Population dynamics of fisheries

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Predator bluefin trevally sizing up schooling anchovies, in the Maldives Moofushi Kandu fish.jpg
Predator bluefin trevally sizing up schooling anchovies, in the Maldives

A fishery is an area with an associated fish or aquatic population which is harvested for its commercial or recreational value. Fisheries can be wild or farmed. Population dynamics describes the ways in which a given population grows and shrinks over time, as controlled by birth, death, and migration. It is the basis for understanding changing fishery patterns and issues such as habitat destruction, predation and optimal harvesting rates. The population dynamics of fisheries is used by fisheries scientists to determine sustainable yields. [1] [2]

Contents

The basic accounting relation for population dynamics is the BIDE (Birth, Immigration, Death, Emigration) model, shown as: [3]

N1 = N0 + BD + IE

where N1 is the number of individuals at time 1, N0 is the number of individuals at time 0, B is the number of individuals born, D the number that died, I the number that immigrated, and E the number that emigrated between time 0 and time 1. While immigration and emigration can be present in wild fisheries, they are usually not measured.

A fishery population is affected by three dynamic rate functions:

If these rates are measured over different time intervals, the harvestable surplus of a fishery can be determined. The harvestable surplus is the number of individuals that can be harvested from the population without affecting long term stability (average population size). The harvest within the harvestable surplus is called compensatory mortality, where the harvest deaths are substituting for the deaths that would otherwise occur naturally. Harvest beyond that is additive mortality, harvest in addition to all the animals that would have died naturally.

Care is needed when applying population dynamics to real world fisheries. Over-simplistic modelling of fisheries has resulted in the collapse of key stocks. [4] [5]

History

The first principle of population dynamics is widely regarded as the exponential law of Malthus, as modelled by the Malthusian growth model. The early period was dominated by demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographic model. A more general model formulation was proposed by F.J. Richards in 1959, by which the models of Gompertz, Verhulst and also Ludwig von Bertalanffy are covered as special cases of the general formulation. [6]

Population size

The population size (usually denoted by N) is the number of individual organisms in a population.

The effective population size (Ne) was defined by Sewall Wright, who wrote two landmark papers on it (Wright 1931, 1938). He defined it as "the number of breeding individuals in an idealized population that would show the same amount of dispersion of allele frequencies under random genetic drift or the same amount of inbreeding as the population under consideration". It is a basic parameter in many models in population genetics. Ne is usually less than N (the absolute population size).

Small population size results in increased genetic drift. Population bottlenecks are when population size reduces for a short period of time.

Overpopulation may indicate any case in which the population of any species of animal may exceed the carrying capacity of its ecological niche.

Virtual population analysis

Virtual population analysis (VPA) is a cohort modeling technique commonly used in fisheries science for reconstructing historical fish numbers at age using information on death of individuals each year. This death is usually partitioned into catch by fisheries and natural mortality. VPA is virtual in the sense that the population size is not observed or measured directly but is inferred or back-calculated to have been a certain size in the past in order to support the observed fish catches and an assumed death rate owing to non-fishery related causes.

Minimum viable population

The minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. More specifically MVP is the smallest possible size at which a biological population can exist without facing extinction from natural disasters or demographic, environmental, or genetic stochasticity. [7] The term "population" refers to the population of a species in the wild.

As a reference standard, MVP is usually given with a population survival probability of somewhere between ninety and ninety-five percent and calculated for between one hundred and one thousand years into the future.

The MVP can be calculated using computer simulations known as population viability analyses (PVA), where populations are modelled and future population dynamics are projected.

Maximum sustainable yield

In population ecology and economics, the maximum sustainable yield or MSY is, theoretically, the largest catch that can be taken from a fishery stock over an indefinite period. [8] [9] Under the assumption of logistic growth, the MSY will be exactly at half the carrying capacity of a species, as this is the stage at when population growth is highest. The maximum sustainable yield is usually higher than the optimum sustainable yield.

This logistic model of growth is produced by a population introduced to a new habitat or with very poor numbers going through a lag phase of slow growth at first. Once it reaches a foothold population it will go through a rapid growth rate that will start to level off once the species approaches carrying capacity. The idea of maximum sustained yield is to decrease population density to the point of highest growth rate possible. This changes the number of the population, but the new number can be maintained indefinitely, ideally.

