+ Author Affiliations
- *Corresponding author. E-mail: robin.gill@forestry.gsi.gov.uk
- Received February 6, 2009.
Abstract
Relatively little information is available to indicate how the impacts of deer vary in relation to densities of deer encountered in lowland environments in Britain. Population densities and impacts of deer on advance regeneration were therefore assessed at 15 sites, embracing a range of densities from 0 to 54.9 deer km−2 in woodland and 0–74.5 km−2 in adjacent fields. Deer densities tended to be higher on sites with drier and more fertile soils, a relationship which may have arisen for either nutritional or management reasons. The log seedling density was negatively correlated with deer density, relative use of woodland vs adjacent fields and deer species (expressed as a proportion of ‘larger’ species, mainly Fallow deer Dama dama). The abundance of smallest seedlings (<30 cm tall) was also correlated with soil moisture content and tree canopy cover; however, these effects were not significant for larger seedlings (30–150 cm tall), which were instead associated primarily with deer variables. Seedling density declined most sharply at relatively low deer densities, indicating that advanced regeneration is particularly sensitive to deer presence. The results indicate that regeneration is most likely to be inadequate at densities above 14 deer km−2.
Introduction
Browsing by deer has a variety of effects on woodland vegetation, reducing the density of young trees and shrubs and causing changes in botanical composition (Côté et al., 2004). Deer populations have been steadily increasing in range and numbers in Britain (Ward, 2005) and there is increasing concern for the effects they have on woodlands (Cooke and Farrell, 2001; Fuller and Gill, 2001). However, to date, relatively little data are available to relate specific levels of damage in lowland woodlands to particular deer densities, information which can play a key part in determining appropriate deer management.
In the Scottish Highlands, deer browsing has long been known to hamper regeneration of native pinewoods (Watson, 1983). A number of investigations have led to recommendations that deer densities need to reduced to between 4 and 8 deer km−2 to enable sufficient seedlings to survive (Holloway, 1967; Beaumont et al., 1995; Miller et al., 1998; Scott et al., 2000). In the lowlands, woodland surveys have noted that regeneration is often insufficient for woodland management, with deer browsing identified as one of the likely causes (Harmer et al., 1997). Investigations elsewhere (mainly in Europe and North America) suggest that there are large differences between regions in the effects of deer and other ungulates in woodlands (Gill, 2006), and some studies have indicated that the relationship between deer and seedling abundance can be non-linear (Tremblay et al., 2007). However, it is difficult to apply these results directly to the UK lowlands, where conditions are in some respects unique. Unlike the uplands, woodlands in the lowlands are highly fragmented, often interspersed with agricultural land, within which deer are commonly seen to feed. In England, small woodlands (<100 ha) comprise 54 per cent of total woodland area, in contrast to only 18 per cent in Scotland (Watts, 2006). Further, introductions, followed by natural expansion, have resulted in a rather unique assemblage of deer species. Roe Capreolus capreolus, fallow Dama dama and muntjac deer Muntiacus reevesi are now widespread and red Cervus elaphus, sika Cervus nippon and Chinese water deer Hydropotes inermis also occur locally. Each of these species have characteristic patterns of range use, diet and habitat selection (Putman, 1989), which can influence relative use of field and woodland habitats and ultimately their impact on vegetation. Studies elsewhere have indicated that access to an alternative food source, either in woodlands or nearby fields, can affect levels of damage to trees (Gill, 1992a; deCalesta and Stout, 1997; Moser et al., 2006; Ward et al., 2008). Among the species present in Britain, fallow, red and sika deer are most likely to include a large proportion of grasses in their diet (Jackson, 1977, Mitchell et al., 1977; Mann and Putman, 1989). Red and fallow deer are also likely to have the largest home ranges, which may be 1–2 orders of magnitude greater than those of roe and muntjac deer (Table 1).
