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Section 5
Professor Donald McFarlane
Lecture 18 Ecology:
Population Growth

Population – group of interbreeding
individuals occupying the same habitat at
the same time
 Water
lilies in a particular lake
 Humans in New York City

Population ecology – study of what factors
affect population size and how these
factors change over space and time
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How populations grow


Life tables can provide accurate information
about how populations grow from generation to
generation
Simpler models can give insight to shorter time
periods
growth – resources not limiting,
prodigious growth
 Logistic growth – resources limiting, limits to growth
 Exponential
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
Per capita growth rate
 Change
in population size over any time period
 Often births and deaths expressed per individual
 100 births to 1000 deer = 0.10
 50 deaths in 1000 deer = 0.05
Net Reproductive Rate, R0, is approximately birth rate – death rate
R0 ~ (b – d) ~ (0.1 – 0.05) = 0.05
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r = “intrinsic rate of increase” = -ln R0
Tgen
The differential growth equation:
dN = rN
dt
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R0 for deer was 0.05
Tgen is 4 years
Therefore r = - ln(0.05)/4 = 0.748
dN = rN
dt
Starting with 10 deer (N0 = 10)
`
N0 = 10
N1 = 17
N2 = 31
N3 = 53
N4 = 94
N5 = 163
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
Exponential growth
 When
r>0, population increase is rapid
 Characteristic J-shaped curve
 Occurs when population growth is
UNREGULATED by the environment
 e.g., growth of introduced exotic species,
yeast in brewing medium, and global human
population
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
400
600
Predicted abundance
Actual abundance
Number of animals
Population size
500
400
300
200
100
200
100
0
0
1970
1980
1990
Year
(a) Tule elk
2000
Survey year
(b) Black-footed ferrets
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
Logistic growth
 Eventually,
resources become limiting as
populations grow
 Carrying capacity (K) or upper boundary for
population
 Logistic equation
dN = rN ( K – N )
dt
K
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Not all individuals in a population are the same
with respect to births and deaths…..
We can account for differences with a LIFE TABLE
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
Age-specific fertility rate, mx
 Proportion
of female offspring born to females
of reproductive age
 100 females produce 75 female offspring
mx=0.75

Age-specific survivorship rate, lx
 Use
survivorship data to find proportion of
individuals alive at the start of any given age
class
 lxmx
= contribution of each age class to
overall population growth
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
Density-dependent factors
 Mortality
factor whose influence varies with the
density of the population
 Parasitism, predation, and competition
 Predators kill few prey when the prey population is
low, they kill more prey when the population is higher
 Detected by plotting mortality against population
density and finding positive slope

Density-independent factor
 Mortality
factor whose influence is not affected by
changes in population size or density
 Generally physical factors – weather, drought, flood,
fire
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
Life history strategies
 Continuum
species – high rate of per capita
population growth, r, high mortality rates
 K-selected species – more or less stable
populations adapted to exist at or near
carrying capacity, K
 r-selected

Lower reproductive rate but lower mortality rates
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
Survivorship curve – plots numbers of
surviving individuals at each age
 Use
log scale to make it easier to examine
wide range of population sizes
 Beavers have a fairly uniform rate of death
over the life span
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
3 patterns of survivorship curves
I – rate of loss of juveniles low and most
individuals lost later in life
 Type II – fairly uniform death rate
 Type

Beaver example
III – rate of loss for juveniles high and
then loss low for survivors
 Type
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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Population (billions)
7
6
2000
5
4
3
2
1
1975
1950
1900
1800
0
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