MSY is extensively used for fisheries management. [10] [11] Unlike the logistic (Schaefer) model, MSY in most modern fisheries models occurs at around 30-40% of the unexploited population size. [12] This fraction differs among populations depending on the life history of the species and the age-specific selectivity of the fishing method.

However, the approach has been widely criticized as ignoring several key factors involved in fisheries management and has led to the devastating collapse of many fisheries. As a simple calculation, it ignores the size and age of the animal being taken, its reproductive status, and it focuses solely on the species in question, ignoring the damage to the ecosystem caused by the designated level of exploitation and the issue of bycatch. Among conservation biologists it is widely regarded as dangerous and misused. [4] [5]

Recruitment

Recruitment is the number of new young fish that enter a population in a given year. The size of fish populations can fluctuate by orders of magnitude over time, and five to 10-fold variations in abundance are usual. This variability applies across time spans ranging from a year to hundreds of years. Year to year fluctuations in the abundance of short lived forage fish can be nearly as great as the fluctuations that occur over decades or centuries. This suggests that fluctuations in reproductive and recruitment success are prime factors behind fluctuations in abundance. Annual fluctuations often seem random, and recruitment success often has a poor relationship to adult stock levels and fishing effort. This makes prediction difficult. [13]

The recruitment problem is the problem of predicting the number of fish larvae in one season that will survive and become juvenile fish in the next season. It has been called "the central problem of fish population dynamics" [14] and “the major problem in fisheries science". [15] Fish produce huge volumes of larvae, but the volumes are very variable and mortality is high. This makes good predictions difficult. [16]

According to Daniel Pauly, [15] [17] the definitive study was made in 1999 by Ransom Myers. [18] Myers solved the problem "by assembling a large base of stock data and developing a complex mathematical model to sort it out. Out of that came the conclusion that a female in general produced three to five recruits per year for most fish.” [15]

Fishing effort

Fishing effort is a measure of the anthropogenic work input used to catch fish. A good measure of the fishing effort will be approximately proportional to the amount of fish captured. Different measures are appropriate for different kinds of fisheries. For example, the fishing effort exerted by a fishing fleet in a trawl fishery might be measured by summing the products of the engine power for each boat and time it spent at sea (KW × days). For a gill-net fishery the effort might be measured by summing the products of the length of each set net and the time it was set in the water (Km × soak time). In fisheries where boats spend a lot of time looking for fish, a measure based on search time may be used. [19] [20] [21]

Overfishing

The Traffic Light colour convention, showing the concept of Harvest Control Rule (HCR), specifying when a rebuilding plan is mandatory in terms of precautionary and limit reference points for spawning biomass and fishing mortality rate. Harvest Control Rule graph.gif
The Traffic Light colour convention, showing the concept of Harvest Control Rule (HCR), specifying when a rebuilding plan is mandatory in terms of precautionary and limit reference points for spawning biomass and fishing mortality rate.

The notion of overfishing hinges on what is meant by an acceptable level of fishing.

A current operational model used by some fisheries for predicting acceptable levels is the Harvest Control Rule (HCR). This formalizes and summarizes a management strategy which can actively adapt to subsequent feedback. The HCR is a variable over which the management has some direct control and describes how the harvest is intended to be controlled by management in relation to the state of some indicator of stock status. For example, a harvest control rule can describe the various values of fishing mortality which will be aimed at for various values of the stock abundance. Constant catch and constant fishing mortality are two types of simple harvest control rules. [22]

Metapopulation

A metapopulation is a group of spatially separated populations of the same species which interact at some level. The term was coined by Richard Levins in 1969. The idea has been most broadly applied to species in naturally or artificially fragmented habitats. In Levins' own words, it consists of "a population of populations". [23]

A metapopulation generally consists of several distinct populations together with areas of suitable habitat which are currently unoccupied. Each population cycles in relative independence of the other populations and eventually goes extinct as a consequence of demographic stochasticity (fluctuations in population size due to random demographic events); the smaller the population, the more prone it is to extinction.

