Lecture 03 & 04 Geometric and Exponential Growth

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

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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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- overlapping generations; continuous reproduction e.g., insects that show little seasonality in recruitment => rare Some insects may have overlapping generations during periods of favorable growth. tropical insects Bacteria are better example. B. Most insect populations are somewhere between these two concepts, but can be treated successfully with one or the other. e.g., mosquitoes in California III. Population growth in discrete generations. A. Population growth occurs by births and deaths at discrete, or separate, times. This is summarized by the following relation: Discrete Difference Equation N t+l = N t + r d N t , where t is time; r d is the discrete growth factor . r d is the proportional change in the population per unit time. N t+l = [1 + r d ]N t N t+l = [1 + birth rate-death rate]N t Here, time is analogous to generation # when a population reproduces in discrete intervals. or N t+l = R 0 N t , where R 0 is the net reproductive rate. The mean number of female offspring produced during the lifetime of an original female in a cohort. It is the multiplication rate per generation ; the multiplication factor by which population size changes each generation. This equation has a solution for population size at any time:
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This note was uploaded on 02/10/2009 for the course BIO Bio 5A taught by Professor Zhu,rao during the Spring '08 term at UC Riverside.

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

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