Population Assessment
In order to set fishing quotas, the state fisheries biologists estimated the number of fish in each lake and then modeled how many fish could be taken by sportfishermen without crashing the population. This was important because many of the lakes in northern Wisconsin are relatively small and isolated from other lakes and streams, making them vulnerable to overfishing and reducing the probability that they will be recolonized by fish dispersing from other populations. Lakes were sampled by fisheries biologists before the beginning of the fishing season using mark-recapture techniques. This is done by capturing fish alive, marking them with tags or by cutting a spine on their fin, releasing them, then catching another sample. They then determined how many of the fish in the "recapture" were marked and how many were unmarked-- this ratio allowed them to come up with an estimate of the whole population.
The population estimate was then compared to what they considered the maximum population size that a lake could sustain. Fisheries managers used models based on "Maximum Sustainable Yield" or MSY, to manage the Walleye fishery in northern Wisconsin. These models are based on the logistic growth equation and have several important assumptions:
Parameters representing reproductive output, life expectancy, and other life history traits are assumed to be the same throughout the population
Population models also assume a fixed carrying capacity that does not change over time (stable environment)
The goal of harvest models is to maximize net productivity
Maximum rate of population increase occurs at a population size of 1/2 K
Maintaining population at a size equal to 1/2 K results is fastest replacement rates
High replacement rates allow high harvest levels
When you look at this graph remember that it represents a rate, which means that when the curve is steep the population is growing very quickly, but when the curve tapers off the rate of growth is slower. Based on this model fisheries managers assume that every female in the population is the same and the amount of food, nest sites, etc. will always be the same (stable carrying capacity). And they assume that when the population gets large, density dependent factors kick in. Density dependence refers to those things that are more severe when the population size is large (when there is a higher density of individuals): high intraspecific competition for food, mates, and breeding sites; increasing rates of disease and parasites; and other density dependent factors that slow the rate of population growth. In other words, there will be more things that cause more individuals to die and cause fewer individuals to be born, and that will slow down the rate at which the population grows.
Fisheries managers assume that the population will be growing the fastest before density dependent factors kick in. This theoretically occurs when the population size is at half of the carrying capacity. If you look at the curve, the steepest slope is at 1/2K, which is defined as the "maximum sustainable yield" or MSY. It is assumed that beyond the population size at 1/2K that when you remove individuals through fishing you are reducing density dependent factors and helping the remaining individuals in the population to maintain a high rate of reproduction and survival.
Both graphs modified from: hhh.gavilan.edu/jhubbard/ecol/Lectures/Lect11Populations.ppt
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