Lecture 9: Population Growth
Estimating Rates for an Annual Plant (P. drummondii)
Overlapping or non-overlapping generations?
Ro = Net reproductive rate
- Average number of offspring produced by an individual in a population during its lifetime.
Ro=Σlxmx
- lx = % pop. surviving to each age (x)
- mx= Average number seeds produced by each individual in each age category
- X = Age interval in days
Ro = Net reproductive rate
Ro < 1
Ro > 1
Ro = 1
- Because P. drummondii has non-overlapping generations and pulsed reproduction, estimate growth rate as geometric rate of increase (λ)
Geometric Rate of Increase (λ):
- λ = N t+1 / Nt
- N t+1 = Size of population at future time
- Nt = Size of population at some earlier time
- λ = 2,408/996
- λ = 2.41
Estimating Rates when Generations Overlap
Common Mud Turtle ( K. subrubrum)
- Ro = 0.601
- Can also calculate:
- Generation Time (T) = Ave. time from egg to egg
T = Σ xlxmx / Ro
x = Age in years
T = 10.6 years
Per Capita Rate of Increase (r) = birthrate – death rate <---- Exponential growth - continuous reproduction
r = ln Ro / T
r = ln (0.601)/10.6 = - 0.05
Fecundity schedule more complicated
- Number of females that nest each year
- Clutch size
- Number of female vs. male offspring
Generation time versus body size
What other factors influence population dynamics?
Exploring population dynamics
- Births, deaths, survivorship
- Age distribution
- Rates of population change
- Dispersal
Dispersal
- Dispersal into populations (immigration)
- Dispersal out of populations (emigration)
Snail kites in Florida
What else regulates population growth?
Density dependent factors
The Malthusian Doctrine (1798)
- Food is necessary for existence (of humans)
- The “passion between the sexes is necessary and will remain nearly in its present state.”
---> Populations will be checked by death from starvation when food resources are exhausted.
Pearl and Reed’s U.S. Population projection
Rather than assume exponential growth, they assumed that r
Decreases as N increases
r = r0(1-N/K)