1 Mon. Tues. Wed. Thurs. Fri. Week of Oct. 20 Week of Oct. 27 Independent project set-up Week of Nov. 3 Forest ecology lab – dress for weather Exam 2 T lab switch? Week of Nov. 10 Independent project analysis

2 What do we measure? Total population size = number of indivduals How they are arranged in space How many are in each age or size class

3 Figure 13.5 There is a simple statistical test to test for distribution Mechanisms?

4 What do we measure? Total population size = number of indivduals How they are arranged in space How many are in each age or size class

5 Outline Introduction How are populations defined and measured? How do populations grow? How does population size change through time and space?

6 Growth = births – deaths + immigration – emigration When calculating growth rate, usually just seeing change in numbers over time

7 Populations grow by multiplication rather than by addition Just like interest in the bank

8 Figure 14.3

9 Exponential growth -new individuals are added (born) to population continuously r = per capita growth rate = contribution of each individual in population

10 dN/dt = rN Rate at which individuals are added = growth rate on a per individual basis x population size = derivative of exponential equation = slope of line Exponential growth

11 Figure 14.4

12 Exponential vs. Geometric Growth Exponential – continuous reproduction - growth is smooth curve Geometric – discrete breeding seasons - calculate growth at discrete intervals

13 Geometric growth Growth rate = = population size at one time point/ size at previous time point N (t+1) = N(t) N(t) = N(0) t

14 Geometric growth: N(t) = N(0) t Exponential growth: N(t) = N(0) e rt = e r Ln = r

15 Figure 14.5 Exponential Per capita growth rate = constant Rate of increase= dN/dt, increases with N

16 Figure 14.6

17 Age structure (# of individuals in each age class) of a population affects population growth Why??

18 Figure 14.8 StableFast growth

19 Age structure of a population affects population growth Life table = a summary by age of the survivorship and fecundity of individuals in a population Shows differences in birth and death rate for different parts of population

20

21

22 Table 14.3

23 Figure 14.7

24 Stable age distribution – the proportion of individuals in various age classes in a population that has been growing at a constant rate - only happens if age-specific birth and death rates are constant over time - each age class grows at same rate

25 What parameters affect growth rate?

26 More common to see this pattern What’s going on?

27 Some metric of population size Some factor that affects growth rate Density dependence Lots of examples in book Common in nature

28 Figure 14.19

29 Some metric of population size Some factor that affects growth rate Density independence Very few examples in book Common in nature

30 Figure Population Size

31 r = r o (1-N/K) r = intrinsic growth rate at small N x the reduction in growth rate due to crowding K = carrying capacity of population Logistic growth R changes as N changes such that

32 dN/dt = r o N (1-N/K) Change in N with time = intrinsic growth rate at small N x population size x the reduction in growth rate due to crowding Logistic growth

33 Figure 14.17

34 Figure 14.16

35 If I give you an equation and a value for K and/or r or, I expect that you can sketch the graph. I expect that you will understand what the terms in the equations mean. I expect that you understand the assumptions of each model and the differences between them. I expect that you know what is in a life table and what parameters affect growth rate and what a life table can be used for.