Lecture 7: Life Tables

1. Lecture 7: Life Tables EEES 3050

2. Exam • 1st Remember there is a test in a week… • Will consist of approx. 50% multiple choice, short answer, and 50% written questions. • 2nd you can help write the exam… • Send me a question via e-mial. • Can be multiple choice, T/F, short answer, essay, etc.

3. Exam • 3rd – • Sigma Xi Research Symposium: • When: Saturday from 9-3:30. Ecology talks are primarily in the morning. • Each student presentation is 15 minutes long. • You can use 3 student talks for your research critique. • Possible extra credit on exam for attending as well. • Guaranteed brownie points.

4. Demographics and vital statistics • Populations can be quantified • Determine mortality rates. • Rates of reproduction • Determine if population should increase or decrease. • Comparisons between different time periods • Comparisons between different populations • Yes this = mathematics and statistics

5. Life Tables • Summary of the mortality/survival of cohort (age group) of individuals. • Life Tables contain information on: • x = age • Nx= number alive at age x • lx = proportion surviving from initial stage to age x • dx = Number dying from age x to x + 1 • qx = per capita rate of mortalityfrom age x to x + 1 • bx = # of offspring per female at age x.

6. Life Tables: background • Originally developed by human demographers. • Used by ecologists starting in 1921 • Raymond Pearl – Three types of survivorship curves.

7. Life tables • How do gather data? • 1) Cohort life table • Following a cohort through time. • 2) Static life table • Based on a cross section of a population. • Why would these tables differ? • Differing birth/death rates.

8. Basic Life Table

9. Basic Life Table lx = nx/n0 or the number in age x divided the initial number. l4 = n4/n0 = 2/115 = 0.017

10. Basic Life Table dx = nx – nx +1 or the number in age x minus number in x+1. d4 = n4 – n5 = 2 - 1 = 1

11. Basic Life Table qx = dx/nx or the dying at age x divided the number alive at age x. q4 = d4/n4 = 1/2 = 0.50

12. Survivorship curves. 1000 No. Alive Time

13. Survivorship curves.

14. 3 Basic survivorship curves.

15. 3 Basic survivorship curves.

16. 3 Basic survivorship curves. • Type 1 • High young survival rates. • Example: Humans • Type 2 • Constant survival rate • Example: birds • Type 3 • High mortality of young • Examples: many fishes, invertebrates

17. Not everything follows these patterns. Mediterranean fruit flies

18. Ecologists and life tables • How do ecologists construct life tables. • Survivorship directly observed. • Possible for short-lived organisms • Age at death observed. • Not easy or common • Need to identify remains of organisms that died naturally. • Example African buffalo • Age structure directly observed. • Get a sample of fish, or core trees, • Relies on many assumptions.

19. Data gathered by collecting skulls of animals that died naturally.

20. So far looked at mortality – now add reproduction… • Termed…intrinsic capacity for increase. • Or Malthusian parameter. • Background on rates: • A numerical proportion between two sets of things. • Example: 27 of 350 fail a test = 7.7% failure rate. • Example: 8 or 12 seedlings die = 66.7% mortality rate.

21. R0 = net reproductive rate. R0 = Sum of lxbx = 0.868 + 0.165 + 0.052 = 1.085

22. Population growth with R0 = 1.085

23. Class Life Table

24. Population growth with R0 = 3

25. Lotka: population change • When population reaches a stable age distribution, can use a differential equation. • dN/dt = rN • Or Nt = N0ert , where e = 2.71828 • Important parameter is r

26. To calculate r… • First need to know generation length defined as “the mean period elapsing between the production of parents and the production of offspring”.

27. To calculate r… • First need to know generation length defined as “the mean period elapsing between the production of parents and the production of offspring”. =1.248

28. To calculate r…

29. N0ert , where e = 2.71828 • r > 0 ? • r = 0 ? • r < 0 ?

30. Finite rate of increase • Finite rate = einstantaneous rate • λ = er • For our example: r = 0.0653 • λ = e0.0653 • λ = 2.718280.0653 = 1.067 • This means that for each individual in time x, there will be 1.067 individuals in time x + 1

31. These rates can be affected by abiotic factors.

33. Reproductive Value • Contribution a female will make to the future population • Or present progeny + expected future progeny

34. Reproductive Value

35. Age distributions • Constant age structure in a population is attained only if the lxand bx distributions are unchanging. • Stationary age distribution • Occurs in a population with a constant size and where fertility equals mortality. • Stable age distribution • Constant age-specific mortality and fertility rates.

36. Age distributions

37. Age distributions Note: Dominant year classes.

38. Evolution of demographic traits. • Examples: • Big-bang reproduction • Salmon – spawn once and die • Repeated reproduction • Oak trees – produce thousands of acorns for 100s of years.

39. Evolution of demographic traits.

40. Summary • Life Tables are a summary of the mortality/survival of cohort (age group) of individuals. • 3 Basic survivorship curves. • Constructing life tables can be difficult • R0 and r • Age distributions can predict future of population.