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Table 1:
Home range sizes reported for deer in UK
However, little quantitative information on the relative use by deer of fields near woodlands is available to date. To address this need, deer densities and impacts were assessed at a range of sites in lowland Britain to establish how levels of damage varied in relation to density. In addition, we investigated how damage was influenced by the deer species present and use of neighbouring fields. In this paper, results focus on relationships between deer abundance, tree regeneration and site factors that affect regeneration, including soil and stand characteristics and canopy cover. The effects of deer on understorey foliage density, and the implications this may have for songbirds, have been reported in a previous paper (Gill and Fuller, 2007).
Methods
Site selection
To explore the full range of effects that deer have on forests, 15 sites were selected with the primary objective of embracing a range of deer densities and therefore included areas with few or no deer (e.g. the Isle of Wight) as well as areas known to have high densities. The sites selected included both coniferous and deciduous woodland as well as land in both private and public ownership.
As home range sizes of deer vary substantially (Table 1), sites were selected that included relatively large areas of woodland. This minimized the possibility that local movements or patterns of habitat selection might produce misleading results. These sites included areas of both contiguous and fragmented woodland. Where the woodland was fragmented (eight sites), sampling was stratified to yield estimates of deer density and impacts within discrete areas of woodland (referred to as a ‘block’). In total, 50 woodland blocks were included in the assessments, with up to nine blocks per site (Table 2).
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Table 2:
Structure and area of sample sites
Within the blocks, impacts were assessed on advance regeneration in mature stands containing mainly broadleaved tree species (85 per cent of basal area). English woodlands are managed using a variety of methods, involving either replanting or natural regeneration, with or without some form of protection (Evans, 1988). Since not all are exposed to deer browsing, the emphasis on advance regeneration ensured the largest possible sample of stands and sites were available to assess the effects of deer on young trees.
Among the mature trees, the most abundant species was oak, Quercus sp. (63 per cent) followed by ash, Fraxinus excelsior (8 per cent) and beech Fagus sylvatica (6 per cent). Among seedlings, the most prevalent species were ash (22 per cent), sycamore Acer pseudoplatanus (12 per cent), oak (12 per cent), holly Ilex aquifolium (12 per cent) and hawthorn Crateagus monogyna (10 per cent). Stands were excluded if thinning had recently taken place because of the disturbance to the understorey vegetation, and stands protected by deer fencing or tree guards were not assessed. To minimize confusion with the effects of other herbivores, any sites with a recent history of livestock grazing were avoided. In the Forest of Dean, only sites located within stock-fenced enclosures (that excluded sheep but not deer) were selected.
Deer density estimation
Deer population assessments adopted previously established methods, using thermal imaging at night for field observations and distance sampling to derive density estimates (Gill et al., 1997; Mayle et al., 1999). Distance sampling is suited to conditions encountered in this study, where detectability of deer varies both in and around woodlands (Buckland et al., 2001), and thermal imaging takes advantage of the fact that deer exploit concealment less at night. The density of deer was also estimated in fields adjacent to each woodland surveyed, up to a distance of ∼500 m from the woodland edge, using a separate detection function to that used for deer in woodland. Where insufficient observations were obtained (<45), data from two or more sites with a similar distribution of detection distances were pooled to derive a common detection function. In two other cases, estimates in fields were based on direct counts because too few transects were needed and too few observations were obtained to make distance sampling worthwhile. Existing paths or tracks were used as sampling transects, and perpendicular distances to each group of deer were estimated from body length and compass bearings or triangulation (Mayle et al., 1999; Hemami et al., 2007). For each group of deer observed, an attempt was made to identify species on the basis of body features, gait or alarm call. Unidentified groups contributed to the overall density estimate but were omitted when calculating population composition.
On account of the differences in habitat use between deer species and the fact that they were distributed unequally between sites, analysis was not confined to a straightforward measure of density. Two additional variables were used to investigate relationships between deer and impacts: the proportion of the deer population in a block using the forest and the proportion of those in the site which were larger species (fallow, red or sika deer). Further, deer density was calculated as the sum of the density of the smaller species (muntjac and roe deer) in each woodland block plus the density of the larger species over the whole site and adjacent fields.
