Population Growth

Learning goals:
* be able to predict changes in population size based on its basic demographic properties
* understand the consequences of a static growth rate term on population growth; know what numeric ranges produce what mathematical functions

The maintenance of species within their geographic range is dependent upon stable or increasing numbers of individuals within populations
Important topic in conservation biology- understanding the controls on the growth of populations (+ and -)  is important in land management decisions that affect species’ persistence

Increases in individuals result from births and immigration, addition of individuals from other populations; recruitment = births + immigration
Decreases result from deaths and emigration, loss of individuals to other populations
Net change in population over time = (births + immigration) – (deaths – emigration)
immigration and emigration are often considered to be small or negate each other

To project how populations are changing through time, data on births and deaths are organized by age classes or cohorts (life table)
survival rate = proportion of individuals reaching next age class
survivorship is proportion of initial individuals surviving to current age class
fecundity is the average number of offspring born to an individual female

Survivorship curves – (# surviving as a function of age) provide useful information about general trends in probability of survival throughout individual liftimes
3 general trends, related to both ecological factors:
Type I, high survival until late in life
Type II, constant death rate
Type III, high initial death rate
patterns of survivorship influence allocation of energy toward reproduction, growth, and protection (life history traits)

Life history tables provide useful information in projecting future trends in population growth; seen intuitively with age structure in populations
Conservation efforts use life tables to focus attention on most important ages

Exponential growth of populations
If on average for the entire population, the birth rate is greater than the death rate, populations will grow at an exponential rate

For populations that have discrete reproductive events:
N_t+1 = lambda * N_t,
where N is the population size at time t and t+1 (discrete interval, geometric growth), and lambda is the “geometric growth rate,” a multiplier (> 0) that incorporates birth and death rates; i.e. or the size of the population at time t+1 is equal to the size of the population at time t time a multiplier that relates the proportional growth or decline of the population

For populations that have continous reproductive events (exponential growth), the addition or loss of individuals to the population is:
dN / dt = r N
where dN is the change in the number of individuals, dt is the change in time, and r is the intrinsic growth rate, a multiplier of how rapidly the population adds or loses new individuals; the term  rN gives the number of individuals that are added to a population over the time period t, and also incorporates birth and death rates

Note that equation for geometric growth gives you the population size, whereas the equation for exponential growth gives you the increase or decrease in individuals, rather than the population size

When lambda = 1 or r = 0, the population stays the same size.
When lambda < 1 or r < 0, the population size will decrease.
When lambda > 1 or r > 0, the population grows geometrically or exponentially
Does any population grow exponentially?