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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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Presentation Transcript
readings
Readings
  • Table 10.1, p. 246
  • Table 10.2, p. 248
  • Life Histories, pp. 284-291
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
Estimating Patterns of Survival
  • Three main methods of estimation:
    • Cohort life table
      • Identify individuals born at same time and keep records from birth.
estimating patterns of survival1
Estimating Patterns of Survival
  • Three main methods of estimation:
    • Static life table
      • Record age at death of individuals.
estimating patterns of survival2
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.
high survival among the young
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
high survival among the young1
High Survival Among the Young
  • Constructed survivorship curve
    • Discovered

bi-modal mortality

      • <1 yr
      • 9-13 yrs
survivorship curves
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
survivorship curves1
Survivorship Curves

Plot

Log10lx vs. X

slide12

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

slide13

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

age distribution
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
age distribution2
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
dynamic population in a variable climate
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
creation of stable age distribution

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

rates of population change
Rates of Population Change
  • Birth Rate: Number of young born per female
  • Fecundity Schedule: Tabulation of birth rates for females of different ages
frequency of reproduction in populations
Frequency of Reproduction in Populations

generation

Discrete,

non-overlapping

Number of offspring

Discrete,

overlapping

Continuous

Time

estimating rates for an annual plant
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
estimating rates for an annual plant1
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
estimating rates when generations overlap
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
life table calculations
Life Table Calculations

Sum =

7.70

14.67

0+2.95+3.06+1.52+0.26 = 7.70