Individual Based Forest Models

The power of digital computation in the middle of the 1960s on what today would be considered primitive computers, inspired the development of a new class of models that simulated the behavior of large complex systems by modeling the dynamics of the individuals in the systems. These included models of forests based on the changes in each individual tree in a simulated forest stand. In these models two implicit assumptions associated with traditional ecological population modeling are not necessary:

1. The assumption that the unique features of individuals are sufficiently unimportant to the degree that individuals are assumed to be identical. This allows the simulation of the numbers of individuals in the population without consideration of sizes or ages of the members of the populations.

2. The assumption that the population is 'perfectly mixed' so that there are no local spatial interactions of any important magnitude.

Individual-based models of forests spring from a rejection of these assumptions. Trees vary greatly in size over their life span. Trees are sessile (so that spatial location matters and every individual in a population does not affect all the other members). This may be one of the reasons that tree-based forest models are among the earliest and most widely elaborated of the individual-based genre of models.

These models were developed by quantitatively oriented foresters in the mid-1960s and focused strongly on production forestry. The earliest such model was developed by R. M. Newnham for even-aged Douglas fir forests. This was followed by similar developments at several schools of forestry in North America. These models were implemented on a digital computer programmed to alter the sizes of trees on a map of the positions of each tree in a forest. When a tree died it was erased from the computer map. Three-dimensional spatial interactions among individual trees were explicitly represented and these initial models are as complex and as detailed as their descendants today.

These dynamic mapping techniques initially were applied to even-aged plantations but applications in more complex forests soon followed. After these first modeling efforts, individual-based tree models tended to feature simplifications of these initial models. The early individual-tree based simulators took what was known from yield tables and other data sets and developed a more flexible, quantitative methodology for prediction. One significant simplification of this class of models was to simulate only the vertical (shading) relations on a small plot dominated by a single large canopy tree. The resultant 'gap models' found wide application in forest ecology of natural, mixed-aged, and mixed-species stands.

Gap models feature relatively simple protocols for estimating the model parameters and synthesize information on the performance of individual trees (growth rates, establishment requirements, and height/diameter relations) to directly estimate model parameters. The simple rules for interactions among individuals (e.g., shading and competition for limiting resources) and equally simple rules for birth, death, and growth of individuals in these models have both positive and negative consequences. The positive aspects largely relate to the ease of estimating model parameters for a large number of species. The negative aspects relate to the lack of physiological mechanism in the description of growth and environmental response. Much of the current research in the subsequent development of gap models relates to overcoming these limitations (Figure 3).

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