Population ecology

Gauguin

• 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

Change in population size

+It -Et+Bt

nt -Dtnt+1=

Mortality

Stages se seedlingsv vegetatives small reproductivem medium reproductivel large reproductive

Growth

Reproductive

effort

2 3-6 9-14 >20Time since fire (years) Quintana-Ascencio et al. (2003)

4

III

III

IVV VI

3

2

11

2

11

3

4

15

4

4

2

2

4

4

4

2

32

32

32

32

42

42

42

54

4

4

2

5-

4

4

4

2

54

4

4

2

54

4

4

2

54

4

4

2

54

4

4

2

Population Matrix

Seeds Seedlings Vegetative Small Medium Large

Seeds 0.82 57 293 423

Seedlings .001 0.04 0.19 0.28

Vegetative 0.37 0.44 0.12 0.00 0.17

Small 0.37 0.22 0.29 0.29 0.00

Medium 0.00 0.00 0.06 0.44 0.17

Large 0.00 0.00 0.00 0.11 0.00

Quintana-Ascencio et al. (2003)

Population in patch 45 (1996-1997), 11 years

Population structure (3 yr post-fire)Lambda=5.52Stable stage

distribution

Observed stage distribution

Population structure (24 yr post-fire)Lambda=0.587

Stable stage distribution

Observed stage distribution

How many offspring does an average individual produce in its lifetime?

• The net reproductive rate

• Ro= l1F1+ l2F2+ … +lnFn=Σ liFi

• Li=probability of surviving from the first census to the xth census (P1P2…Pn)

• Fi= Fecundity of an average individual in age class x

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

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 (liFi/lambdai), from i=x to infinite

Denominator =lx/lambdax-1

Hypericum cumulicola:

Ln (lambda) on time since fire

Quintana-Ascencio et al. (2003)

Population growth & fire

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 or

Beyond interpolation, input pooled matrices

Year 3 matrix 3.2

or

fire

Median observed cumulative aboveground plant density

Quintana-Ascencio et al. (2003)

Population dynamics &

fire

Projected median cumulative aboveground plant density

Extinction probabilitySimulation

interval (years)

No fire