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Chapter 10 Population Dynamics
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Estimating Patterns of Survival
Three main ways of estimating patterns of survival within a population: Identify a large number of individuals that are born about the same time (=cohort) and keep records of them from birth to death ---> cohort life table Record the age at death of a large number of individuals ---> static life table Determine patterns of survival for the population from the age distribution
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Static Life Tables and Survivorship Curves
Example: Survival pattern of Dall sheep Plotting number of survivors against age produces a survivorship curve
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Types of Survivorship Curves
Type I Survivorship Curve A pattern in which most of the individuals of the population survive to maturity Or, most individuals of the population do not die until they reach some genetically programmed uniform age
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Types of Survivorship Curves cont.
Type II Survivorship Curve Relatively constant death rates with age Equal probability that an individual will die at any particular age
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Types of Survivorship Curves cont.
Type III Survivorship Curve A pattern in which their is an extremely steep juvenile mortality and a relatively high survivorship afterward Most offspring die before they reach reproductive age
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Age Distribution Age distribution can tell you a lot about a population – periods of successful reproduction; periods of high and low survival; whether older individuals are being replaced; whether a population is growing, declining, etc.
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Age Distribution and Stable Populations
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Age Distribution and Declining Populations
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A Dynamic Population in a Variable Climate
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Rates of Population Change: Combining a Cohort Life Table with a Fecundity Schedule
Fecundity schedule - the tabulation of birth rates (the number of young born per female per unit time) for females of different ages in a population By combining the information in a fecundity schedule with data from a life table, we can estimate several important characteristics of a population
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Example: A Population with Discrete Generations
nx, the number of individuals in the population surviving to each age interval lx, survivorship, the proportion of the population surviving to each age x mx,average number of progeny produced by each individual in each age interval lx mx, the product of l and m Net reproductive rate, R0 R0 = lx mx To calculate the number of progeny produced by a population in a given time interval, multiply R0 by the initial number of individuals in the population. Example: x 996 plants = 2408
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Geometric Rate of Increase
The ratio of population increase at two points in time: = Nt+1 n Where, Nt+1 is the size of the population at a later time, and Nt is the size of the population at an earlier time Example: = = 996
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More on net reproductive rate:
R0 is an indication of the expected number of female offspring which a newly born female will produce during her life span It’s an indication of whether a female replaces herself in the population R < 1, the population will decline R = 1, the population will remain constant R > 1, population will increase (more offspring produced than needed to replace the female)
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Mean Generation Time (T)
T = [∑ (x lx mx ] / Ro where x is age Example from the common mud turtle: These turtles have an average generation time of 10.6 years: = 6.4/0.601 = 10.6
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per capita rate of increase (r)
r = ln Ro / T Turtle example: r = ln (0.601) / 10.6 r = -0.05
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