Models of Clonal Plant Growth Based on Population Dynamics and Architecture

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Abstract
The branching pattern of Lycopodium annotinum, a modular and clonal vascular cryptogram with a stoloniferous/rhizomatous growth form, was simulated using a combination of architectural and population dynamics models. Data on morphology, survival and fecundity were collected in the field in Swedish Lapland and used to generate a series of growth rules in two models. An initial, simple, deterministic growth model reflected the growth form of L. annotinum in a homogeneous environment. From this model, conclusions, were drawn that apical dominance and branching angles are two important internal controls which optimize the balance between ground exploitation and the avoidance of competition for light, water and nutrients within plants (plants being defined as the aggregations of branches physically connected by living tissues). The introduction of stochastic elements into the model, based on field data, produced a wide range of simulated plant forms, clearly comparable to those in the field. Lateral spread in simulated plants varied greatly in shape, from compact, dense forms with short annual segments to loose widely spread forms with long annual segments. Both guerilla and phalanx growth forms occurred in the simulations simply as part of a stochastic process. Survival of clones (i.e. aggregations of plants from a common ancestor) varied from 1 yr to the duration of the simulation, indicating their potential for indefinite growth, although a substantial number (51%) survived for only 2 to 5 yr. The architectural model based on population dynamics was robust and a sensitivity analysis showed that survival probabilities had to be changed by 20% before the clone reacted, while a much greater degree of change of fecundity values was required (-100% to +50%) to overcome the stochastic element of the model. This reflects the robustness suggested for clonal plants also indicated by their low sensitivity values from transition probability matrices, but is marked contrast to the great sensitivity of transition probability matrices in general. The sensitivity analysis also showed that the most sensitive age classes were 2 to 6 yr. A major limitation of the stochastic model is that the population processes of age-specific death and fecundity, the growth processes of root production and segment elongation, and the geometry of the plant all vary "unintelligently". A mechanistic approach is now required to relate these processes to environmental variables and internal feedback.