Population ecology

1
Population ecology
Gauguin
2
Demographic data

• 15 populations (various patch sizes)
• Time since fire 0 to gt30 years
• 9 years (1994-2004)
• gt80 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)

3
Change in population size
4
Stages se seedlings v vegetative s small
reproductive m medium reproductive l large
reproductive
Time since fire (years)
2 3-6 9-14 gt20
Quintana-Ascencio et al. (2003)
5
2
II
I
2

11
1
3
3
1
3
3
4
4
5
4
3
5
1
3
III
5-
5
5
5
IV
V
VI
5
4
6
Population Matrix
Quintana-Ascencio et al. (2003)
Population in patch 45 (1996-1997), 11 years
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
7
Population structure (3 yr post-fire)
Lambda5.52
Stable stage distribution
Observed stage distribution
8
Population structure (24 yr post-fire)
Lambda0.587
Stable stage distribution
Observed stage distribution
9
How many offspring does an average individual
produce in its lifetime?

• The net reproductive rate
• Ro l1F1 l2F2 lnFnS liFi
• Liprobability of surviving from the first census
  to the xth census (P1P2Pn)
• Fi 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 S (liFi/lambdai), from ix to infinite
Denominator lx/lambdax-1
12
Population growth fire
Quintana-Ascencio et al. (2003)
13
Modeling samples from matrices by time since
fire. In this (simplified) example, the fire
return interval is 3 years
Year 0 fire matrix
Use this
Year 1 matrix 1.1
Year 1 matrix 1.2
Year 1 matrix 1.3
or
or
Choose 1
Weighted interpolation between yrs 1 and 3 if no
yr 2 matrix...
or
Use this
Beyond interpolation, input pooled matrices
reset
fire
14
Median observed cumulative aboveground plant
density
Population dynamics fire
Quintana-Ascencio et al. (2003)
15
Extinction probability
Simulation interval (years)
No fire