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Readings

Readings. Table 10.1, p. 246 Table 10.2, p. 248 Life Histories, pp. 284-291. 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.

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Readings

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  1. Readings • Table 10.1, p. 246 • Table 10.2, p. 248 • Life Histories, pp. 284-291

  2. 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

  3. Estimating Patterns of Survival • Three main methods of estimation: • Cohort life table • Identify individuals born at same time and keep records from birth.

  4. Estimating Patterns of Survival • Three main methods of estimation: • Static life table • Record age at death of individuals.

  5. Estimating Patterns of Survival • Three main methods of estimation: • Age distribution • Calculate difference in proportion of individuals in each age class. • Assumes differences from mortality.

  6. Cohort vs Static Life Tables

  7. 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

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

  9. Survivorship Curves • Type I: Majority of mortality occurs among older individuals. • Dall Sheep • Type II: Constant rate of survival throughout lifetime. • American Robins • Type III: High mortality among young, followed by high survivorship. • Sea Turtles

  10. Survivorship Curves Plot Log10lx vs. X

  11. Dall sheep (Ovis dalli) Life Table

  12. 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

  13. 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

  14. 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

  15. Age Distribution

  16. 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

  18. Age Structure

  19. 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

  20. Rates of Population Change • Birth Rate: Number of young born per female • Fecundity Schedule: Tabulation of birth rates for females of different ages

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

  22. 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

  23. 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

  24. 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

  25. Fecundity (Fertility) Schedule

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

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