Tree mortality in undisturbed tropical rain forest lies on average between 1 and 3 % per year (Swaine 1989; Phillips & Gentry 1994; Condit et al. 1995b; van der Meer &
Bongers 1996).
Different types of mortality are included in the model.
Normal mortality: If field data indicate functional relationships between tree mor-tality and tree sizeMD=f(d) (Okuda et al.
1997), or diameter growth MI = f(dinc)
0 10 20 30 40 50 Stem diameter d [cm]
0.0 0.1 0.2 0.3 0.4
MortalityrateMD[-]
Figure 4.8: Size-depending mortality rate MDat the site Sabah, Malaysia.For trees with a diameterd >10cm MD= 0.
(Swaine 1989) they can be added to the ba-sic mortalityMBs,h. Well known significant differences in mortality rates between differ-ent successional status and maximum tree height are covered in MB. Thus, early suc-cessionals have shorter lifetimes, and tree mortality is lower in high growing trees.
The basic equation for mortality rates is Mi =MBs,h+MD+MI. (4.23) Mortality of small trees is significantly higher than average (Fig. 4.8):
MD=
MD0−MD0/MD1·d : d < MD1
0 : else
(4.24) MD0, andMD1: parameters. In a field study in Pasoh, Malaysia mortality of seedlings reached up to 20 % y−1 (Okuda et al. 1997).
Functional relationships of mortality and diameter increment are not used in the present applications (MI= 0).
Falling trees: Gap creation through falling large trees plays an important role in rain forest dynamics and contributes signif-icantly to mortality rates. In a field study in South America 90 % of total mortality was caused by falling trees (van der Meer &
Bongers 1996).
Dying trees with a diameter d ≥ 10 cm can fall over (probability W) and cre-ate gaps of different sizes in neighbouring
patches. The number of trees NF destroyed from total number Np in target patch p is calculated from crown projection area fF of the falling tree relative to patch size A:
NF =NpfF
A, (4.25)
Individuals are chosen randomly with the restriction that only trees smaller than the one falling can be destroyed, and contribute with different NFi to tree losses in the co-horts of target patch.
Self-thinning: In sites with a high tree density, mortality is significantly increased.
This phenomenon is called self-thinning. In the model NT trees in patches with crown closure (F(z) > 1) are randomly extracted until crown coverage F(z) decreases below its maximum value of 1.0.
As second main equation covering changes in tree numbers of each cohort we obtain:
dNi
dt =−(Mi·Ni+NTi+NFi). (4.26) In cohorts with high tree numbers (Ni ≥ 100) and small individuals (d <10 cm) de-terministic mortality takes place. Thus, mortality rate Mi corresponds to the num-ber of trees dying each year. In all other cases (Ni < 100, or d ≥10 cm) mortality is determined stochastically, and Mi repre-sents the probability of each tree dying.
Recruitment
Recruitment is modelled with a seed pool.
For input of new seeds into the pool two different recruitment mechanisms were in-corporated in the model.
(1) Scenario seed pool: The simplest approach consists of assuming that an in-tact forest surrounding the simulation area is supporting a constant seed input rateNSs within the simulated patches.
(2) Scenario seed tree: The second ap-proach takes into account the dispersal of
0 100 200 300
Figure 4.9: Seeds dispersal kernels for a Gaussian distribution with different average dispersal distances XR.Crown diameter was fixed at cd=20 m.
seeds produced within each patch from lo-cal parent trees, which are trees exceeding a certain diameter DRh. Recruitment strate-gies are highly variable in rain forests, with interspecific differences in the fruiting pe-riod, seed sizes varying in a six-fold range (Westoby, 1995), dispersal strategies, dis-persal agents, disdis-persal distances, seed sur-vival, germination probabilities and matur-ing size of seed dispersers (Denslow 1987;
Garwood 1983; Whitmore 1983). Thus, some fundamental assumptions on the most important trends have to be drawn.
Flowering, fruiting and seed produc-tion vary in duraproduc-tion and frequency across species, some species fruiting after sev-eral years of unfecundity (Garwood 1983).
Other species flower and fruit continu-ally throughout the year in Malaysian rain forests (Putz 1979). Seasonal differences in seed production are not taken into consid-eration.
The rate of seed production NRs varies widely among species (Whitmore 1998).
Various studies have analysed different dis-persal strategies and lengths (review in Clark et al. 1999b). A major result is that migration velocity found in paleoeco-logical records can only be explained with a seed dispersal kernel which allows a reason-able amount of seed establishments far away
from the mother tree (Clark 1998; Clark et al. 1998a)].
Different dispersal agents (e.g. wind, birds, mammals) are not directly distin-guished in our model, but the resulting av-erage dispersal distance XRs depends upon the tree species and should match with the parameter set. From the dispersal kernels discussed by Clark et al. (1999) we use the Gaussian distribution (as used by Chave 1999b). Assuming rotation symmetry, the probability density f of seeds to be dis-persed at the distance r from the mother tree is with cd, the crown diameter (see Fig. 4.9).
Thus, 99% of the seeds are dispersed in a distance less than 2.14×(XR+cd/2). The actual dispersal distance r is randomly drawn from this probability distribution, and the direction is drawn uniformly. The resulting seed shadow is the product of the rate of seed production and the dispersal kernel (Clark et al. 1999b).
For both recruitment mechanisms, in-coming seeds will be added to a seed pool, taking into account the average seed mor-tality rateMSs across functional groups (cf.
Garwood 1983, 1989). These seeds corre-spond to the reproductive success and are those which can potentially be established as seedlings at the minimum diameter of 1 cm (Ribbens et al. 1994; Chave 1999b).
Seed loss due to predators is implicitly in-cluded in relative low seed production rates.
The actual seed germination depends upon
• a minimum light intensity at the forest floorIF ≥ISs (Whitmore 1998), and
• a not fully closed lowest canopy layer.
If conditions for ingrowth are fulfilled ad-ditional cohorts are created. The state vari-ables biomass Bi and tree number Ni are initialised with biomass corresponding to
seedlings diameterDS and number of seeds of PFT available for ingrowth in seed pool of current patch.