Define population
All of the individuals of a species that live and reproduce in a particular place
Population size
Number or individuals alive at a particular time in a particular place. Influenced by births, deaths and migration.
N
Population size. Always rounded to nearest whole number
B
Number of individuals born
D
Number of individuals who died
t
Time/generation
b
Per capita birth rate
d
Per capita death rate
r
Per capita growth rate. r = b - d
r > 0
Population is growing
r < 0
Population is shrinking
Population size at t+1
N_t+1 = (1+r)N_t
N_t
N_t = N_o (1+r)^t
Exponential model of population growth
r max. Predicts growth under ideal conditions but does not exist in reality.
r max
Maximum intrinsic rate of increase. Always constant and positive. Varies by species and scales hypometrically with body size
Bacteria r max
~10
Human r max
~0.0001
Larger organisms r max
Lower. Slower intrinsic rate of growth.
Smaller organisms r max
Higher. Faster intrinsic rate of growth
What limits population growth?
Factors that impact birth and death rates. Food, sunlight, predators, disease, shelter, water, mating partners, etc.
As abundance increases, r will…
Decrease
K
Carrying capacity. Point where births and deaths are equal and r=0
Logistic model of population growth
Predicts population growth based on changing growth rates as populations reach carrying capacity (K). Assumes r decreases as population size increases.
As N increases, r will…
Decrease