Quantification of neighbourhood-dependent plant growth by Bayesian hierarchical modelling

1. The effects of neighbours on the growth of individual plants are fundamental to dynamics in plant populations and can be described by means of mathematical functions, so-called competition kernels, in formal spatiotemporal models. Little is known about the form and components such functions should have.

2. We evaluate some properties of kernel functions using data on the growth of Arabidopsis thaliana plants in replicated, even-aged stands of many individuals. Because of the essential non-independence of plant growth in stands, we employed a Bayesian hierarchical modelling approach to estimate values and uncertainties of kernel parameters in location-dependent models of interacting plants.

3. During the experiment plant size and a simple measure of neighbourhood crowding became strongly correlated, plants tending to be small where local crowding was intense, indicating that local competition was an important process in the growth of the plants.

4. Competitive interactions between plants of different sizes were strongly asymmetric, the larger individual acquiring a disproportionately greater share of resources. Competition increased with plant size and attenuated rapidly at distances of a few centimetres, but the exact shape of the attenuation function was less important.

5. Kernel functions with the same kind of structural features were similar in their predictive ability. However, a simple zone-of-influence model, based on overlap of pairs of individuals, with competition favouring the larger individual, was arguably the most parsimonious.

6. Neighbourhood competition in stands of even-aged plants may be successfully captured with relatively simple kernel functions. The results should inform and enhance the formal theory of spatiotemporal plant population and community dynamics. Bayesian hierarchical modelling is a powerful tool with which to analyse complex, spatially dependent data, and has potential as a widely applicable statistical approach for plant ecology.