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| Introduction
Age-Structured Population Growth
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In 1931 Russell developed a rather simple model of the effect of fishing on fish
stocks. There are a number of factors that effect the fishery. First, there is
natural mortality, which removes fish, and growth, which adds biomass, as well
as new recruits. This means there are two sets of factors which add and subtract
from the population biomass.
S2 = S1 + R + G M F S2 = amount of fish at end of year S1 = amount of fish at beginning of year R = weight of new recruits G = growth of fish still alive M = weight of fish dying F = yield to fishing If we want our fishery and fish population (biomass) to remain the same over time what two factors here to we want to be equal? S2 = S1 If this is true then: R + G = M + F Therefore if fishing occurs then for the population to be stable other factors have to change---M must decrease or R and G must increase. The important point here is that for a stable population at any population density this equation must be true. This is actually not very satisfying if you are interested in potentially maximizing harvest. A more important question is that of what density of fish permits the largest harvest to be safely removed? Graham in 1935 proposed the sigmoid-curve theory. Basically he suggested that population growth follows the logistic growth curve which means that if you want to remove the greatest amount yield and maintain a stable population then you should exploit the part of the curve that is increasing the fastest. Example where we will pull out a number of points along the logistic curve. R = 1.0, K = 200, starting pop = 20
You can see where you should be able to remove the largest number of fish without effecting the populationat N = ½ K. This is an example of what are called Logistic-type models, also known as surplus yield, stock production, or Schaefer models.
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