Quantifying neighbour effects on tree growth: Are common 'competition' indices biased?

1. Interactions among neighbouring plants are key determinants of plant growth. To characterise the cumulative effect of all neighbours on the growth of a focal plant, neighbourhoods are often described by 'competition' indices. Common competition indices calculate the summed size of neighbour plants (focal-independent index [FII]) whilst others include the summed ratio of the neighbour size relative to focal plant size (focal dependent). A frequently overlooked statistical artefact is that focal-dependent indices (FDIs) may lead to biased estimates of neighbourhood effects on plant growth when growth is size dependent. 2. Here, we conduct a literature search to determine the most common index types used to explain neighbour effects on tree growth. We then assess the ability of two common index types-focal dependent and focal independent-to correctly infer neighbourhood effects in (1) observations of tree growth in an experimental forest in south-east Tasmania, Australia, and (2) an artificially created dataset where tree growth is unrelated to the neighbourhood. 3. Both indices detected the competitive neighbourhood effect on tree growth observed in our own dataset but differed in their conclusion regarding neighbour effects in the simulated data. Despite the simulated dataset being generated so there was no relationship between tree growth and their neighbourhood, the FDI detected strong, competitive neighbourhood effects when intrinsic growth was incorrectly related to tree size. In contrast, when we considered the FII as the neighbourhood metric, we correctly did not detect any neighbourhood effects in the simulated data regardless of how size-dependent growth was described. 4. Synthesis. 'Competition' indices are a useful method to characterise the cumulative neighbourhood effect on plant growth; however, we demonstrate that indices which include the size of the focal plant in their calculation can be biased by an inherent relationship between tree growth and initial size. Whilst this bias typically overstates the strength of competition in determining focal tree growth, we show that it can be mitigated by correctly describing intrinsic growth. We discuss the limitations of both index types, provide recommendations for performing statistical modelling and outline how to check for accurate neighbour inference.