Inheritance and Variation of Traits in Vegetation Simulation

The new features of the model are variation and inheritance of traits. In a previous version of the model LAVESI (Kruse et al., 2016 ), almost all traits were the same for every individual (only maturation height being randomly assigned) of the same species, which is referred to as the uniform type throughout this article. In this work, we created variation and adaptation for the seed weight and the drought resistance. Both use the same following principles in their trait value determination.
Trait variation gives every newly produced seed a random value from a uniform distribution with upper and lower limits. Therefore, every seed that is either introduced or created by a tree during the simulation has the same chance of having any trait value from the distribution. This allows for variability in the traits present in the model permitting plastic responses but no adaptation while not being computationally much more intensive.
The inheritance (adaptive traits) system (Fig. 1), on the other hand, calculates a new seed value for every new seed production that is a function of the trait value of the mother tree and the pollen source (Geber and Griffen 2003 ). To calculate the likely pollen source, it was necessary to create a level of abstraction as calling every tree for every seed production proved too computationally intensive (Kruse et al., 2018 ). For this reason, a pollen grid was introduced with grid cells of, in this case, 100 m². The trait information of the pollen-producing trees is averaged per cell and these mean grid-cell values used as the trait values for that pollen source. The new seed's trait value is calculated by either using a mixture distribution, created by combining the two parental normal distributions, or by a normal distribution around a weighted average of the pollen source and the seed-producing tree. For the normal distributions the Box-Muller transform is used (Box and Muller, 1958 ). The mixed distribution is achieved by creating normal distributions for both parents and randomly selecting one or the other. For the northern tree expansion both methods are used and two different weights are applied to the second method, with the weight applied being equal in one case and 75% for the seed-producing tree in the other case, to assess the different options. Since all three methods produce comparative results (not shown) only the mixed distribution is used for the drought experiment.Fig. 1

Scheme showing the inheritance system. The upper part shows a schematic path from the pollen to the seed-producing tree and from the seeds to the offspring. Red vertical lines in the lower part show the trait values of individuals within a range of possible trait values represented by the black bars along the x axis. The specific trait values are examples and could be anywhere within the range. The blue curve shows the distribution of likely trait values, around the individuals own trait value, for the offspring based on the pollen and the orange based on the seed-producing tree. The right shows the offspring uses a mixed distribution resulting from these two to determine their trait values. The green dotted lines for the offspring show three possible trait values as examples that could be created by these two parent trees.

Fig 1