Appendix S1
Construction and parameterisation of the transition matrices
The Tachigali vasquezii population was divided into 15 size categories: 5 categories for seedlings
and juvenile trees, 5 for pre-reproductive trees and 5 for reproductive trees. The transition matrix
A describes the transitions between these 15 categories, following the life cycle graph in Figure
A1. Each element aij of A is either the probability that an individual in category j (column) will
move to category i (row) in one time step, or it is the number of new individuals in category j
produced by individual in category i in one time step. These transitions can be grouped into
progression (G - moving to the next category), stasis (P - remaining in the same category),
attaining reproductivity (R - moving to the reproductive category with individuals of the same
size), combined progression and attaining reproductivity (RG) and fecundity (F). Transition
probabilities were calculated from the vital rates σ (annual survival probability), γ (annual
probability of moving to next size category of a surviving individual), Pr (annual probability of
becoming reproductive) and f (number of seedlings produced annually by a reproductive tree).
The following equations were used to calculate transition probabilities:
for categories 1-5:
Gj = j  j
Pj = j  (1-j)
for categories 6-10:
Gj = j  j  (1-Prj)
Rj = j  (1-j)  Prj
RGj = j  j  Prj
Pj = j  (1-j)  (1-Prj)
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for categories 11-15:
Gj = j  j
Pj = j  (1-j)
Fj = fj
The vital rate  for category j is calculated from data on the observed mean growth rate (g, in cm
y-1) of individuals in a category and the width (c, in cm) of that category: j = gj / cj . Vital rate fj is
calculated as fj = init  Sdj, in which init (y-1) is the fraction seeds germinating and surviving
during the first year after seed fall and Sdj is the number of seeds produced by a reproductive tree
in category j during one year.
Values of vital rates for the T. vasquezii transition matrix are included in Table A1. The matrix
for an imaginary polycarpic tree was also based on the above equations and using the same
categories. In this transition matrix, those vital rates that differed between T. vasquezii and
polycarpic species from the community were changed (Table A1). The most important difference
between these matrices was in the survival of reproductive individuals ( in categories 11-15)
which was 0.98 for the polycarpic tree and zero for T. vasquezii, causing G and P transitions to be
0 in the T. vasquezii matrix. Other vital rates that differed were growth, survival and seed
production.
2
P2
1
2
R6
G2
3
4
P6
G6
5
F11
RG6
6
7
8
9
10
11
12
13
14
15
P11
G11
Figure A1. Life cycle graph for T. vasquezii and an imaginary polycarpic tree. Text boxes
indicate the type of transitions. Category descriptions are in Table A1.
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Table A1. Characteristics and vital rates of size categories used in transition matrices for T.
vasquezii and an imaginary polycarpic tree. Range is the size range of individuals in a category.
Vital rates included are survival probability (σ), growth rate (g), probability of becoming
reproductive (Pr) and number of seeds produced per reproductive tree (Sd). Size range and
growth of categories 1-2 is expressed in cm seedling height; that for the other categories in cm
diameter at breast height (DBH). Pr was not different for T. vasquezii and polycarpic matrices.
Category
Range
σTachi
σpoly
[cm]
[yr-1]
[yr-1]
gTachi
gpoly
[cm yr-1] [cm yr-1]
Pr
SdTachi
Sdpoly
[yr-1]
[yr-1]
[yr-1]
1
8-50
0.66
0.66
3.21
3.21
2
51-150
0.91
0.97
4.00
5.60
3
1-10
0.95
0.95
0.10
0.02
4
11-20
0.95
0.95
0.58
0.12
5
21-30
0.98
0.98
1.17
0.23
6
31-40
0.98
0.98
1.76
0.35
0.18
7
41-50
0.98
0.98
2.35
0.47
0.18
8
51-60
0.98
0.98
2.94
0.59
0.18
9
61-70
0.98
0.98
3.53
0.71
0.18
10
>70
0.98
0.98
11
31-40
0.00
0.98
0.35
5888
2165
12
41-50
0.00
0.98
0.47
9733
3578
13
51-60
0.00
0.98
0.59
14540
5346
14
61-70
0.00
0.98
0.71
20308
7466
15
>70
0.00
0.98
27037
9940
Seedling &
Juvenile
Prereproductive
Reproductive
0.18
Values of vital rates for T. vasquezii were obtained from different sources. Survival and growth of
seedlings in category 1 were obtained from 1362 seedlings around three reproductive T. vasquezii
trees in the reproduction study described in the Materials and Methods (Seed production and
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dispersal). Growth and survival of category-2 seedlings is as in Figure 3. The survival probability
used for trees in categories 3-5 is an estimate based on the fraction of T. vasquezii trees surviving
a 7-y period in Permanent Sample Plots in El Tigre (PSPs; see Materials: Adult growth and
survival). Survival of larger non-reproductive T. vasquezii individuals was taken to be equal to
the community-wide survival obtained from the PSPs (Poorter et al. 2001). Growth of T.
