Population Growth
Population growth deals with the net change in individuals for a given population
- Birth and immigration into
- increase population
- Death and emigration away
- decrease population=emigratio
We can define a change in population () as a function:
where =birth, =death, =immigration, =emigration
What if we want to know the rate at which the change in population is occurring?
- We must determine the per capita (intrinsic) growth rate (), which depends on time:
where =change in population, = change in time, =initial population size
- intrinsic growth rate: maximum rate of growth
- no environmental factors limit population increase
If we want to determine what the population size will be sometime in the future, then we use the following formula:
where = future population, =intrinsic growth rate, =time
- Exponential growth: when the is constant through time
- The number of individuals added to the population at any time is proportional to the size of the population at that tim
Density Dependence
- Density Independent Factors: forces that do not depend on population size
- Often environmental disasters Examples: Fire, Lightning
- Density Dependent Factors: forces that are related to population size
- Predation and disease Examples: High density populations are at high risk of disease outbreaks
- As a population grows, crowding results in a decrease in available space
- Carrying Capacity (K): the maximum number of individuals any habitat can support.
- Population is typically below K due to predation and parasitism.
- These do not effect K since K is based on the habitat
- Small populations:
- resources are not limiting
- Growth rate = r
- Large populations:
- Populations near or at K
- Overcrowding reduces available resources
- Growth rate < r
- Determine how close the population is to K:
where K= carrying capacity, N=population number
- Intrinsic growth rate () is also scaled by how close the population is to K:
