Population Growth

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

2. 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

3. Effect on Determinants • The determinants vary from species to species • Environmental Conditions • Fecundity • Potential for a species to produce offspring in one lifetime vs.

4. Limits on Fecundity • Fertility often less than fecundity • Food availability • Mating success • Disease • Human factors • Immigration/Emigration

5. 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

6. Type II • Uniform risk of mortality throughout life

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

8. 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

9. Open/Closed Population • Growth can depend on type of population • Open: influenced by natality, mortality and migration • Closed: determined by natality and mortality alone

10. Biotic Potential • The maximum rate a population can increase under ideal conditions • Or intrinsic rate of natural increase • Represented as r

11. Carrying Capacity • Maximum number of organisms sustained by available resources • Represented as k

12. Population Growth Models • Basic model • No inherent limit to growth Hypothetical model

13. 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)

15. 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

16. 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

18. 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

20. 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

21. 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

22. Population size after each of 4 doubling times: Td = 23 hrs, initial population = 2500

23. Curve Shapes Exponential = J-shaped curve Smooth vs. geometric, which fluctuates

24. 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

25. 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

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

28. Useful model for predictions • Fits few natural populations perfectly

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

31. 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

32. 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

34. Work: Text Page 669, # 1-5