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: Type II: Type III: . Dall Sheep
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 =
prop surviving (l1) = 623/752 = 0.828
Age class x = 2
only 509 survive =
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. Creation of Stable Age Distribution
1st Gen.
2nd Gen.
3rd Gen. 3 2 1
Age 1 65 34
20%
30%
50% 10 35 55 10 35 55
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
= 7.70