Lecture 03 & 04 Geometric and Exponential Growth

# Lecture 03 & 04 Geometric and Exponential Growth -...

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INSECT ECOLOGY -- ENTOMOLOGY/BIOLOGY 127 LECTURES 3 and 4-- GEOMETRIC & EXPONENTIAL GROWTH POPULATION GROWTH I. Processes affecting population growth A. Fundamentally four processes affect population growth and decline, but we will concentrate on just two for now: birth and death. IF we assume that the population is closed (no migration) and population growth is continuous, then we can model population growth for infinitesimal small periods of time. Population growth rate: Δ N/ Δ t = dN/dt = B - D B = b N, where b is the instantaneous birth rate of births individual -1 unit time -1 ; a per capita rate => per individual D = d N, where d is the instantaneous death rate of deaths individual -1 unit time -1 ; a per capita rate => per individual (NOTE: dN d N) dN/dt = ( b - d )N; assumes b and d are constant and not affected by population size = r N; r is the instantaneous rate of increase , r is also called the intrinsic rate of natural increase . B. The rate of change of size of a population is the difference between birth and death rates: r = rate of population size change = instantaneous birth rate – instantaneous death rate dN –– = rN dt C. This fundamental relation summarizes all development of descriptions about population growth and dynamics. Starting point for more complex models . II. Describing population growth: A. Populations can grow in two distinct ways. These are: Discrete generations: - non-overlapping generations e.g., insects that reproduce annually: a single generation per year Continuous generations: Lecture 3 and 4, page 1

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