Understanding Population Dynamics: Models and Transitions

1. Ch. 5: Population Structure and Changes

2. Population Models • 2) Continuous time models • dN/dt=Nrmax Ideal conditions…

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

4. Population Models • 2) Continuous time models • dN/dt=Nrmax (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 (lx): 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 (R0): • R0 = ∑ lx bx

20. Population Models • R0 = ∑ lx bx • Ex: • Age Survivorship (lx) Fecundity (bx) Reproduction • 0-1 1.0 0 • 1-2 0.2 3 • 2-3 0.1 5 • 3-4 0 0 • R0 = 1.1

21. Population Models • R0 >1, • R0 =1, • R0 <1,

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

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 year 1 seed rosette flowering 20 0.2 0.1 seed 0.5 0.2 0 0 0.2 0.5 year 2 rosette flowering Note: columns not summing to 1.0 includes mortality