Chapter 10 Population Dynamics

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

Static Life Tables and Survivorship Curves

Plotting number of survivors against age produces a survivorship curve

Example: Survival pattern of Dall sheep

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

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

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

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.

Age Distribution and Stable Populations

Age Distribution and Declining Populations

A Dynamic Population in a Variable Climate

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

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: 2.4177 x 996 plants = 2408

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:

= 2408 = 2.4177 996

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)

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

per capita rate of increase (r)

r = ln Ro / T

Turtle example:

r = ln (0.601) / 10.6

r = -0.05