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Population Growth. December 7, 2010 Text p . 660-669. 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

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population growth

Population Growth

December 7, 2010

Text p. 660-669

population dynamics
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
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
Limits on Fecundity
  • Fertility often less than fecundity
    • Food availability
    • Mating success
    • Disease
    • Human factors
    • Immigration/Emigration
survivorship
Survivorship
  • 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
type ii
Type II
  • Uniform risk of mortality throughout life
type iii
Type III
  • High mortality rates when they are young
  • Those that reach sexual maturity have reduced mortality rates
calculating changes in population size
Calculating Changes in Population Size

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
open closed population
Open/Closed Population
  • Growth can depend on type of population
  • Open: influenced by natality, mortality and migration
  • Closed: determined by natality and mortality alone
biotic potential
Biotic Potential
  • The maximum rate a population can increase under ideal conditions
  • Or intrinsic rate of natural increase
  • Represented as r
carrying capacity
Carrying Capacity
  • Maximum number of organisms sustained by available resources
  • Represented as k
population growth models
Population Growth Models
  • Basic model
    • No inherent limit to growth

Hypothetical model

geometric growth model
Geometric Growth 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)
geometric growth model1
Geometric Growth Model

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

slide16

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

exponential growth model
Exponential Growth Model
  • 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
slide20

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

slide21

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

slide22

Population size after each of 4 doubling times:

Td = 23 hrs, initial population = 2500

curve shapes
Curve Shapes

Exponential = J-shaped curve

Smooth vs. geometric, which fluctuates

logistic growth model
Logistic Growth Model
  • 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
logistic growth model1
Logistic Growth Model
  • 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

logistic growth curve
Logistic Growth Curve
  • S-shaped curve (sigmoidal)
  • 3 phases
  • Lag, Log, Stationary
  • At stationary phase, population is in dynamic equilibrium
slide28

Useful model for predictions

  • Fits few natural populations perfectly
r k selection
r & K Selection
  • Species can be characterized by their relative importance of r and K in their life cycle
r selected species
r-Selected Species

Carrying capacity, K

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

Population numbers (N)

r-selected species

Time

k selected species
K-Selected Species

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

slide34

Work:

Text Page 669, # 1-5

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