Journal of Ecology 2001, 89 (6), . DOI: 10.1046/j.0022-0477.2001.00622.x

Supplementary Material

Appendix 1

Background information on matrix models for the six study species

In this appendix we present information on the matrix models used for the simulations in the paper, including the mean and SD of vital rates used for the simulations. Tables S1–S6 contain these vital rate values for the six study species.

Primula vulgaris. Of the various populations studied by Valverde & Silvertown (1998), a population under intermediate canopy openness was selected (SF). This population is located in Northamptonshire, UK. Data for 1992–93 were used. In the original matrix, five categories were distinguished based on rosette size. Progression and retrogression elements in the matrix were based on directly observed transitions. One transition (a45) based on one individual was omitted from the simulations. Reproduction (capsule production) was calculated by multiplying the probability of being reproductive and the number of capsules produced per reproductive individual.

Geonoma deversa. We used a ramet matrix model in which data from three nearby populations in a moist tropical forest in northern Bolivia were combined for one year (1996–97; Zuidema 2000). The population was divided into six size categories, based on number of juvenile-type leaves (categories 1–2), number of adult-type leaves (3), and stem-length (4–6). Transitions for categories 1 and 2 were based on observed transitions; progression from 3 to 4 on leaf production and in categories 4–6 on stem length growth. Production of new seedlings was modelled as the product of the probability of being reproductive and the number of new seedlings encountered per reproductive ramet (based on densities of seedlings and reproductive ramets). Production of new ramets was calculated as the probability that a ramet in a certain category would produce a new ramet.

Euterpe precatoria. A transition matrix for a population in moist tropical forest in northern bolivia was used for a year with normal precipitation (zuidema 2000). The population was divided into 11 categories, of which the first four were based on leaf length and the remaining seven categories (5–11) were based on stem height. For categories 1–4, transitions were based on direct observations (1–2) or average leaf growth (3–4); for categories 5–11, mean growth rate was determined using a non-linear growth function (hossfeld IV equation) that relates growth to initial size. Standard deviations for growth rates were based on a measure of deviation from the growth function. The difference between observed growth and that predicted by the equation was used to obtain an estimate of the standard deviation for growth rate per category (SDi): SDi = sqrt(S[(o-p)2]/n), where o is observed diameter increment of an individual, p is the value predicted by the equation for an individual of the same size, n is the sample size and the summation is over all individuals in a category. Survival probability was lower for category 1 than for all other categories, but for the remaining categories no size-dependent patterns were found. Production of new seedlings was calculated as the product of the probability of being reproductive and the number of new seedlings encountered per reproductive ramet.

Duguetia neglecta. The matrix model for a population in undisturbed, evergreen rain forest in central Guyana was used (Zagt 1997). Data were collected in 1991–95. The population was divided into 12 size categories: four for seedlings (classified by stem length and number of leaves per unit stem length), two for juveniles, and six for reproductive individuals (both classified by diameter). Transitions between seedling categories were based on observed transitions and contained many multiple-step transitions. Growth rates for juvenile and adult categories were determined using the same non-linear growth function as for Euterpe. Survival for juvenile and adult categories was based on a double logistic regression of survival against diameter (Zagt 1997), allowing for a lower survival probability for both small and large individuals. Production of new seedlings was calculated as the product of the probability of being reproductive and the number of new seedlings encountered per adult.

Bertholletia excelsa. A matrix model for a population in moist tropical forest located in northern Bolivia was used (site 'El Sena'; Zuidema 2000, Zuidema & Boot, in press), with data for a year with normal precipitation. The population was divided into 17 size categories: four for seedlings (classified by stem length), seven for juveniles and six for reproductive individuals (both classified by stem diameter). Transitions between seedling categories were based on growth in stem height; those for juvenile and adult categories were based on diameter growth (using the same non-linear growth function as for Euterpe). No size-dependent pattern was found for survival. Production of new seedlings was calculated by multiplying the probability of being reproductive, the number of fruits produced and the number of new seedlings per fruit produced (from densities of fruits and seedlings).

Chlorocardium rodiei. The matrix model for an undisturbed population in evergreen rain forest in central Guyana was used, containing data collected in 1991–95 (Zagt 1997). The population was divided into 15 size categories: one for seeds, six for seedlings (classified by stem length and number of leaves per unit stem length), four for juveniles and four for reproductive individuals (both classified by diameter). Progression, retrogression and stasis transitions for seedlings, juveniles and adults were calculated as for Duguetia. Seed production was calculated as the density of current year's seeds divided by density of adult trees. Information on between-individuals variation in seed production was derived from a seed-fall study of 16 trees in the same area (Ter Steege et al. 1996, p. 30).

Table S1 Vital rates for Primula vulgaris. Mean (and SD) of survival (s), growth to next category (g(1)) and to a larger category, skipping one category (two-step progression: g(2)), negative growth to previous category (r), probability of being reproductive (Pr{rep}) and number of seedlings produced by a reproductive individual are shown

 Stages g(1) g(2) r Pr{rep} Seedl. prod. 
1Seedling0.471(0.121)0.625(0.171)0.375(0.171)
2Juvenile0.900(0.067)0.389(0.115)0.333(0.111)0.150(0.080)2.00(1.00)
3
4
Adult 1
Adult 2
0.954
0.992
(0.026)
(0.008)
0.484
0.362
(0.063)
(0.045)
0.113
(0.040)

0.052

(0.021)
0.292
0.720
(0.056)
(0.041)
2.74
4.59
(1.91)
(2.74)
5Adult 30.988(0.012)0.173(0.042)0.963(0.021)10.23(6.59)

