8_Population growth cheat sheet_BI370

Population growth formula

Nt+1 = Nt + B - D + I - E; where Nt = population at time t, Nt+1 = population at one time step after time.

Per capita rate of increase (Rm)

Rm = (B - D) / N; a measure of population growth with discrete time steps (breeding seasons)

Finite rate of increase (λ)

λ = Rm + 1; used to predict population size at the next time step.

Population multiplication rate formula

Nt+1 = Nt * λ; used to predict the population size based on the finite rate of increase.

Geometric growth equation

Nt = N0 * λ^t; predicts population size at any time given initial size and growth rate.

Intrinsic rate of increase (r)

r = b - d; where b = birth rate and d = death rate. Used for exponential growth

Exponential growth equation

Nt = N0 * e^(rt); predicts population size in continuously growing populations.

Doubling time formula

td = ln(2) / r

Life tables

A table that summarizes the age structure, survivorship (lx), and fecundity (Fx) of a population.

Net reproductive rate (R0)

R0 = ∑(lx * Fx); measures the average number of offspring per individual at age x

Generation time (G)

G = ∑(x * lx * Fx) / R0; average time between the birth of parents and the birth of their offspring.

Logistic growth (density-dependent growth)

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

Logistic growth for time Nt

Nt = K/(1+((K-No)/No)e^rt

Survivorship (lx)

lx = (Nx/No)

r (intrinsic rate of increase) from life table

r = (lnRo)/G

Geometric growth to exponential growth

e^r= λ; r=ln( λ)

lambda (λ)

λ = Nt+1/Nt