1 / 28

Population Dynamics

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

anne-tate
Download Presentation

Population Dynamics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

  16. 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

  17. Age Structure

  18. 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

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

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

  21. 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

  22. 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

  23. 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

  24. Fecundity (Fertility) Schedule

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

More Related