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
Example: Survival
pattern of Dall sheep
Plotting number of
survivors against age
produces a survivorship
curve
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