DOI: 10.5061/dryad.tmpg4f53b
title: Data from: Quantifying neighbour effects on tree growth: are common “competition” indices biased?

description: 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.
description: 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:
 <em>Eucalyptus</em> <em>delegatensis</em>,
 <em>E. regnans</em>, <em>Pomaderris</em>
 <em>apetala</em> and <em>Acacia</em>
 <em>dealbata</em>. 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 <em>E. delegatensis</em> and
 58 <em>E. regnans</em> focal trees in the centre of an
 approximately 2 m radius neighbourhood (12.6 m<sup>2</sup>
 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 &lt; 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<sup>-2</sup> (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.