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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
• 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
• Three main methods of estimation:
• Cohort life table
• Identify individuals born at same time and keep records from birth.
Estimating Patterns of Survival
• Three main methods of estimation:
• Static life table
• Record age at death of individuals.
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
• 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 Young
• Constructed survivorship curve
• Discovered

bi-modal mortality

• <1 yr
• 9-13 yrs
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 Curves

Plot

Log10lx vs. X

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

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 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 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
• 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

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
• Birth Rate: Number of young born per female
• Fecundity Schedule: Tabulation of birth rates for females of different ages
Frequency of Reproduction in Populations

generation

Discrete,

non-overlapping

Number of offspring

Discrete,

overlapping

Continuous

Time

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 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
• 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

Sum =

7.70

14.67

0+2.95+3.06+1.52+0.26 = 7.70