The epidemiology and severity of ash dieback (ADB), the disease caused by the ascomycete fungus, Hymenoscyphus fraxineus, has been linked to a variety of site conditions, however, there has been a lack of analysis at an individual-tree scale. 
 
Symptoms of ADB were scored on ca. 400 trees of Fraxinus excelsior (ash) in permanent sample plots during two successive years in a UK natural woodland reserve. Using comprehensive plot records maintained since 1945, and detailed spatial records updated since 1977, we assembled an array of potential explanatory variables, including site environment factors, ash tree density, previous and present tree condition and near neighbourhood summary statistics (NNSS), such as species mingling and size dominance. Their impact on the severity of ADB of focal ash trees was tested with generalised linear mixed effects models (GLMM).
 
The severity of ADB was much greater in the lower slope parts of the site with moister soils and least in a managed area subject to tree thinning in the previous 35 years. Severity of ADB had a negative association with focal ash tree prior relative growth rate over a period of a decade immediately before the disease was detected at the site. Greater ADB severity was also significantly associated with smaller diameter-at-breast-height of ash trees. Additionally, ADB was significantly positively associated with a greater proportion of heterospecific trees amongst the six nearest neighbours of the focal tree. 
 
Synthesis. The relationship of the severity of ADB disease with site environment, tree condition and neighbourhood is complex but nevertheless important in the progression of the disease. The findings suggest some silvicultural interventions, such as thinning to increase the vigour of retained ash trees, might reduce the impact of ADB.

There is a long history of monitoring at the site with rare longitudinal records from repeated censuses of all trees in ten long thin permanent sample plots, termed “transects”. Hand-drawn maps of the locations of the centre of each individual woody plant ≥1.3 m height in transects I-VI were recorded on a Cartesian coordinate grid by reference to transect edge markers with a regular 30.5-m spacing in 1977. Transects VII-X were similarly mapped in 1984–85. These records were updated and checked for accuracy at each successive enumeration of each transect, including in 2013 before ADB was first observed in the woodland and in anticipation of its arrival. For the present study, these maps were scanned digitally using Esri ArcGIS Pro® 2.7.3 (2021) software onto Ordnance Survey digital maps and allocated their British National Grid coordinate values. The geographical location of the centre of each tree was normalised for slope. After the initial enumeration of each transect, all woody plants ≥ 1.3 m height (with no minimum diameter limit) in transects I-IX were identified to species, recorded as live or dead and measured for diameter at breast height (1.3 m, dbh) in 1955, 1977 and 1983, and in all ten transects in 1986, 1992, 2000, 2002, 2010, 2013 and 2018. In the case of the many multiple-stemmed coppice stools, an equivalent single diameter was assigned, calculated from the sum of their stem cross-sectional areas. 

A total of 464 F. excelsior trees across the ten permanent transects, representing all live individuals ≥1.3 m height at the start of the study in 2019, were assessed for ADB symptoms in July and August 2019, and 381 during August 2020. The lower number in the second year is due to the increased restriction on field-work due to risk assessment and restriction of available time under that constraint. Therefore, our main statistical models were only applied to the more complete data set recorded in 2019. We have used the 2020 data solely to assess the overall rate of progression of the disease at the time of the study.

The severity of crown dieback was scored between 0 and 100% based on a visual estimation of proportionate level of defoliation, similar to the assessment methods used in other studies of ADB (Turczanksi, 2020; Grosdidier et al., 2020; Lenz et al., 2012). Two observers surveyed each focal tree according to an agreed scale of crown defoliation in scoring classes of 0–10%, 10–20%, 20–30%, 30–40%, 40–50%, 50–60%, 60–70%, 70–80%, 80–90%, 90–100%, with their assessments calibrated at regular intervals against photographs of previously agreed percentage defoliation scores to ensure scoring did not drift over the study. Independent scoring of the same tree by each of the observers was conducted periodically to guard against observer bias and the scoring of the transects was carried out in random order to avoid confounding with topographic/stand type. Ash trees with a score of 0% crown dieback and no trunk sprouting or other visible sign of infection were classified as uninfected.

