Population Growth December 7, 2010 Text p

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 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) λ t

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) = – 150 Geometric Growth Rate (λ) = 2800 = Year 2 (t = 2): N(t) = N(0) λ t 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 size dN = instantaneous growth rate of population dt Population Growth Rate: dN = rN dt Population’s Doubling time (t d ) = 0.69 r

2500 yeast cells growing exponentially. Intrinsic growth rate (r) is per hour Initial instantaneous growth rate: dN = rN dt = x 2500 = 75 per hour Amount of time for population to double in size: T d = 0.69 = 0.69 = 23 hrs r 0.030

Population size after each of 4 doubling times: T d = 23 hrs, initial population = 2500

Curve Shapes Exponential = J-shaped curve Smooth 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 (r max ) In reality, resources become limited over time Population nears the ecosystem’s carrying capacity, and growth rate drops below r max

Logistic Growth Model Growth levels off as size of population approaches its carrying capacity Instantaneous growth rate: r max : maximum intrinsic growth rate N: population size at any given time K: 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 Population numbers (N) Time r-selected species

K-Selected Species Exist near K most of the time Competition for resources important Fewer offspring Longer lives Population numbers (N) Time K-selected species Carrying capacity, K

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