1. Population ecology Gauguin

2. 15 populations (various patch sizes) Time since fire: 0 to >30 years 9 years (1994-2004) >80 individuals per population each year Over 7000 plants in study through 2004 Censuses twice per year 6 stage classes defined by optimization algorithm Field and greenhouse experiments (seed and seedling dynamics) Demographic data

3. Change in population size +I t -E t +B t ntnt -D t n t+1 =

4. Mortality Stages se seedlings v vegetative s small reproductive m medium reproductive l large reproductive Growth Reproductive effort 2 3-6 9-14 >20 Time since fire (years) Quintana-Ascencio et al. (2003)

5. I II III IV V VI 3 2 1 2 1 1 3 4 1 5 3 3 3 3 4 4 4 5 5-5- 5 5 5 5

6. Population Matrix SeedsSeedlingsVegetativeSmallMediumLarge Seeds 0.8257293423 Seedlings.0010.040.190.28 Vegetative 0.370.440.120.000.17 Small 0.370.220.29 0.00 Medium 0.00 0.060.440.17 Large 0.00 0.110.00 Quintana-Ascencio et al. (2003) Population in patch 45 (1996-1997), 11 years

7. Population structure (3 yr post-fire) Lambda=5.52 Stable stage distribution Observed stage distribution

8. Population structure (24 yr post-fire) Lambda=0.587 Stable stage distribution Observed stage distribution

9. How many offspring does an average individual produce in its lifetime? The net reproductive rate R o = l 1 F 1 + l 2 F 2 + … +l n F n =Σ l i F i L i =probability of surviving from the first census to the x th census (P 1 P 2… P n) F i = Fecundity of an average individual in age class x

10. Reproductive value Individuals of different stages do not make equivalent contributions to future population growth. The reproductive value of different stages or ages give us a measure of the effects of different kinds of individuals on future population growth

11. Reproductive value R.V. = Proportion of future births in the population to individuals now in age x Proportion of the population now in age x Numerator =Σ ( l i F i /lambda i ), from i=x to infinite Denominator = l x /lambda x-1

12. Hypericum cumulicola: Ln (lambda) on time since fire Quintana-Ascencio et al. (2003) Population growth & fire

13. Year 0 fire matrix Year 1 matrix 1.1 Year 1 matrix 1.2 Year 1 matrix 1.3 Year 3 matrix 3.1 Modeling samples from matrices by time since fire. In this (simplified) example, the fire return interval is 3 years: Use this: Choose 1: Weighted interpolation between yrs 1 and 3 if no yr 2 matrix... Use this: reset or Beyond interpolation, input pooled matrices Year 3 matrix 3.2 or fire

14. Median observed cumulative aboveground plant density Quintana-Ascencio et al. (2003) Population dynamics & fire Projected median cumulative aboveground plant density

15. Extinction probability Simulation interval (years) No fire