This chapter shows how the population size spectrum can be calculated using the vital rates of the individuals within the population: the growth rate, the reproduction rate, and the mortality as functions of size. It discusses the physiological mortality at length, and attempts to estimate its value from meta-analyses of mortality and growth rate in fish. In obtaining solutions of the population size spectrum, the chapter follows two parallel tracks: a simplified analytical solution, and a full numerical solution. The analytical solution offers insights into the governing scaling relationships between asymptotic size and population-level measures, such as spawning stock biomass, reproductive output, and lifetime reproductive output. Meanwhile, the numerical solution allows us to explore the effects of size-based fishing in the next chapter.
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