Topic+9.+Population+Structure

# Frequency histogram gives a picture ii important

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Frequency histogram gives a picture: II. Important terms Defs A. cohort : Def -- Those individuals in a population born during a specific time, e.g., January 1, 1990, and December 31, l990. How many individuals in that cohort here? B. x survivorship . Def -- The fraction of individuals in a cohort surviving to age x – the same as the probability of surviving to age x. Very important for insurance purposes in humans, Lotka famous mathematical demographer worked for Metropolitan Life. C. m x fecundity . Def -- number of offspring produced by an individual of age x while at that age.

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III. Types of survivorship curves. Slide of Fig. 9.5 from text Type I – Low initial mortality. Humans, other mammals, a few lizards Type II – Constant probability of dying per time. Most lizards, birds, some mammals Type III – High initial mortality. Many fish, Most insects, many plants See also Fig. 9.6 in text: slide
IV. R 0 is net reproductive rate = x x x m R 0 The summation of the product of x and m x for all x (so not just equal to Σm x ) x x m x x m x 1 .9 0 0 2 .8 1 0.8 3 .6 2 1.2 4 .2 1 0.2 5 .1 0 0 R 0 = 2.2 If R 0 = 1, population N is stable. R 0 > 1 means increasing N. R 0 < 1 population N is declining. Can be because x , m x or both are low. V. Generation time. Has common meaning, but here very precise Def – Average age of reproduction. A. Roughly T = (α + ω)/2 α = first age of reproduction, ω = last age of reproduction. Example: when α = 12, ω = 52, T = 32. B. More exact: 0 R m x T x x x = Takes into account life-table numbers. Weights age x by x and m x When R 0 = 1, get the numerator only.

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VI. Reproductive Value V A . A. Def – How many offspring one could expect from an animal of age A for the rest of its life. B. Famous plot for Australian women C. For constant population (R 0 = 1) formula is: x A x A x A m V = = ϖ A is age and ω last age of reproduction. x / A is a conditional probability. Given that you lived to age A, what is probability of living to age x?
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