1. Section 5 Professor Donald McFarlane
Biology 44
Section 5
Professor Donald McFarlane
Lecture Ecology: Population Growth

2. 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

3. 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
Exponential growth – resources not limiting, prodigious growth
Logistic growth – resources limiting, limits to growth

4. 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

5. dt r = “intrinsic rate of increase” = -ln R0 Tgen
The differential growth equation:
dN = rN dt

6. 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

7. 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

9. (b) Black-footed ferrets
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600
400
Predicted abundance
Actual abundance
500
400
200
Number of animals
Population size
300
200
100
100
2000
2001
2003
2004
2005
2006
1970
1980
1990
2000
Year
Survey year
(a) Tule elk
(b) Black-footed ferrets

10. 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

13. Not all individuals in a population are the same with respect to births and deaths…..
We can account for differences with a LIFE TABLE

14. 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

16. 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

18. Life history strategies
Continuum
r-selected 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
Lower reproductive rate but lower mortality rates

20. 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

22. 3 patterns of survivorship curves
Type I – rate of loss of juveniles low and most individuals lost later in life
Type II – fairly uniform death rate
Beaver example
Type III – rate of loss for juveniles high and then loss low for survivors

24. Population (billions)
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2000 5
Population (billions) 4
1975 3
1950 2
1900 1
1800
1 C.E
1000 C.E
2000 C.E
7000 B.C.E
6000 B.C.E
5000 B.C.E
4000 B.C.E
3000 B.C.E
2000 B.C.E
1000 B.C.E