Summary Lecture 12 Slides

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 ecologyDensity 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

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