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) whilst others include the summed ratio of the neighbour size relative to focal plant size (focal-dependent). A frequently overlooked statistical artifact is that focal-dependent indices 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 focal-dependent index detected strong, competitive neighbourhood effects when intrinsic growth was incorrectly related to tree size. In contrast, when we considered the focal-independent index 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.

We used tree growth data from the Australian Forest Evenness Experiment (AFEX; Gerwin et al., 2020) to demonstrate how neighbour indices can be correctly incorporated into a regression analysis of tree growth. The AFEX is a cool temperate experimental forest established in April 2013 with seeds of four locally-dominant native tree species: Eucalyptus delegatensis, E. regnans, Pomaderris apetala and Acacia dealbata. Permission to establish the experiment and to access the site for measurements was provided by Sustainable Timbers Tasmania who manages the site on behalf of the State Government of Tasmania, Australia. In winter 2018, 114 permanent mapped neighbourhood plots were established around 56 E. delegatensis and 58 E. regnans focal trees in the centre of an approximately 2 m radius neighbourhood (12.6 m² total area). We refer to the focal trees in these neighbourhoods as ‘non-isolated’. The 2 m radius was substantially larger than a previous recommendation of 40 times the mean focal tree diameter (0.95 cm) (Sutherland et al., 1991) and was selected as the largest neighbourhood within which we could feasibly sample all neighbouring plants. For every tree in the neighbourhood sampling area (focal and neighbours) we recorded the height (m), diameter at breast height (DBH; cm) and GPS location (accuracy of < 10 cm). In total, 114 non-isolated focal trees and 7854 neighbours were mapped and measured, capturing a range of community compositions ranging in density from 0.8–13.5 plants m^-2 (Supporting Information Fig S1). In addition, in winter 2018, we measured the height and DBH of 34 focal trees that had no neighbours within 2 m, which we refer to as ‘isolated’ focal trees. All focal trees (non-isolated and isolated) were remeasured in winter 2019, 2020 and 2021 to determine three years of annual incremental growth.