1. Populations change over time Changes in U.S. Bird Populations by habitat Science News 2009

2. Are Populations increasing? Decreasing? # breeding pairs Year

3. Easy to tell with long term data sets

4. What about short term data sets?

5. Exponential Growth Model Population size 2005 = 100 Population size 2006 = 200

6. Exponential Growth Model Assumption: all individuals are equal. Is this assumption is wrong???

7. Age in relative units Number of survivors (log scale)

8. Competing models Population size 2005 = 100 Population size 2006 = 200 Model #1Model #2 Not all individuals are equalAll individuals are equal Juvenile survival = 0.45 Adult survival = 0.9 0.33 Juveniles become adults Adults produce 13 offspring each Population size 2005 = 100 90 Juveniles, 10 adults Population size 2006 = 200

9. Year Population Size Year 2 = 200 for both

10. Year Population Size Huge difference!

11. Stage and Size predict survival and fecundity Plants- seed, seedling, adult Invertebrates- number of molts, larva-pupa-adult Fish- size predicts sex and number of eggs produced Amphibians- egg-tadpole-adult Birds- egg-chick-adult Mammals- newborn, juvenile, adult

12. In fish, fecundity > with size

13. Exponential growth model N t =30 individuals Age-structured model Nt =Nt = 20 8 2 newborns 1-year olds 2-year olds

14. Exponential growth model N t =30 individuals Age-structured model 0 0 S0S0 F1F1 S1S1 0 F2F2 0 0 012 F1F1 F2F2 S0S0 S1S1

15. Exponential growth model N t =30 individuals Age-structured model N t+1 = 0 0 S0S0 F1F1 S1S1 0 F2F2 0 0 20 8 2

16. Age vs. Stage or size Models 0 0 S0S0 F1F1 S1S1 0 F2F2 0 0 012 S S S FMFM S S FLFL S S SML

17. From Eby et al. 2005 S S S FMFM S S FLFL S S SF

18. What about growth rate? R = Growth Rate, or λ (lambda) Luckily, λ is an intrinsic property of the matrix N t+1 = 0 0 S0S0 F1F1 S1S1 0 F2F2 0 0 20 8 2 Only one solution For Lambda for each matrix

19. Natural log of lambda Model output from paper There are many values, because – they varied hypoxia and effects on juvenile growth rate and calculated a lambda value for each simulation. Hypoxia No Hypoxia