Midterm formulas Flashcards
Discrete Growth Formula
N(T) = λ^T * N(0)
Continuous Growth Formula
N(t) = e^(rt) * N(0)
Relationship between λ and r
λ = e^r
Discrete time leads to what kind of growth?
Geometric Growth
Continuous time leads to what kind of growth?
Exponential Growth
How do you find r?
r = (lnN2 - lnN1)/(t2-t1)
Assumptions of exponential growth model?
- No immigration, no emigration
- No change in environmental factors
- No genetic structure
- Constant birth and death
- Continuous growth with no time lags
- No age or size structure
What is a generation?
All individuals produced within a single life cycle
What is generation time?
The average duration of a life cycle between birth and reproduction
Net reproductive rate
∑bxlx = R(0)
Generation time formula
G = ∑xbxlx/∑bxlx
Intrinsic rate of increase per year for age structured population (Per capita rate of increase)
r = lnR(0)/G
Direct factors of density dependent regulation
- Aggression
- Cannibalism
- Territoriality
- etc
Most important indirect factor of density dependent regulation
Resource exploitation
Example of indirect regulation of population through density dependence
Overpopulation leads to fewer resources, leading to decreased fecundity
The logistic equation for density dependent population growth
r = -[r(0)/K]*N + r(0)
What is K?
Carrying capacity
Properties of the logistic equation
- Has a solution
- Describes a sigmoid curve
- For N(0)>K, regulates down to carrying capacity
- Rate of change of population size is zero for N=0 and N=K
- Rate of change of population size is an inverted parabola as a fcn of N
- The per capita rate of change of population size is a linearly decreasing fcn of N
What is the Ricker Model used for?
Density dependent growth in discrete time
Ricker Model formula
N(t+1) = N(t)e^[r(0)(1-{N(t)/K)]
What is a closed population?
No emigration or immigration
What characterizes an open population?
There is emigration and immigration
What is a metapopulation?
A population within a group of populations between which members of the different populations migrate.
