L16 Population Growth

exponential growth

change in the size of a population by a constant proportion at each instant in time

What are the two ways to measure exponential population growth?

for species with continuous reproduction (exponential growth), for species with discrete reproduction (geometric growth)

Measuring with continuous reproduction

N_t = N₀e^rt

Measuring with geometric growth (discrete reproduction)

N_t = Lambda x N₀

Describe the meanings of each variable of the growth equations

N = population size

r = exponential growth rate or the per capita intrinsic rate of increase (if 0 no change)

e = 2.718

t = time point

lambda = geometric population growth rate or the finite rate of increase (1 no change)

logistic growth

a pattern in which abundance increases rapidly at first then stabilizes at a population size known as the carrying capacity (K)

What do we assume for logistic growth models?

the population rate of increase declines as population density increases

Equation for logistic growth

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

Describe the meanings of the variables in the logisitc growth equation

dN/dt = rate of change in population size at time t

N = population size at time t

r = exponential growth rate or the instrinsic rate of increase 

K = carrying capacity

as dN/dt approaches 0 then…

…the population is nearing carrying capacity

what does (1-N/K) represent?

the net effect of factors that reduce the population growth rate from the constant rate r

density dependence

factors that limit population growth in a density-dependent matter

density-independent factors

factors that influence population growth but not influenced by the density of the population

What four processes affect population size changes?

births, deaths, immigration, emigration

population dynamics equation

N_t+1 = N_t+B+I-D-E

Four patterns of population growth and change

exponential growth, logistic growth, fluctuating density, population cycles

Fluctuating density

natural variation in number of individuals in a population, most common, sometimes has exponential and logistic growth, density dependent and independent factors

population cycles

regular and predictable fluctuations in population density

r and lambda fluctuations can lead to what and is more severe in smaller populations?

extinction, more severe in smaller populations

Allee effect

population’s per capita growth rate is positively linked to size or density

metapopulations

set of distinct populations that are linked to dispersal

metapopulations: source

(B>D) more emigration than immigration

metapopulations: sink

(D>B) immigration greater than emigration

rescue effect

population can go extinct than be recolonized, likelihood of extinction based on patch size, recolonization based on distance from current extant population (source) and extinct population patch size