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Population Growth

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Population Growth

December 7, 2010

Text p. 660-669

- 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

- The determinants vary from species to species
- Environmental Conditions
- Fecundity
- Potential for a species to produce offspring in one lifetime

vs.

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

- 3 patterns in survivorship of species
- Type I
- Low mortality rates until past reproductive years
- Long life expectancy
- Slow to reach sexual maturity, produce small numbers of offspring

- Uniform risk of mortality throughout life

- High mortality rates when they are young
- Those that reach sexual maturity have reduced mortality rates

Population Change = [(birth + immigration) – (deaths + emigration)] x 100

(%)initial population size (n)

- Can be used to calculate growth rate of a population in a give time period
- Positive Growth: Birth + Immigration > Death + Emigration
- Negative Growth: Birth + Immigration <Death + Emigration

- Growth can depend on type of population
- Open: influenced by natality, mortality and migration
- Closed: determined by natality and mortality alone

- The maximum rate a population can increase under ideal conditions
- Or intrinsic rate of natural increase
- Represented as r

- Maximum number of organisms sustained by available resources
- Represented as k

- Basic model
- No inherent limit to growth

Hypothetical model

- In humans, growth is continuous (deaths and births all times of year)
- In other organisms deaths may be year round, but births may be restricted
- Population typically grows rapidly during breeding season only
- Growth rate is constant at fixed intervals of time (breeding seasons)

λ = the geometric growth rate

N = population size

t = time

N (t + 1) = population size in year X

λ = N (t + 1) or N(t + 1) = N(t) λ

N (t)

So...

N(t) = N(0) λt

Initial population of 2000 harp seals, gives birth to 950 pups, and during next 12 months 150 die

Assuming geometric growth, what is the population in 2 years?

Year 1, Population Change = 950 births – 150 deaths

= 800

Initial Population N(0) = 2000

Population at end of Year 1, N(1) = 2000 + 950 – 150

Geometric Growth Rate (λ) = 2800 = 1.4

2000

Year 2 (t = 2): N(t) = N(0) λt

N(2) = (2000) (1.4)2 = 3920

- Populations growing continuously at a fixed rate in a fixed time interval
- The chosen time interval is not restricted to a particular reproductive cycle
- Can determine the instantaneous growth rate, which is the intrinsic (per capita) growth rate

Intrinsic growth rate (r)

N = population size

dN = instantaneous growth rate of population

dt

Population Growth Rate:

dN = rN

dt

Population’s Doubling time (td) = 0.69

r

2500 yeast cells growing exponentially. Intrinsic growth rate (r) is 0.030 per hour

Initial instantaneous growth rate: dN = rN

dt

= 0.030 x 2500

= 75 per hour

Amount of time for population to double in size:

Td = 0.69 = 0.69 = 23 hrs

r 0.030

Population size after each of 4 doubling times:

Td = 23 hrs, initial population = 2500

Exponential = J-shaped curve

Smooth vs. geometric, which fluctuates

- Geometric and exponential assume population will grow at same rate indefinitely
- This means intrinsic growth rate (r) is a maximum (rmax)
- In reality, resources become limited over time
- Population nears the ecosystem’s carrying capacity, and growth rate drops below rmax

- Growth levels off as size of population approaches its carrying capacity
Instantaneous growth rate:

rmax: maximum intrinsic growth rate

N: population size at any given time

K: carrying capacity of the environment

- S-shaped curve (sigmoidal)
- 3 phases
- Lag, Log, Stationary
- At stationary phase, population is in dynamic equilibrium

- Useful model for predictions
- Fits few natural populations perfectly

- Species can be characterized by their relative importance of r and K in their life cycle

Carrying capacity, K

- Rarely reach K
- High biotic potential
- Early growth
- Rapid development
- Fast population growth

Population numbers (N)

r-selected species

Time

Carrying capacity, K

- Exist near K most of the time
- Competition for resources important
- Fewer offspring
- Longer lives

K-selected species

Population numbers (N)

Time

Work:

Text Page 669, # 1-5