Assessment of deer impacts and site variables
Within each block, between 1 and 19 stands (satisfying the constraints mentioned above), were randomly selected (Table 2). Seedling densities and browsing damage were assessed in plots spaced evenly throughout each stand. This was achieved by positioning the plots along straight parallel transect lines, with the spacing S, between transects and between plots calculated from 
, where A is the stand area in square metres and n is the number of plots. The position of the first transect was random. Normally, 10 plots were sampled per stand, although this was increased or reduced in a few of the largest and smallest stands, respectively. The number of blocks, stands and plots used in each site are listed in Table 2.
, where A is the stand area in square metres and n is the number of plots. The position of the first transect was random. Normally, 10 plots were sampled per stand, although this was increased or reduced in a few of the largest and smallest stands, respectively. The number of blocks, stands and plots used in each site are listed in Table 2.In each plot, the number of naturally regenerating tree seedlings and number damaged by deer were counted in each of two height classes. Trees 0–30 cm tall were recorded in a circular plot of 200 cm radius and trees 30–150 cm tall in a plot of 350 cm radius. Where natural regeneration in any of these height classes was prolific, only 15 trees nearest the plot centre were assessed and the radius from the plot centre to midway between the 15th and 16th tree was measured. This method of varying plot sizes was used in only 3.3 per cent (n = 47) of the plots for smaller seedlings and 1.9 per cent (n = 27) of the plots for larger seedlings.
Soil data were obtained from the Soil Survey 1:250K map of England and Wales. Values for available water capacity (depth of water accessible to trees per unit depth of soil millimetre/meter), soil moisture regime (scored 1–8 representing very wet—very dry) and soil nutrient regime (scored 1–6 representing very poor—carbonate) were obtained for the locations of each plot as recorded using a global positioning system receiver during field survey.
For each plot, the stocking density (stems per hectare) and basal area (ratio stem cross-sectional area × 104: plot area) of mature canopy trees were recorded, defined as 6/пr2 and 
respectively, where r is the distance (metre) from the plot centre to the mid point between the 6th and 7th closest trees and d is the d.b.h. (centimetre) of the six closest trees. Overhead canopy cover was estimated at each plot visually as a percentage of the sky obscured by the canopy.
respectively, where r is the distance (metre) from the plot centre to the mid point between the 6th and 7th closest trees and d is the d.b.h. (centimetre) of the six closest trees. Overhead canopy cover was estimated at each plot visually as a percentage of the sky obscured by the canopy.To check for evidence of the presence of herbivores other than deer, each plot was searched for signs of herbivores (livestock, deer, rabbits Oryctolagus cuniculus and hares Lepus europeaus), including dung or pellet groups, tracks or beds.
Data analysis
Data analysis was carried out at the level of the forest block since this was the smallest geographical unit at which deer density could be resolved. Further, significant differences in deer density between blocks were obtained at most sites (Table 3). For all other variables (seedling density, stand and soil variables), mean values were calculated from the plots within each block.
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Table 3:
Summary of deer density estimates obtained for each site
A correlation matrix was used first to explore associations between each of the explanatory variables. Relationships between log seedling abundance, deer density and site variables were then analysed using generalized linear models (McCullagh and Nelder, 1989), using a Poisson error distribution and log link. The log of the number of plots was treated as an offset, which standardizes for the differing number of plots per block. Overdispersion in the Poisson model was accounted for by scaling the SEs (see McCullagh and Nelder, 1989). An all subsets approach was used to search for significant combinations of variables. Only those combinations with all coefficients significant at the 5 per cent level are reported. Models reported are also compared using an adjusted R2 statistic. As only a relatively small number of variables were considered, the process is reasonably robust to problems of false discovery rates (see Benjamini and Hochberg, 1995).
For the proportion damaged, a binomial generalized linear model with a logit (McCullagh and Nelder, 1989) was used with the number damaged as the response variable and the number of seedlings as the binomial denominator. The same procedure for modelling was used as described above. All models were fitted using GenStat (Payne, 2007).
