Population Ecology Part V

Story of Reindeers (St. Matthew Island, Alaska)

• 29 reindeers released on island (1944)

• David Klein visited island-counted 1350 (1957)

• Klein counted (1962) population to be 6000.

• Recounted (1966) found 42 reindeer left. (1 male, rest female 2yr+) 

The logistic Growth Model

Only the model takes into consideration the effects of the environment on population growth (differs from geometric and exponential) 

*Not constant with population size (density). 

density dependent model 

Carry Capacity (K)

The number of individuals of a particular species that an environment can support. Population size at which growth stops or needs to stabilize.

Consequences of Carry Capacity

• N«K, population can show exponential growth (r>>0)

• N starts to approach K, population grows slowly until it reaches a plateau/equilibrium.

• N=K (birth rate equals mortality rate)(r=0)

N=(1/2)K

Equation (carry capacity)

dN/dt = r/N (1-N/K)

Stages of logistic growth 

1) Lag phase 

2) Exponential growth phase 

3) Deceleration phase

4) Equilibrium phase  

For sigmoidal curve (logistic Growth). Growth equation

N=K/(1+((K-N₀)/N₀)e^-rt

Assumption to exponential and logistic growth models

Population size are instantaneous.

usually there is a lag in population

Time lag equation (𝜏)

(𝜏)=1/r

Determine “trajectory dynamics” of N around K as follows

• 𝜏 between 0-0.37: population grows accordance with logistiic growth curve: reaching K.

• 𝜏 between 0.37-1.57: damped oscillations around K 

• 𝜏 1.57 or higher: stable limit cycles, population continually oscillates about K (never remains at K).