Two periods of recorded prior growth rates were selected: 1977 to 2013, and 2000–2002 to 2013. Basal area of each tree was also calculated from the dbh measurements as an explanatory variable in its own right for focal ash trees, but also to calculate further explanatory variables, such as the total basal area of the stand. Basal area of larger trees (bal), an indicator of the level of competition for light on the focal tree at the stand level (Pommerening & Grabarnik, 2019; Wykoff, 1990), was calculated as the total basal area of all trees larger or equal to the basal area of the focal tree i in the same sub-plot at a particular time t (see Table 2, formula 5 in the MS).  By “sub-plot” here we mean the regular subdivisions of the transect plots permanently marked by stakes at 400-ft (121.9-m) intervals down the slope, which were used for ease and accuracy of the successive enumerations of the transects but were also, it transpired during our study, the most ecologically appropriate for near-neighbour spatial analysis. The size of each sub-plot of the transects was 19.8 m x 121.9 m (2414 m²) and they were arranged so that each lay entirely within either the "old growth" or "young growth" stands". An alternative measure of a focal tree’s crown dominance relative to its neighbours was provided by the recording, in previous enumerations, of each tree’s crown position in four categories: ground, understorey, sub-canopy, and canopy.

Spatial point-process methods were used to compute the Euclidean distances between nearest-neighbour points within each 2414 m² sub-plot (as illustrated in Figure 2 in the MS). The ‘spatstat’ package in R was used to estimate near neighbour summary statistics (NNSS). Using ‘spatstat’, a number of established individual-tree neighbourhood indices were calculated (Baddeley, Rubak & Turner, 2015; Illian et al., 2008; Pommerening & Grabarnik, 2019) for use as explanatory variables, as outlined below. We used the minus-sampling “NN1” nearest neighbour edge-correction method outlined by Pommerening & Grabarnik (2019), in turn, based on Hanisch (1984), for all these NNSS.

 (i) Species mingling (mi) and weighted species mingling (wmi)

Both species mingling (mi) and richness-weighted species mingling (wmi) are spatially-explicit diversity indices. Species mingling (mi) is a calculated value between zero and one representing the proportion of heterospecific (rather than conspecific) trees in the near neighbourhood of the focal tree (see Table 2, formula 1 in the MS). So, if there are four neighbours counted and three are heterospecific, the focal tree is given a species mingling value of 0.75. The total number of nearest neighbours (k) can be varied according to the ecological context. We used a version of the formula which incorporates weighting by the number of species in the k nearest neighbours, known as “richness-weighted species mingling” (wmi) (Hui et al., 2011), with the weighting effect limited by the number of species present in the focal tree’s sub-plot (which sets the maximum possible number of species in k + 1 trees at that location) (Wang et al. 2021) (Table 2, formula 2). The wmi index is thus a more sophisticated version of the mingling index, which encompasses the component of species richness in a tree’s heterospecific near neighbourhood, producing a greater variation in index values between trees. However, to test the use of wmi for assessing the dominance of ash trees’ neighbourhoods by heterospecific trees, we examined the linear correlation of wmi with mi for the 464 ash trees included in the study; the Pearson correlation co-efficient (r) was 0.89 giving us full confidence in selecting wmi for this purpose.

 (ii) Size dominance (ui)

The size dominance index (ui) measures the size of a focal tree relative to its k nearest neighbours (see Table 2, formula 3 in the MS). We used stem diameter (dbh) to describe size, but other size characteristics are also possible. The calculation of this index is similar to that of the species mingling index, with a value between zero and one, and the potential to vary k (Hui et al., 1998; Aguirre et al., 2003; Pommerening & Grabarnik, 2019).

 (iii) Local tree density (l)

Local tree density around a focal tree (l) was calculated using a kernel smoothing function in R (Baddeley, Rubak & Turner, 2015). It was originated by Diggle (1985) as “a method for estimating the local intensity” as a point process, and it includes edge correction within the formula (see Table 2, formula 4 in the MS). 

R, Spatstat, Excel