1. Measuring and Modelling Population Change

2. Carrying Capacity
An ecosystem has finite biotic (living) and abiotic (non-living, e.g. light, space, temperature, water) resources
There is a limit to the number of individuals an environment can support at any given time
Carrying Capacity: the maximum number of organisms that can be sustained by available resources over a limited period of time
(this number is always changing)
Different populations are limited by different factors

3. Factors that Affect Population Growth
Depending on the species and the conditions, populations can fluctuate hourly, daily, seasonally or annually
Size changes due to natality (births), mortality (deaths), immigrations, and emigrations
Population Dynamics: changes in population characteristics
Fecundity: the potential for a species to produce offspring in one lifetime (e.g. fish vs. mammals)

4. Patterns of Survivorship
Type I: Low mortality rate and long life expectancy (e.g. humans)
Type II: Show a uniform risk of mortality throughout life (e.g. coral)
Type III: Very high mortality rates when young, but lowers when sexual maturity is reached. Often produce large numbers of offspring. Low average life expectancy. (e.g. green sea turtle)

5. Population Change
population change = [(births + immigration) – (deaths + emigration)] x 100
initial population size (n)
What would be the percent increase of a population of penguins in one year that began with 567 individuals and had:
121 births
54 deaths
11 penguins join to colony
8 penguins leave

6. Open population: a population that is influences by the factors of natality, mortality and migration
Closed population: a population in which only natality and mortality occur (this is rare, and mainly only happens on secluded islands)
Biotic potential: the maximum rate a population can increase under ideal conditions (e.g. bacteria on a petri dish of nutrients, before the nutrients are used up)

7. Population Growth Models
Geometric Growth
Exhibited in populations with a breeding season
Population typically grows rapidly during the breeding season and then declines for the rest of the year
Growth rate is constant and can be determined by comparing the population size in one year to the population size at the same time the previous year
E.g. white-tailed deer
λ = N (t + 1)
N (t)

8. Population Growth Models cont’d
Exponential Growth:
Populations growing continuously at a fixed rate in a fixed time period
Can use the same formula for population growth, but the chosen time interval is not that of reproductive cycle
The instantaneous growth rate can be determined
dN = rN where dN/dt = instantaneous growth rate
dt r = growth rate per capita (birth rate – death rate)
N = population size

9. Exponential Growth continued
Doubling time: the time needed for a population to double in size (constant for exponential growth)
td = 0.69 r
Read example on page 665 and try question #2.

10. Population Growth Models cont’d
Geometric and exponential growth models assume that populations will continue to rise at the same rate indefinitely
Of course, this doesn’t happen in the real world (limiting factors interfere)
When births slow down and begin to resemble the number of deaths, the carrying capacity (K) has been reached

11. Population Growth Models cont’d
Logistic Growth
Represents the effects of carrying capacity on the growth of a population
dN = rmaxN (K – N)
dt K
dN/dt = population growth rate at a given time
rmax = maximum intrinsic growth rate
N = population size at any given time
K = carrying capacity of the environment
Go over sample problem on page 667 and try question #3.

12. Logistic Growth continued:
Lag phase: initial stage in which population is small and increasing slowly
Log phase: the stage in which population experiences very rapid growth
Environmental resistance: factors which limit a population’s ability to increase as it nears carrying capacity
Stationary phase: occurs at or close to carrying capacity – population is said to be in dynamic equilibrium

13. Density-Dependent Factors
a factor that influences population regulation, having a greater impact as population density increases or decreases
e.g. competition for resources among zebra mussels will eventually limit growth in these populations

14. 1) Intraspecific competition: when the individuals of a population of the same species rely on the same resources for survival
As population density increases, there is more competition among individuals for resources so the growth rate slows
E.g. In a deer population, the stronger deer that are able to obtain food will survive, while the weaker deer will either starve or will risk death by moving to another habitat

15. 2) Predation: an ecological interaction in which a predator catches, kills and consumes prey (usually a member of another species)
E.g. usually sharks will prey on fish that are slower or do not have a place to hide – these populations of fish will be regulated by sharks (by predation)
3) Disease: in overcrowded or dense populations, pathogens are able to pass from host to host with greater ease
E.g. the overcrowding of farm animals can lead to the spread of disease

16. 4) Allee effect: density-dependent phenomenon that occurs when a population cannot survive or fails to reproduce enough to offset mortality once the population density is too low – such populations usually do not survive
thought to have played a large role in the extinction of the passenger pigeon
a small population can also result in inbreeding and the loss of genetic variation
minimum viable population size: the smallest number of individuals needed for a population to continue for a given period of time

17. Density-Independent Factors
Human intervention (pesticide application, loss of habitat, etc.)
Biomagnification (e.g. DDT)
Extreme weather changes or other environmental conditions (temperature, etc.)
Limiting factor: any essential resource that is available in short supply or unavailable. Of all the resources that a population requires, the resource in shortest supply is the limiting factor.
e.g. a plant needs nitrogen, sunlight, water, CO2