1. Chapter 10 Population Dynamics

2. 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

3. Static Life Tables and Survivorship Curves
Example: Survival pattern of Dall sheep
Plotting number of survivors against age produces a survivorship curve

4. 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

5. 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

6. 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

7. 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.

8. Age Distribution and Stable Populations

9. Age Distribution and Declining Populations

10. A Dynamic Population in a Variable Climate

11. 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

12. 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

13. 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

14. 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)

15. 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

16. per capita rate of increase (r)
r = ln Ro / T
Turtle example:
r = ln (0.601) / 10.6
r = -0.05