Population Dynamics

1. Population Dynamics • Fundamental Equation: • N(t+1) = N(t) + B – D + I – E • N(t+1) - N(t) = B – D + I – E • = N = B – D + I – E B E D I

2. Estimating Patterns of Survival • Three main methods of estimation: • Cohort life table • .

3. Estimating Patterns of Survival • Three main methods of estimation: • Static life table • .

4. Estimating Patterns of Survival • Three main methods of estimation: • Age distribution • Calculate difference in proportion of individuals in each age class. • .

5. Cohort vs Static Life Tables

6. High Survival Among the Young • Murie collected Dall Sheep skulls, Ovis dalli • Major Assumption: Proportion of skulls in each age class represented typical proportion of individuals dying at that age • Reasonable given sample size of 608

7. High Survival Among the Young • Constructed survivorship curve • Discovered bi-modal mortality • <1 yr • 9-13 yrs

8. Survivorship Curves • Type I: • Dall Sheep • Type II: • American Robins • Type III: • . • Sea Turtles

9. Survivorship Curves Plot Log10lx vs. X

10. Dall sheep (Ovis dalli) Life Table

11. Static life table for Dall Sheep x = age class nx = number alive dx = number dead lx = proportion surviving S1000 = # per 1000 alive Ovis dalli dalli

12. Static life table for Dall Sheep Age class x = 0 = newborns = 100% survive Age class x = 1 only 623 in this age class = 752-129 prop surviving (l1) = 623/752 = 0.828 Age class x = 2 only 509 survive = 623-114 prop surviving (l2) = 509/752 = 0.677

13. Age Distribution • Age distribution of a population reflects its history of survival, reproduction, and growth potential • Miller published data on age distribution of white oak (Quercus alba) • Determined relationship between age and trunk diameter • Age distribution biased towards young trees. • Sufficient reproduction for replacement • Stable population

14. Age Distribution

15. Age Distribution • Rio Grande Cottonwood populations (Populus deltoides wislizenii) are declining • Old trees not being replaced • Reproduction depends on seasonal floods • Prepare seed bed • Keep nursery areas moist • Because floods are absent, there are now fewer germination areas

17. Dynamic Population in a Variable Climate • Grant and Grant studied Galapagos Finches. • Drought in 1977 resulted in no recruitment • Gap in age distribution • Additional droughts in 1984 and 1985 • Reproductive output driven by exceptional year in 1983 • Responsiveness of population age structure to environmental variation

19. Age Structure

20. 1 20% 10 10 65 30% 35 35 34 50% 55 55 Creation of Stable Age Distribution 1st Gen. 2nd Gen. 3rd Gen. 3 2 1 Age Not Stable Not Stable Stable

21. Rates of Population Change • Birth Rate: • Fecundity Schedule:

22. Frequency of Reproduction in Populations generation Discrete, non-overlapping Number of offspring Discrete, overlapping Continuous Time

23. Estimating Rates for an Annual Plant • P. drummondii • Ro = Net reproductive rate; Average number of seeds produced by an individual in a population during its lifetime • Ro=Σlxmx • X= Age interval in days • lx = % pop. surviving to each age (x) • mx= Average number seeds produced by each individual in each age category

24. Estimating Rates for an Annual Plant • Because P. drummondii has non-overlapping generations, can estimate growth rate • Geometric Rate of Increase (λ): • λ =N t+1 / Nt • N t+1 = Size of population at future time • Nt = Size of population at some earlier time

26. Estimating Rates when Generations Overlap • Common Mud Turtle (K. subrubrum) • About half turtles nest each yr • Average generation time: T = Σ xlxmx / Ro • X= Age in years • Per Capita Rate of Increase: r = ln Ro / T • ln = Base natural logarithms

27. Fecundity (Fertility) Schedule

28. Life Table Calculations Sum = 7.70 14.67 0+2.95+3.06+1.52+0.26 = 7.70