Lecture 12 - Population Growth and Regulation, Part 1 10/26

Population Change.

Births, immigration, deaths, emigration

BIDE: (B+I)-(D+E)

Per Capita Rates

r = (B+I)-(D+E) (r) per capita growth rate

Simple population model

"Nt = λtN0"

λ = per capita geometric rate of increase

t = time

N0 = population at t=0

Lambda λ

Population @ t / Population @ t-1(present/past)

λ= "Nt⁄Nt-1" Discreet time model

Predicting the future – Discreet time model (an example)

7 weebles in today, λ = 2, How many Weebles in year 5?

"Nt = λtN0"

"N5 = 27" x"7"

"N5" = (128)(7) = 896 (wow! Hope there’s room for them)

Continuous Time Model

Rate of change in population = per capita growth rate*population

N(t)=N(0)e^rt

r= ?

Instantaneous rate of change

Per capita exponential growth rate

Relative growth rate

r=log"e" λ

λ= e^r

No Growth

r = 0 or λ = 1

Population Increasing

r > 0 or λ >1

Population Decreasing

r < 0 or 0 < λ < 1

r versus λ

r describes populations w/overlapping generations and continuous reproduction

λ non overlapping and discreet breeding seasons

Population doubling times

Rule of 70

t = 0.69/r r is per capita

Population Constraints

Negative feedback

In ecologyDensity dependent

Carrying capacity (k)

Total number of organisms that the environment can support.

Above k, r is negative, population declines

Below k, r is positive, population increases

At k, r = 0

1 – N/k proportion of utilized resources.

Factors affecting population size and growth rate.

Population Regulation

An equilibrium density towards which the population is attracted.

“Regulating” factors generate and maintain equilibria.

Population Oscillations

All populations fluctuate over time.

Large r, oscillatory

Live Fast Stable, Slow recovery