1. Ch. 5: Population Structure and Changes

2. Population Models 2) Continuous time models –dN/dt=Nr max Ideal conditions…

3. Population Models 2) Continuous time models –Limiting conditions –Logistic growth.

4. Population Models 2) Continuous time models dN/dt=Nr max (K-N)/K N small: (K-N)/K almost 1 N near K: (K-N)/K very small

5. Population Models Plant Point 1: K based on density Animals: most individuals have certain size Plants: high modular growth/plasticity Crowding capacity: combine density with biomass per individual.

6. Population Models Plant Point 2: “Law” of constant yield Yield same Great Phenotypic Plasticity

7. Population Models 3) Discrete-time period models (complex): life tables BIOL 3060 Cemetery lab

8. Population Models Types: –Cohort life table: follow –Static life table: assume

9. Oldest known tree Bristlecone Pine (Pinus longaeva). High mtns. How age?

10. Oldest known tree Increment borer: extract

11. Oldest known tree Oldest was 4,950 yr (NV mountains)

12. Oldest known tree Now oldest (“Methuselah”) 4,767 yr.

13. Population Models Survivorship (l x ): proportion orig.

14. Population Models Survivorship curves: mortality Type I: Annual plants. Type II: Type III: Perennial Note log scale on Y axis!

15. Age distributions Predictive? Ex, pine/hardwood succession

16. Age distributions Often, stable pop’n L-shaped Ex, red spruce (Picea rubens)

17. Age distributions Some species: episodic establishment –Sporadic Jack…

18. Age/stage distributions Serotinous cones (closed-cone pine) –Seed

19. Population Models 3) Model: life table info + fecundity info Fecundity: age- Survivorship & fecundity give net reproductive rate (R 0 ): R 0 = ∑ l x b x

20. Population Models R 0 = ∑ l x b x Ex: Age Survivorship (l x ) Fecundity (b x ) Reproduction 0-11.00 1-20.23 2-30.15 3-400 R 0 = 1.1

21. Population Models R 0 >1, R 0 =1, R 0 <1,

22. Population Models 4) Transition matrix models Life history stages + matrix algebra Fig. 5.6 Matrix.. Trillium! SL 1L 3L

23. Population Models Matrix algebra Matrix: numbers rows/columns

24. Population Models Ex: Column matrix (vector) = pop’n status: population vector Life history stages: s=seeds, r=rosettes, f=flowering 140 16 10 # seeds # rosettes # flowering Lab 1: who am I? Rosette forming perennial

25. Population Models Transition matrix: probability transition

26. Population Models Ex: teasel (Dipsacus sylvaticus) Perennial pasture/roadside weed.

27. Population Models Transition matrix: teasel (Dipsacus sylvaticus) Note columns don’t always sum to 1.0: accounts for mortality

28. Population Models Model: pop’n vector X transition matrix New matrix: pop’n structure next time

29. Population Models Ex: 3 stages. Seed, rosette, flowering Pop’n vector 140 20 10 # seeds # rosettes # flowering

30. Population Models Ex: 3 stages. Seed, rosette, flowering Transition matrix 0.5 0.2 0 seed rosetteflowering seed rosette flowering year 1 year 2 0 0.2 0.5 20 0.2 0.1 Note: columns not summing to 1.0 includes mortality