Although individual populations have finite life-spans, the population as a whole is often stable because immigrants from one population (which may, for example, be experiencing a population boom) are likely to re-colonize habitat which has been left open by the extinction of another population. They may also emigrate to a small population and rescue that population from extinction (called the rescue effect ).

Age class structure

Age can be determined by counting growth rings in fish scales, otoliths, cross-sections of fin spines for species with thick spines such as triggerfish, or teeth for a few species. Each method has its merits and drawbacks. Fish scales are easiest to obtain, but may be unreliable if scales have fallen off of the fish and new ones grown in their places. Fin spines may be unreliable for the same reason, and most fish do not have spines of sufficient thickness for clear rings to be visible. Otoliths will have stayed with the fish throughout its life history, but obtaining them requires killing the fish. Also, otoliths often require more preparation before ageing can occur.

An age class structure with gaps in it, for instance a regular bell curve for the population of 1-5 year-old fish, excepting a very low population for the 3-year-olds, implies a bad spawning year 3 years ago in that species.

Often fish in younger age class structures have very low numbers because they were small enough to slip through the sampling nets, and may in fact have a very healthy population.

Population cycle

A population cycle occurs where populations rise and fall over a predictable period of time. There are some species where population numbers have reasonably predictable patterns of change although the full reasons for population cycles is one of the major unsolved ecological problems. There are a number of factors which influence population change such as availability of food, predators, diseases and climate.

Trophic cascades

Trophic cascades occur when predators in a food chain suppress the abundance of their prey, thereby releasing the next lower trophic level from predation (or herbivory if the intermediate trophic level is an herbivore). For example, if the abundance of large piscivorous fish is increased in a lake, the abundance of their prey, zooplanktivorous fish, should decrease, large zooplankton abundance should increase, and phytoplankton biomass should decrease. This theory has stimulated new research in many areas of ecology. Trophic cascades may also be important for understanding the effects of removing top predators from food webs, as humans have done in many places through hunting and fishing activities.

Classic examples
  1. In lakes, piscivorous fish can dramatically reduce populations of zooplanktivorous fish, zooplanktivorous fish can dramatically alter freshwater zooplankton communities, and zooplankton grazing can in turn have large impacts on phytoplankton communities. Removal of piscivorous fish can change lake water from clear to green by allowing phytoplankton to flourish. [24]
  2. In the Eel River, in Northern California, fish (steelhead and roach) consume fish larvae and predatory insects. These smaller predators prey on midge larvae, which feed on algae. Removal of the larger fish increases the abundance of algae. [25]
  3. In Pacific kelp forests, sea otters feed on sea urchins. In areas where sea otters have been hunted to extinction, sea urchins increase in abundance and decimate kelp [26]

A recent theory, the mesopredator release hypothesis, states that the decline of top predators in an ecosystem results in increased populations of medium-sized predators (mesopredators).

Basic models

Predator–prey equations

The classic predator–prey equations are a pair of first order, non-linear, differential equations used to describe the dynamics of biological systems in which two species interact, one a predator and one its prey. They were proposed independently by Alfred J. Lotka in 1925 and Vito Volterra in 1926.

An extension to these are the competitive Lotka–Volterra equations, which provide a simple model of the population dynamics of species competing for some common resource.

In the 1930s Alexander Nicholson and Victor Bailey developed a model to describe the population dynamics of a coupled predator–prey system. The model assumes that predators search for prey at random, and that both predators and prey are assumed to be distributed in a non-contiguous ("clumped") fashion in the environment. [30]

In the late 1980s, a credible, simple alternative to the Lotka–Volterra predator-prey model (and its common prey dependent generalizations) emerged, the ratio dependent or Arditi–Ginzburg model. [31] The two are the extremes of the spectrum of predator interference models. According to the authors of the alternative view, the data show that true interactions in nature are so far from the Lotka–Volterra extreme on the interference spectrum that the model can simply be discounted as wrong. They are much closer to the ratio dependent extreme, so if a simple model is needed one can use the Arditi-Ginzburg model as the first approximation. [32]

See also

Related Research Articles

<span class="mw-page-title-main">Theoretical ecology</span>

Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis. Effective models improve understanding of the natural world by revealing how the dynamics of species populations are often based on fundamental biological conditions and processes. Further, the field aims to unify a diverse range of empirical observations by assuming that common, mechanistic processes generate observable phenomena across species and ecological environments. Based on biologically realistic assumptions, theoretical ecologists are able to uncover novel, non-intuitive insights about natural processes. Theoretical results are often verified by empirical and observational studies, revealing the power of theoretical methods in both predicting and understanding the noisy, diverse biological world.

