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