Table S2 Vital rates for Geonoma deversa. Variables as in Table S1, with addition of the number of new ramets produced by an individual through vegetative reproduction

 Stages g r Ramet prod.Pr{rep}  
1Seedling0.614(0.042)0.176(0.033)
2Seedling0.933(0.041)0.046(0.034)0.376(0.079)
3Juvenile0.957(0.049)0.313(0.442)
4Adult0.991(0.006)0.101(0.072)0.014(0.007)0.044(0.012)
5Adult0.991(0.004)0.055(0.042)0.023(0.007)0.840(0.017)
6Adult0.980(0.008)0.027(0.009)0.998(0.003)

Table S3  Vital rates for Euterpe precatoria. Variables as in Table S1

Stages g r Pr{rep}  
1Seedling0.722(0.036)0.061(0.019)
2Seedling0.941(0.021)0.098(0.042)0.133(0.048)
3Seedling0.941(0.021)0.047(0.179)
4Seedling0.941(0.021)0.024(0.090)
5Juvenile0.957(0.009)0.050(0.141)
6Juvenile0.957(0.009)0.086(0.170)
7Juvenile0.957(0.009)0.127(0.092)
8Juvenile0.957(0.009)0.115(0.071)
9Adult0.957(0.009)0.076(0.095)0.027(0.021)
10Adult0.957(0.009)0.035(0.031)0.685(0.052)
11Adult0.957(0.009)0.998(0.005)

Table S4 Vital rates for Duguetia neglecta. Variables as in Table S1; r(2) denotes negative growth to the category before the previous one (2-step retrogression). Survival of category 3 equalled 1, as no individuals died; this survival rate was therefore not used in simulations

Stages g(1) g(2) or r(2)r(1) Pr{rep}   
1Seedling0.749(0.064)0.162(0.063)0.009a(0.017)
2Seedling0.943(0.039)0.115(0.056)0.030(0.030)
3Seedling1.0000.066(0.045)0.044(0.038)
4Seedling0.976(0.028)0.047(0.040)0.011b(0.020)0.047(0.040)
5Juvenile0.992(0.004)0.057(0.011)0.007(0.004)
6Juvenile0.994(0.004)0.016(0.051)
7Adult0.994(0.006)0.032(0.056)0.110(0.024)
8Adult0.993(0.008)0.047(0.062)0.290(0.044)
9Adult0.991(0.011)0.057(0.080)0.535(0.060)
10Adult0.990(0.013)0.061(0.049)0.535(0.066)
11Adult0.988(0.023)0.058(0.067)0.535(0.106)
12Adult0.984(0.026)0.535(0.104)
a Refers to g(2); b Refers to r(2)

Table S5 Vital rates for Bertholletia excelsa. Variables as in Table S1. The values for fruit production are ln(no. fruits + 1)

Stages g Pr{rep} Fruit prod.  
1Seedling0.546(0.041)0.167(0.196)
2Seedling0.735(0.073)0.200(0.366)
3Seedling0.914(0.064)0.146(0.220)
4Seedling0.988(0.020)0.169(0.135)
5Juvenile0.985(0.016)0.010(0.024)
6Juvenile0.985(0.016)0.028(0.039)
7Juvenile0.995(0.005)0.047(0.042)
8Juvenile0.995(0.005)0.110(0.053)
9Juvenile0.995(0.005)0.148(0.085)
10Juvenile0.995(0.005)0.157(0.082)
11Juvenile0.995(0.005)0.143(0.092)
12Adult0.995(0.005)0.053(0.031)0.971(0.032)4.08(0.48)
13Adult0.995(0.005)0.032(0.035)0.998(0.007)4.23(0.30)
14Adult0.995(0.005)0.019(0.009)1.000(0.002)4.37(0.86)
15Adult0.985(0.011)0.011(0.012)1.000(0.001)4.51(0.48)
16Adult0.985(0.011)0.007(0.019)1.000(0.000)4.65(0.67)
17Adult0.985(0.011)1.000(0.000)4.83(0.86)

Table S6 Vital rates for Chlorocardium rodiei. Variables as in Table S1; r(2) denotes negative growth to the category before the previous one (2-step retrogression)

Stages g(1) g(2) r(1) r(2) g or r  
1Seed0.377(0.032)0.456(0.033)0.134(0.023)0.096a(0.020)
2Seedling0.280(0.029)0.138(0.022)0.220(0.027)0.078a(0.017)
3Seedling0.457(0.060)0.110(0.038)0.089(0.034)0.358(0.058)
4Seedling0.495(0.025)0.070(0.013)0.031(0.009)0.045(0.010)0.004a(0.003)
5Seedling0.870(0.022)0.006(0.005)0.032(0.012)0.277(0.029) 0.031(0.011)0.029b(0.011)
6Seedling0.683(0.049)0.114(0.033)0.006(0.008)0.059(0.025)0.129(0.035)0.005c(0.008)
7Seedling0.963(0.014)0.027(0.012)0.072(0.019)0.032(0.013)0.008a(0.006)
8Juvenile0.985(0.011)0.014(0.023)
9Juvenile0.990(0.015)0.016(0.030)
10Juvenile0.993(0.020)0.014(0.009)
11Juvenile0.993(0.016)0.007(0.005)Seed prod. 
12Adult0.992(0.016)0.014(0.007)116(156)
13Adult0.991(0.015)0.007(0.003116(156)
14Adult0.988(0.018)0.006(0.003)116(156)
15Adult0.986(0.033)116(156)
a Refers to 3-step progression; b refers to 3-step retrogression; c refers to 4-step retrogression.