readings table 10.1, p. 246 table 10.2, p. 248
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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
I
ED
B
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.
Cohort vs Static Life Tables
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 PlotLog10lx vs. X
Dall sheep (Ovis dalli)
Life Table
Static life table for Dall Sheepx nx dx lx S1000
0 752 129 1.000 1000
1 623 114 0.828 828
2 509 113 0.677 677
3 396 81 0.527 527
4 315 78 0.419 419
5 237 59 0.315 315
6 178 65 0.237 237
7 113 55 0.150 150
8 58 25 0.077 77
9 33 9 0.044 44
10 24 8 0.032 32
11 16 7 0.021 21
12 9 2 0.012 12
13 7 1 0.009 9
14 6 4 0.008 815 2 2 0.003 3
total 752
x = age class nx = number alive
dx = number dead
lx = proportion surviving
S1000 = # per 1000 alive
Ovis dalli dalli
Static life table for Dall Sheepx nx dx lx S1000
0 752 129 1.000 1000
1 623 114 0.828 828
2 509 113 0.677 677
3 396 81 0.527 527
4 315 78 0.419 419
5 237 59 0.315 315
6 178 65 0.237 237
7 113 55 0.150 150
8 58 25 0.077 77
9 33 9 0.044 44
10 24 8 0.032 32
11 16 7 0.021 21
12 9 2 0.012 12
13 7 1 0.009 9
14 6 4 0.008 815 2 2 0.003 3
total 752
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
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
Age Structure
Creation of Stable Age Distribution
321
Age
1st Gen. 2nd Gen. 3rd Gen.
Not Stable Not Stable Stable
1
65
34
20%
30%
50%
10
35
55
10
35
55
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
Time
Num
ber o
f offs
prin
g
Discrete, non-overlapping
Discrete, overlapping
Continuous
generation
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
Fecundity (Fertility) Schedule
Life Table Calculations
0+2.95+3.06+1.52+0.26 = 7.70
X(lx)(m
x)
(lx )(mx ) Generation Time
(1*2.95)(2 *3.06)3*1.52)(4 *0.26)7.70
14.677.70
1.905
7.70Sum = 14.67
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