Population Growth Models Test 3

Population growth rate (dN/dt)

Change in population size N per unit time.

Birth rate (b)

Per-capita rate at which individuals are added by births.

Death rate (d)

Per-capita rate at which individuals are lost by deaths.

Intrinsic growth rate (r)

Per-capita rate of increase: r = b − d. r max occurs when b is highest and d is lowest

Maximum intrinsic growth rate (rmax)

Growth rate when births are highest and deaths lowest under ideal conditions.

Exponential growth equation

dN/dt = rN, assuming no immigration or emigration.

Exponential growth

Population increases at a constant per-capita rate with unlimited resources.

Density-independent growth

Exponential

Graph: exponential population growth

J-shaped curve: population grows increasingly rapidly when r is positive and constant.

Founding or recovering population

A small population that may experience exponential growth under favorable conditions.

Exponential growth assumptions

Unlimited resources and space; constant per-capita growth; no immigration or emmigration in the lecture model.

Graph: apple thrip abundance by year

Abundance varies sharply between years.

Logistic growth

Population initially grows rapidly, slows, and fluctuates near carrying capacity.

Logistic growth equation

dN/dt = rrel N(1 − N/K).

Relative growth rate (rrel)

how an individual can reproduce relative to the influence population size has on that individual

Carrying capacity (K)

Point at which the population size is in equilibrium with resources Number of individuals of a species that the environment can support Number of individuals that can survive in the environment Changes with environmental changes

N less than K

positive population growth.

N equal to K

constant population growth.

N greater than K

negative population growth.

Density dependence

Survivorship and fecundity change as population density changes.

Density independence

Factors affect birth or death rates regardless of population density.

Graph: logistic population growth

S-shaped curve with initial rapid growth, slowing growth, and leveling near K.

Graph: negative density dependence in terns

The graph plots breeding pairs of roseate terns over time at three islands. Different colony trajectories illustrate that local population growth can vary with density.

Graph: population growth vs. N in logistic model

Growth is zero at N = 0 and K, and greatest near N = K/2.

Exponential growth: three assumptions

Unlimited resources, unlimited space, and a constant per-capita growth rate (r).

Logistic graph: inflection point to K

Population size still rises, but dN/dt decreases as population approaches K.

Exponential growth: distinguish r from dN/dt

r is per-capita growth; dN/dt is the total change in population size per unit time.

Exponential growth: if r = 0

The model predicts no net population growth because dN/dt = rN = 0.

Logistic growth: why does growth slow?

As density increases, limited resources reduce survivorship or fecundity.

Logistic growth: where is dN/dt highest?

At the inflection point, approximately N = K/2 in the simple logistic model.

Logistic graph: before inflection point

Population size rises and the total growth rate dN/dt increases.

Logistic graph: after inflection point

Population size rises, but total growth rate dN/dt decreases as N approaches K.

Logistic graph: K changes over time

The environment can support different population sizes when resources or conditions change.

Graph: logistic dN/dt versus population size

Hump-shaped curve: zero at N = 0 and N = K; maximum at N = K/2.

Graph: logistic N versus time

S-shaped curve: rises rapidly, bends at inflection, and levels off near carrying capacity.