relation to the empirical distribution of the individual stomach content for more than 4000 North Sea whiting in the length range 20–30 cm. Implications of identical meals and variable meal sizes, exemplified by the log-normal distribution, are considered. Estimated average meal searching time and meal size as well as the average rate of food consumption decrease considerably in the more realistic case of variable meal sizes. The model is able to account for the high frequency of empty stomachs, which occurs simultaneously with a relatively high observed mean stomach content. Need and direction for further developments of fish stomach theory are discussed.

Higher Order Moments and Conditional Asymptotics of the Batch Markovian Arrival Process

We consider the number of arrivals in a Batch Markovian Arrival Process (BMAP) and derive matrix analytic expressions for its moments of arbitrary order. These expressions consist of decomposition formulas connected to the semigroup structure of the moments, forward and backward differential equations, and recursive as well as direct integral formulas. This extends earlier work by Narayana and Neuts on the first two factorial moment matrices. We next turn to the terminating BMAP, i.e., a BMAP with an absorbing state in which no arrivals occur. We consider the asymptotic behavior of the moments conditional on the process not yet having terminated. We show that the conditional mean and variance possess affine asymptotics and derive the coefficients explicitly. Finally, we discuss how parts of our work also apply to the more general class of Rational Arrival Processes (RAPs).

Some aspects of modelling the long-term behaviour of aquatic ecosystems

Abstract The present paper deals with the modelling process in relation to the class of computerized, time-continuous, deterministic models. Following a brief discussion of the formulation of the modelling process to which the paper relates, a description of the System Analysis and System Synthesis stages of the modelling of the eutrophication process in a sill fiord is given. Special emphasis is put on the modelling of a general column of the fiord system. Numerical solution methods relevant for long-term studies are discussed and the requirements, which these methods should meet with respect to stability and accuracy, are formulated. The goal-statements of Sensitivity Analysis are presented, followed by a description of two approaches in the understanding of model behaviour. The possibility of determining the sensitivity of a non-linear system through linearization is discussed, as is the possibility of determining the sensitivity to not well estimated constants working directly on the non-linear system. A way of constructing a model of the entire fiord is outlined. Finally, attention is brought to the superior modelling goals through a discussion of the utilization of a hypothetical, credible model of the eutrophication process in the fiord as an element in a tool for resource planning in pollution control.

Geostatistical modelling of the spatial life history of post-larval deepwater hake Merluccius paradoxus in the Benguela Current Large Marine Ecosystem

Optimal and sustainable management of fish resources cannot be ensured without a thorough understanding of the migration patterns and population (demographic stock) structure. Recent studies suggest that these aspects of the economically and ecologically important deepwater hake Merluccius paradoxus are not reflected in the current assessment and management practices for the Benguela Current Large Marine Ecosystem. In this study, we compiled data from multiple demersal trawl surveys from the entire distribution area and applied state-of-the-art geostatistical population modelling (GeoPop) to estimate growth rate, mortality, and spatial and temporal distribution patterns of M. paradoxus. The data and the model enabled us to follow temporal and spatial changes in the distribution and infer movements from the recruitment/nursery areas, through the juvenile phase and the adults’ migration to the spawning areas outside/upstream of the nursery areas. The results indicated one primary recruitment/nursery area on the west coast of South Africa and a secondary less-productive recruitment/nursery area on the south coast near Port Elizabeth. Juveniles initially migrated away from the main recruitment area, followed by natal homing by larger individuals. This pattern was highly consistent through the time-series of the study. This perception of a, primarily, panmictic population that performs transboundary migrations between Namibia and South Africa corresponds largely to the hypothesis and data plots given in recent studies. We recommend that fisheries assessment, advice and management take into consideration these aspects of the distribution and population (stock) structure of M. paradoxus.

Multispecies Models of an Exploited Sea

Man’s impact on the sea has increased to the point where it is obvious that the living resources are by no means inexhaustible. This shows clearly in the present year’s commercial fisheries of the North Atlantic where catches have been constant or even decreased in spite of more effort put into operation. Even on a world scale landings have tended to stabilize on the present level of about 60 million tons. This figure should be compared with the FAO estimate of 100 million tons as the maximum sustainable yield on a world scale if each stock could be properly managed. It is expected that only 80 million tons is achievable due to mixed fisheries problems, etc. The crux of the matter is that careful management of the fish stocks is required if these 80 million tons as a stable long term yield is the objective.