In population ecology and economics, maximum sustainable yield (MSY) is theoretically, the largest yield that can be taken from a species' stock over an indefinite period. Fundamental to the notion of sustainable harvest, the concept of MSY aims to maintain the population size at the point of maximum growth rate by harvesting the individuals that would normally be added to the population, allowing the population to continue to be productive indefinitely. Under the assumption of logistic growth, resource limitation does not constrain individuals' reproductive rates when populations are small, but because there are few individuals, the overall yield is small. At intermediate population densities, also represented by half the carrying capacity, individuals are able to breed to their maximum rate. At this point, called the maximum sustainable yield, there is a surplus of individuals that can be harvested because growth of the population is at its maximum point due to the large number of reproducing individuals. Above this point, density dependent factors increasingly limit breeding until the population reaches carrying capacity. At this point, there are no surplus individuals to be harvested and yield drops to zero. The maximum sustainable yield is usually higher than the optimum sustainable yield and maximum economic yield.

The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:

<span class="mw-page-title-main">Overfishing</span> Removal of a species of fish from water at a rate that the species cannot replenish

Overfishing is the removal of a species of fish from a body of water at a rate greater than that the species can replenish its population naturally, resulting in the species becoming increasingly underpopulated in that area. Overfishing can occur in water bodies of any sizes, such as ponds, wetlands, rivers, lakes or oceans, and can result in resource depletion, reduced biological growth rates and low biomass levels. Sustained overfishing can lead to critical depensation, where the fish population is no longer able to sustain itself. Some forms of overfishing, such as the overfishing of sharks, has led to the upset of entire marine ecosystems. Types of overfishing include growth overfishing, recruitment overfishing, and ecosystem overfishing.

<span class="mw-page-title-main">Sustainable fishery</span> Sustainable fishing for the long term fishing

A conventional idea of a sustainable fishery is that it is one that is harvested at a sustainable rate, where the fish population does not decline over time because of fishing practices. Sustainability in fisheries combines theoretical disciplines, such as the population dynamics of fisheries, with practical strategies, such as avoiding overfishing through techniques such as individual fishing quotas, curtailing destructive and illegal fishing practices by lobbying for appropriate law and policy, setting up protected areas, restoring collapsed fisheries, incorporating all externalities involved in harvesting marine ecosystems into fishery economics, educating stakeholders and the wider public, and developing independent certification programs.

<span class="mw-page-title-main">Fisheries management</span> Regulation of fishing

The goal of fisheries management is to produce sustainable biological, environmental and socioeconomic benefits from renewable aquatic resources. Wild fisheries are classified as renewable when the organisms of interest produce an annual biological surplus that with judicious management can be harvested without reducing future productivity. Fishery management employs activities that protect fishery resources so sustainable exploitation is possible, drawing on fisheries science and possibly including the precautionary principle.

<span class="mw-page-title-main">Population ecology</span> Study of the dynamics of species populations and how these populations interact with the environment

Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment, such as birth and death rates, and by immigration and emigration.

<span class="mw-page-title-main">Fish stocks</span> Semi-discrete subpopulations of a particular species of fish

Fish stocks are subpopulations of a particular species of fish, for which intrinsic parameters are traditionally regarded as the significant factors determining the stock's population dynamics, while extrinsic factors are traditionally ignored.

<span class="mw-page-title-main">California sheephead</span> Species of fish

The California sheephead is a species of wrasse native to the eastern Pacific Ocean. Its range is from Monterey Bay, California, to the Gulf of California, Mexico. It can live for up to 20 years in favorable conditions and can reach a size of up to 91 cm (3 ft) and a weight of 16 kg (35 lb). It is carnivorous, living in rocky reef and kelp bed habitats, feeding primarily on sea urchins, molluscs, and crustaceans.

