Changes in Population Size

Population Dynamics

• Populations always changing in size– Deaths, births

• Main determinants (measured per unit time):– Natality = number of births– Mortality = number of deaths– Emigration = # of individuals that move away– Immigration = # of individuals that move into an

existing population

Effect on Determinants

• The determinants vary from species to species• Environmental Conditions• Fecundity

– Potential for a species to produce offspring in one lifetime

vs.

Limits on Fecundity

• Fertility often less than fecundity– Food availability– Mating success– Disease– Human factors– Immigration/Emigration

1. Population Change (∆N) = [(births + immigration) – (deaths + emigration)]- just plug in the values as determined.

2. To calculate the rate of population growth: gr = ∆N/∆t

eg. Snail population in Banff Springs is 3800 in 1997, but falls to 1800 in 1999. Calcluate the growth rate.

gr = 1800-3800 2 years

= - 1000 snails/year

the population declined at a rate of 1000 snails per year.

Calculating Changes in Population Size

Calculating Changes in Population Size3. Calculating the per capita growth rate (cgr): ∆N/N (N= initial pop. size)

cgr = [(birth + immigration) – (deaths + emigration)] x 100 (%)initial population size (n)

• Positive Growth: Birth + Immigration > Death + Emigration• Negative Growth: Birth + Immigration <Death + Emigration

Calculate:

a) the change in a population in which there were 20 births, 25 immigrants, 10 deaths, and 5 emigrants.b) What is the per capita growth if the original population was 75?.

+ 30 + 40%

Open/Closed Population• Growth can depend on type of population• Open: influenced by natality, mortality and

migration• Closed: determined by natality and mortality

alone

Population Growth in Unlimited Environments

• Under ideal conditions – no predators and unlimited resources…

• A species can reach its biotic potential - the highest possible per capita growth rate for a population.

• Factors that determine biotic potential are related to fecundity:

• # of offspring per reproductive cycle• # of offspring that survive to reproduce• The age of reproductive maturity• # of times that an individual reproduces in its life span• the life span of the individuals

Population Growth Models1) Exponential Population Growth:•Population grows at its max. biotic potential•Starts with a lag phase and forms a J-shaped curve.•Really only see in lab conditions.

Hypothetical model

Example

• A petri dish contains a population of bacteria that is growing exponentially. If the intrinsic growth rate (r) is equal to 0.02 per hour and the initial population is 1000. – A) what is the initial instantaneous growth rate of

the population– B) what is the time it would take for the

population to double in size?

Pop. Growth in Limited Environments

• If one bacterium divided every 30 minutes for 4 days – the mass would be greater than that of the earth.

• Doesn’t happen – resources run low and growth rate slows.• Eventually, the habitat reaches its carrying capacity: the maximum

number of organisms that can be sustained by available resources.• This is shown by a logistic growth curve:

Logistic Growth Curve• S-shaped curve (sigmoidal)• 3 phases:

• Lag (slow growth)• Log (rapid growth)• Stationary (no growth)

• At stationary phase, population is in dynamic equilibrium, it will fluctuate around the carrying capacity of its habitat.

• carrying capacity changes in response to environmental conditions – resource supply, predation, limited space, disease etc.

Example

• A population is growing continuously. The carrying capacity of the environment is 500 individuals and its maximum growth rate is 0.25. Determine the population growth based on a population size of 10, 50, 100, 200, 350, and 500

Geometric Growth Model

• Births are restricted to one part of the year – “breeding season”

• Growth rate is constant and is calculated from yearly change

Example

• A population of Lynx was studied in Northern Ontario. There was an initial population of 120 lynx. During the next 12 months, 10 lynx were born into this population and 40 adults died. – What is the growth rate for this population?– If this growth rate remains constant, what would

the population be in 5 years?

Population Growth Models and Life History:

•Organisms use strategies to maximize the # of offspring that survive to reproductive age.

•Theoretically, the best idea is• reach sexual maturity early• have a long life span• produce large #s of offspring• provide them with high quality care until they can reproduce.

•Not realistic…

•There are different life strategies which relate to the environment in which the organism lives.

•These are known as r-selected or K-selected strategies

r-selected strategy

•Species that have an r-selected strategy live close to their biotic potential.

•In general, these organisms:• Have a short life span• Become sexually mature at a young age• Produce large broods of offspring• Provide little or no parental care to their offspring.

•Insects, annual plants and algae are examples – take advantage of favorable conditions in the summer – reproduce exponentially, but die at the end of the season.

K-selected strategy:

•Organisms with a K-selected strategy live close to the carrying capacity of their habitats.

•In general, these organisms:• Have a relatively long life span• Become sexually mature later in life• Produce few offspring per reproductive cycle• Provide a high level of parental care

•Mammals and birds are examples of organisms that use this.

•Many populations are in-between these strategies and describing a population usually involves a comparison – rabbits could be described as K-selected…compared to mosquitoes. Compared to bears, rabbits are r-selected.