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 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 Plot Log10lx vs. X

Dall sheep (Ovis dalli) Life Table

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

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 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

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

Fecundity (Fertility) Schedule

Life Table Calculations Sum = 7.70 14.67 0+2.95+3.06+1.52+0.26 = 7.70