1. Population Ecology pp. 959-965; 972
Review definition of population.
Concerns of population ecologists-
Spatial distribution of populations
Numbers, age distributions, sex ratios
Birth rates and mortality rates
Population growth rates
Limits to population growth

2. Spatial distribution
Individuals may be randomly distributed, evenly spaced, or clumped.
Even spacing is least common, but may result from competition or territoriality.
Clumping is most common. It is caused by:
Living near favorable resources
Social or family groupings
Other factors (e.g. seeds piled up by wind)

3. Population Age Distributions
Show what ages are present in a population at a single point in time.
As time goes by, the age distribution may change.
The age distribution at any point in time reflects the history of past birth and death events.

5. Life Tables A life table follows the fate of a cohort.
“Cohort” = group of individuals all born at about the same time.
Calculations include:
Survivorship (fraction of original cohort surviving to each age)
Survival rate (fraction of age x who survive to age x+1)
Mortality rate (fraction of age x who die before age x+1) (Survival rate = 1 – Mortality rate)

7. Survivorship curves These are just a graph of survivorship versus age.
Note that there is no reproduction included in the data. Therefore, the line on the graph can only go down, not up.
Pattern of decline indicates when mortality typically occurs for this species.

9. Population Growth
Now we will introduce reproduction into the graphs, so they can go up.
Populations do not grow in a linear manner (adding a fixed number of offspring per year).
Instead, they grow exponentially (the more mothers there are, the more babies can be produced).

11. The math of exponential growth
dN/dt represents the rate at which the population is growing at any point in time, i.e. the slope of the line at that instant.
N = the number of individuals in the population.
rmax = (b – d) which is the per-capita birth rate minus the per-capita death rate, under ideal conditions (also called “intrinsic rate of increase”)

12. However, populations do not grow exponentially forever
Something always limits population growth.
One common type of population growth graph starts off exponential, but then slows down and levels off.
This is called “logistic growth.”

15. The math of logistic growth
where K = the carrying capacity of the environment.
When N is very low, the term in parentheses is approximately 1, so growth is exponential
When N approaches K, the term in parentheses approaches zero, so growth stops (dN/dt = 0).

16. What exactly is K?
The maximum number of individuals the environment can support.
Factors include:
Finite supply of food and water.
Increased transmission of diseases.
Limited habitat (space, territory, nest sites, etc.)
Behavioral effects of overcrowding (increased aggression, decreased reproduction)

17. Not all limitations are density-dependent
Logistic growth is “density-dependent” – population growth slows down when the population density gets high.
Some populations may be limited by external fluctuations in the weather or other unpredictable resources. This is called “density-independent” regulation. It results in fluctuating populations.

18. The human population
The global human population has been growing exponentially since the industrial revolution about 200 years ago.
Previous factors in the carrying capacity, such as food availability and disease, have been greatly reduced.

19. The population explosion
Understand: It’s not that the maximum age of humans is getting longer.
Increases in average life expectancy are because of reduced infant and childhood mortality.
This has a huge impact on population, because it not only keeps those individuals alive, but also allows them to reproduce and add their descendents to the population.

21. How long can populations increase?
No one really knows, but no natural populations ever grow exponentially forever.
Eventual approach to carrying capacity will probably increase death rates, unless we take steps to slow population growth.