Population Growth

December 7, 2010Text 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– 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

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• Uniform risk of mortality throughout life

Type III• High mortality rates when they are young• Those that reach sexual maturity have

reduced mortality rates

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

migration• Closed: determined by natality and mortality

alone

Biotic Potential• The maximum rate a population can increase

under ideal conditions• Or intrinsic rate of natural increase• Represented as r

Carrying Capacity

• Maximum number of organisms sustained by available resources

• Represented as k

Population Growth Models• Basic model– No inherent limit to growth

Hypothetical 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 Modelλ = the geometric growth rateN = population sizet = timeN (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 – 150Geometric 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• 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 sizedN = instantaneous growth rate of populationdt

Population Growth Rate:dN = rNdt

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

Curve ShapesExponential = J-shaped curveSmooth vs. geometric, which fluctuates

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 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 timeK: carrying capacity of the environment

Logistic Growth Curve• 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

r & K Selection

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

r-Selected Species

• Rarely reach K• High biotic

potential• Early growth• Rapid

development• Fast population

growth

Carrying capacity, K

Popu

latio

n nu

mbe

rs (N

)

Time

r-selected species

K-Selected Species

• Exist near K most of the time

• Competition for resources important

• Fewer offspring• Longer livesPo

pula

tion

num

bers

(N)

Time

K-selected species

Carrying capacity, K

Work:

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