Recruitment and Establishment

FORMIND 3.0 includes two different possibilities to model recruitment:

  • by using global constant in-growth rates or
  • by seed production and dispersal of mother trees.

Global in-growth rates

The number of recruited seeds is assumed to be brought into the local community from an intact forest community surrounding the simulated area. This number $N_{\text{seed}} [\frac{1}{\text{yr ha}}]$ is thereby a constant type-specific parameter independent of the density of individuals already existing on the simulated area.

The recruited seeds directly enter the seed pool, but they may only germinate and establish in the next time step. Each patch is assigned an own seed pool. The recruited seeds are distributed uniformly across the patches and added to the corresponding seed pool in an amount of

\[ N_{\text{pool}} = \left\lfloor \frac{N_{\text{seed}}}{\text{#patches}} \right\rfloor \]

If the number of ingrowing seeds $ N_{\text{seed}} $ is not a multiple of the number of patches #patches, a certain number of seeds will remain which are distributed randomly to the patches. For this, the patches are considered one by one incrementally starting with the first. Within each considered patch and for each remaining seed, which has not been distributed yet, its probability of assignment to the currently considered patch is compared with a random number (uniformly distributed in [0;1]). In the case of successful assignment (i.e. random number $ \leq $ 1/#patches), the seed number per patch $ N_{pool} $ is incremented and the number of remaining seeds decremented. At the end, the last patch receives all remaining seeds.

Before the start of the simulation, $ N_{\text{init}} $ seeds already existing in the seed pool per patch (i.e. $ N_{\text{pool}} $ = $ N_{\text{init}} $ ) can be defined for each type, which may germinate and establish as seedlings already in the first time step.

Seed production and dispersal of mother trees

Before the start of the simulation, it is obligatory to assign to the seed pool of each patch a type-specific number of seeds $ N_{\text{init}} $.

During the simulation, each individual of a cohort per patch is able to produce a predefined type-specific number of seeds $ N_{\text{seed}} $ on its own as a mother plant if it reaches apredefined stem diameter $ D_{\text{rep}} $. These produced seeds are dispersed among the neighboring patches surrounding that patch the mother plant is located in. The dispersal is dependent on a defined dispersal kernel, the crown diameter $ C_D $ of the mother plant and a predefined type-specific average dispersal distance $ dist $.

There is no distinction between different dispersal agents (e.g. wind, birds, mammals). The dispersal kernel is assumed to be Weibull distributed with a shape parameter of 2 and a scale parameter of $ (dist + C_D / 2)^2 $. Presuming rotation symmetry, the probability density $ f_{\text{disp}} $ that seeds are dispersed at a distance $r$ from the mother plant is defined as

\[ f_{\text{disp}}(r) = \frac{2 \cdot r}{\left(dist + \dfrac{C_D}{2} \right)^2 } \cdot \exp\left({-\frac{r^2}{ \left( dist + \frac{C_D}{2} \right)^2 }} \right) \]

For each seed per mother plant per patch, a distance $r$ is stochastically drawn from the dispersal kernel $ f_{\text{disp}} (r) $. Using the calculated distance $r$ and a random direction $DIR$ (drawn from a uniform distribution in the range of [0°;360°]), the target coordinates of the dispersed seed are determined in the following way

\[ x_{\text{seed}} = x_{\text{ind}} + r \sin \left( 2\pi \frac{DIR}{360} \right) \]

\[ y_{\text{seed}} = y_{\text{ind}} + r \cos \left( 2\pi \frac{DIR}{360} \right) \]

where $ (x_{\text{ind}}, y_{\text{ind}}) $ is a randomly generated position of the mother plant within its corresponding patch and $ (x_{\text{seed}}; y_{\text{seed}}) $ is the calculated virtual position of the dispersed seed on the simulation area. As in FORMIND 3.0 individuals do not have spatially explicit positions within the patches, the corresponding patch number of the dispersed seed is calculated from the coordinates $ (x_{\text{seed}}; y_{\text{seed}}) $.

The sum of those produced seeds, which are dispersed to a certain patch are added first to its corresponding seed pool $ N_{\text{pool}} $ before they are able to germinate and establish in the next time step.

Germination of seeds

Before seeds can germinate from the seed pool and establish successfully, light and space conditions are checked. Per type a minimum number of seeds can be withheld in the seed pool, which is by default set to 0.

For determining the light conditions, the incoming irradiance on the floor is divided by the incoming irradiance above canopy (see section Competition and environmental limitations for their calculation). This results in the percentage of incoming irradiance on the floor $ I_{\text{floor}} $, which is possibly reduced due to shading of already existing individuals. Dependent on a minimum percentage of light $ I_{\text{seed}} $ required for seed germination and seedling establishment for each type, it is checked whether $ I_{\text{floor}} $ is sufficient:

$$ N_{\text{germ}} = \begin{cases} N_{\text{pool}} & I_{\text{floor}} \geq I_{\text{seed}} \\ 0 & I_{\text{floor}} < I_{\text{seed}} \end{cases} , $$

where $ N_{\text{germ}} $ is the number of germinated seedlings. If light requirements are not sufficient for seeds of a specific type, they remain in the seed pool and may germinate in future time step as far as conditions become favorable. By this, seeds may accumulate in the seed pool if light conditions remain unfavorable over a period of time.

Seeds waiting in the seed pool for favorable germination conditions may be affected by seed pool mortality. For each type a mortality rate $ M_{\text{pool}} \left[ \frac{1}{\text{yr}} \right] $ is defined prior to the start of the simulation. A rate of $ M_{\text{pool}} = 0$ represents, for example, an unlimited accumulation of seeds in times of unfavorable conditions. In contrast, a rate of $ M_{\text{pool}} = 1$ would not allow any accumulation of seeds in the seed pool.

The density of germinated seedlings can be regulated as well. To this end, for each type and patch, the number $ N_{\text{germ}} = 0$ is truncated at a predefined value $ max_{\text{dens}} $.

Establishment of seedlings

If light requirements are fulfilled for successful seedling germination, it is secondly checked whether enough space is available for their establishment. Germinated seedlings start with a predetermined stem diameter $ D_{\text{min}} $, irrespective of type or species. Using the chosen functional relationships describing the geometry of an individual (see section Geometry, their corresponding height $ H_{\text{min}} $ can be calculated. If space at the respective height is already filled by more than 100% with existing individuals, none of the germinated seedlings would be able to establish:

$$ N_{\text{est}} = \begin{cases} N_{\text{germ}} & CCA_l < 1 \\ 0 & CCA_l \geq 1 \end{cases},$$

where $ N_{\text{est}} $ is the number of successfully established seedlings and $ CCA_{l} $ denotes the cumulative crown area at the height layer $ l $ (of height $ \Delta h : [\text{m}] $) that corresponds to $ H_{\text{min}} $:

$$ l=\left\lfloor \frac{H_{\text{min}}}{\Delta h} \right\rfloor. $$

See section Mortality for the calculation of the cumulative crown area $ CCA $ of all height layer of the aboveground discretized space.