Unformatted text preview:

Population Growth1. Reproduction and survival in population ecology2. Exponential growtha. Exponential model- Nx+1 = Nx + b – d + i – eo Let i=e=0- Nx+1 = Nx + b – d  Nx+1 - Nx = b – d  ΔN/Δt = b – d  dN/dt = b – d o Let b and d e expressed per capita- dN/dt = (b-d)No let (b-d)=r; r is the intrinsic rate of natural increase- dN/dt = rNo J-shaped curveb. Integral form of model- Nt = N0 . ertc. Calculating r- r can be calculated from life-table and fecundity schedule data- fecundity scheduleo Fx = total number of offspring produced during stage or interval xo mx = number of offspring produced per individual during stage or age interval x mx = Fx/Nxo R0 = net reproductive rate; per capita offspring per individual of original cohort R0 = Σ(Fx)/N0 = Σ(lx . mx) R=1 population stays same R>1 population size increases R<1 population size decreases- Obtaining r o Nt = N0 . ert  r = ln (R0)/T T = mean generation time—average length of time between the birth of a mother and the birth of her offspring T = Σ(x . lx . mx)/R03. Assessment of modela. Examples from real populations—handout- Most lab and natural examples s-shaped curves- Pheasants nearly exponential- Humans exponentialb. Is the exponential growth model wrong or just incomplete?- Population crasheso E.g. willows with rabbitso E.g. wildebeests and rinderpest (virus)- Post-crash population growtho Initially nearly exponentialo But growth slows, yielding an s-shaped curve- * model incomplete—potential to grow exponentially but not for longc. the meaning of r, the intrinsic rate of natural increase- r = individuals per individual per unit time—units: time-1d. possible modifications of the model4. Logistic models (to be covered in “Competition”)5. Stochastic growth models--Deterministic models predict an exact numerical outcome- Always yields the same outcome given the same starting parameters- Nt = N0 . ert--Stochastic models permit chance variation in r a. Random variation in r - Let R0 = 4 - Heads: 0 Tails: 8- Reproductive bout1 2 3 4Female A 0 0 8 0Female B 0 8 8 8Female C 0 8 8 0b. probability of extinction under stochastic growth - is a function of population size- equation: probability extinction = (d0/b0)^N- when r is positive: non-zero chance of becoming extinct by chance aloneo probability extinction > 0o as N decreases, probability extinction increases- when r is zero: certain to go extinct by chance alone, given enough timeo probability extinction=1o expected time to extinction decreases as N decreases- note how important population size is for understanding probabilities of extinction by chance alone6. Population projection for loggerhead sea turtle—see

View Full Document

Pitt BIOSC 0370 - Population Growth

Download Population Growth
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...

Join to view Population Growth and access 3M+ class-specific study document.

We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Population Growth 2 2 and access 3M+ class-specific study document.


By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?