<span class="mw-page-title-main">Environmental impact of fishing</span>

The environmental impact of fishing includes issues such as the availability of fish, overfishing, fisheries, and fisheries management; as well as the impact of industrial fishing on other elements of the environment, such as bycatch. These issues are part of marine conservation, and are addressed in fisheries science programs. According to a 2019 FAO report, global production of fish, crustaceans, molluscs and other aquatic animals has continued to grow and reached 172.6 million tonnes in 2017, with an increase of 4.1 percent compared with 2016. There is a growing gap between the supply of fish and demand, due in part to world population growth.

The sustainable yield of natural capital is the ecological yield that can be extracted without reducing the base of capital itself, i.e. the surplus required to maintain ecosystem services at the same or increasing level over time. This yield usually varies over time with the needs of the ecosystem to maintain itself, e.g. a forest that has recently suffered a blight or flooding or fire will require more of its own ecological yield to sustain and re-establish a mature forest. While doing so, the sustainable yield may be much less.

This is a glossary of terms used in fisheries, fisheries management and fisheries science.

<span class="mw-page-title-main">Raitt's sand eel</span> Species of fish

Raitt's sand eel, also known as the lesser sand eel, is a small semi-pelagic ray-finned fish found in the North Atlantic Ocean. The Raitt's sand eel is member of the family Ammodytidae which includes all 31 species of sand eels, often referred to as sand lances. Contrary to their name sand eels, including Raitt's sand eel, are not true eels and instead belong to the order of “weever-like” fishes, the Trachiniformes.

Fish mortality is a parameter used in fisheries population dynamics to account for the loss of fish in a fish stock through death. The mortality can be divided into two types:

<span class="mw-page-title-main">Stock assessment</span> Process used in fisheries management

Stock assessments provide fisheries managers with the information that is used in the regulation of a fish stock. Biological and fisheries data are collected in a stock assessment.

The paradox of the pesticides is a paradox that states that applying pesticide to a pest may end up increasing the abundance of the pest if the pesticide upsets natural predator–prey dynamics in the ecosystem.

The stable ocean hypothesis (SOH) is one of several hypotheses within larval fish ecology that attempt to explain recruitment variability. The SOH is the notion that favorable and somewhat stable physical and biological ocean conditions, such as the flow of currents and food availability, are important to the survival of young fish larvae and their future recruitment. In the presence of stable ocean conditions, concentrations of prey form in stratified ocean layers; more specifically, stable ocean conditions refer to “calm periods in upwelling ecosystems ” that cause the water column to become vertically stratified. The concept is that these strata concentrate both fish larvae and plankton, which results an increase of the fish larvae feeding because of the density-dependent increase in predator-prey interactions. Lasker is attributed with constructing this hypothesis in the late 1970s by building on previous larval fish research and conducting his own experiments. He based the SOH on case studies of clupeid population fluctuations and larval experimentation.

A slot limit is a tool used by fisheries managers to regulate the size of fish that can legally be harvested from particular bodies of water. Usually set by state fish and game departments, the protected slot limit prohibits the harvest of fish where the lengths, measured from the snout to the end of the tail, fall within the protected interval. For example, on a body of water where there is a protected slot limit on largemouth bass between 12 and 16 inches, largemouth between those lengths may not be harvested. In this example largemouth bass shorter than 12 inches (30 cm) and longer than 16 inches (41 cm) may be removed from the water and kept for personal use in accordance with local fishing regulations.

The following outline is provided as an overview of and topical guide to fisheries:

<span class="mw-page-title-main">Fisheries-induced evolution</span> Evolution of fishes driven by the fishery industry

Fisheries-induced evolution (FIE) is the microevolution of an exploited aquatic organism's population, brought on through the artificial selection for biological traits by fishing practices. Fishing, of any severity or effort, will impose an additional layer of mortality to the natural population equilibrium and will be selective to certain genetic traits within that organism's gene pool. This removal of selected traits fundamentally changes the population gene frequency, resulting in the artificially induced microevolution by the proxy of the survival of untargeted fish and their propagation of heritable biological characteristics. This artificial selection often counters natural life-history pattern for many species, such as causing early sexual maturation, diminished sizes for matured fish, and reduced fecundity in the form of smaller egg size, lower sperm counts and viability during reproductive events. These effects can have prolonged effects on the adaptability or fitness of the species to their environmental factors.

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Further reading