vasquezii in categories 3-10 was based on DBH measurements in the PSPs (1995-2002) and
additional measurements in a neighbouring forest ("Verdum", 2000-2002; Total N=101). Annual
DBH growth per individual was regressed against initial DBH and fitted using a logarithmic
function (DBH growth (cm y-1) = 1.2* Ln(DBH(cm)) - 2.8; R2=0.35). Growth rate per category
was obtained by substituting the midpoint DBH of the category in the equation.
The probability of becoming reproductive (Pr) was obtained in a survey of reproductive status of
90 trees >30 cm DBH, carried out along transects and trails in El Tigre in August 2003. Of these
90 trees, 40 had been reproductive during the previous 2 years or were flowering or fruiting at the
moment of the survey. Based on the degree of decay of the trunk and branches, experienced tree
spotters were able to estimate whether trees had reproduced and died 0, 1 or 2 years before the
survey. We calculated the proportion of trees that had reproduced 0, 1 and 2 years ago as follows:
for 2 years this was 15/90 = 0.17 (15 reproductive trees, of a total of 90 trees); for 1 year this was
12/75 = 0.16 (12 reproductive trees, of a total of 90-15 trees); for 0 year this was 13/63=0.21 (13
reproductive trees of 90-37 trees initially). As the proportion of reproductive and nonreproductive trees did not differ between years (Chi-square test, χ2 =0.587, P>0.05, n=228), we
used the average value of the three years as the probability of becoming reproductive (0.18).
We also tested whether the probability of reproduction was related to size (DBH) for trees >30
cm DBH (the lower limit of reproduction), but no effect was found in a logistic regression (n=90;
P>0.05). The lack of size-dependence in Pr was confirmed by the finding that average DBH for
reproductive and non-reproductive trees in the sample of surveyed trees was not different (t=0.667, P>0.05, n=90). We checked whether these results agree with the expectation that
5
reproduction in monocarps should be delayed when a higher reproductive output is to be expected
in future (when accounting for the additional mortality risk; in Metcalf et al. 2003). Using vital
rates in Table A1, we found that delaying reproduction to the next size category would always
yield a higher reproductive output than reproducing in the current size category (modified eq. 5 in
Metcalf et al. 2003). Our observations of an even distribution of reproductive trees among size
categories is not in accordance with the predicted delaying behaviour of this deterministic model.
The onset of flowering therefore appears to be co-determined by other (partly stochastic) factors,
such as differences in biomass or crown are among individuals that are not revealed by DBH,
spatial variability in environmental conditions that trigger flowering, historical conditions of
flowering trees, herbivory and genetic differences among individuals (cf. Metcalf et al. 2003).
Our own field observations of groups of different-sized T. vasquezii trees at short distances that
flower simultaneously also point to the importance of such non-deterministic factors.
Seed production was based on the value per cm2 basal area of Figure 1. The probability of
germination and initial survival during the first year (init = 0.034) was obtained from the
reproduction study in El Tigre, using an initial amount of 6687 seeds (see Materials and Methods
- Seed production and dispersal).
Vital rates for the transition matrix of the imaginary polycarpic tree differed only from those of
the T. vasquezii matrix if significant differences were found. In those cases, the median values for
the polycarpic species group in the boxplots were used to represent an "average" polycarpic tree.
This was done for seed production (Fig. 1b), sapling height growth and survival in category 2
(Figs 3b and c) and tree DBH growth for categories 3-15 (Fig. 4b). For the latter rate, the DBH
growth rates for each category obtained from the equation mentioned above were adjusted,
applying a factor-5 reduction in growth relative to the median of the polycarpic species. The
probability of becoming reproductive (Pr) was not measured for polycarpic trees, but was found
to have an extremely low impact on population growth () when changed between 0.1 and 0.9.
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