Results
Deer density estimates
The estimates of deer density revealed considerable variation between sites, species composition and relative use of fields (Table 3; Figure 1a,b). The estimates of density in woodlands obtained in each site ranged from 0 to 48.5 km−2 and up to 54.9 km−2 in individual blocks. The extent of adjacent fields and relative use of these by deer varied considerably between sites and between blocks within sites. There were no fields immediately adjacent to woodlands at one site (Dean) and at two others deer were not observed making use of them (High Meadow and Lower woods). However, at some other sites (e.g. Chiddingfold), the density was greater in fields than in woodland. Site average field densities ranged from 0 to 38.5 km−2 and up to 74.5 km−2 for individual blocks (Table 3).
Figure 1.
Bar charts indicating the deer species composition and density of deer in each site. For sites including more than one block of woodland, figures are based on block means. (a) Deer observed in woodland and (b) deer observed in adjacent fields.
At sites where more than one deer species was present, 78.3 per cent of the deer observed (n = 2159) were seen clearly enough to identify species. The species present mostly included roe, muntjac and fallow deer in various combinations, with the exception that muntjac only occurred at sites where roe deer were also present (Figure 1a). Small numbers of red or sika deer were also recorded at three sites. There was also a conspicuous difference between species in relative use of fields (χ2 = 135.2; P < 0.005; calculated on 918 identifiable groups seen in sites where fields were available). Fallow deer generally formed a greater proportion of deer observed in fields than in the adjacent forest and muntjac the least (Figure 1b).
There was a significant difference in density between privately owned woodlands and Forestry Commission (publicly owned; Table 4).
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Table 4:
Comparison between mean values obtained for deer and soil variables in FC and private estates
Examination of the plots for signs of the presence of herbivores revealed evidence of deer in 672 (48.2 per cent), rabbits in 17 (1.2 per cent), hares in 11 (0.8 per cent) and sheep in 2 (0.1 per cent). In a further 16 plots (1.1 per cent), signs were observed that could not be attributed to any species group. The absence of signs of lagomorphs was probably due to the fact that in woodland, rabbits focus most activity in woodland edges or rides not the stand interior (Trout, 2003), and relatively few of our sites were located in eastern England, where hares are most abundant. In view of the general lack of herbivores other than deer, they were not considered further in the subsequent analyses.
Relationships between deer density, site variables and seedling abundance
Before investigating relationships with seedlings, associations between the explanatory variables were investigated first using a correlation matrix. There was no significant correlation between the three deer variables (deer density, per cent deer in forest and per cent larger species), suggesting that they were effectively independent. Significant correlation coefficients were obtained among some of the soil variables (soil moisture vs soil nutrient regime, r = 0.546, P < 0.01 and available water capacity vs soil moisture, r = −0.747, P < 0.01) as well as between stocking density and basal area (r = 0.535, P < 0.01).
Significant correlations were obtained between deer density and the soil variables, revealing a tendency for higher deer density on drier and more fertile sites (deer density vs soil moisture r = 0.659, P < 0.01 and deer density vs soil nutrient regime r = 0.478, P < 0.01). There was also a significant difference in soil moisture and nutrient regime on sites of different ownerships: Forestry Commission woodlands had wetter less fertile soils than private woodlands (Table 4).
In spite of substantial differences between sites in the extent of woodlands and fields, there was no direct association between deer density and either woodland or field area; however, deer density had a quadratic relationship to the ratio of woodland to field area, with the lowest densities in sites dominated by either woodland or fields and the highest in sites comprising ∼55 per cent woodland (d = 86.3w–78.4 w2; F = 39.5; d.f. = 2,48; P < 0.001, where d = deer km−2 and w = block woodland area total area−1). The type of field also appears to be important: deer density was significantly higher in sites associated with arable farming and lowest in pastoral (mean woodland deer densities: arable 36.0; mixed 13.1; pastoral 11.2; F = 17.6; d.f. = 3,50; P < 0.001). This result may, however, reflect the previous association with soil characteristics since arable sites had more fertile soils (soil nutrient levels: arable 4.6; mixed 4.0; pastoral 3.3; F = 11.8; d.f. = 3,31; P < 0.001).
Seedling abundance
Seedling density was highly variable with a skewed distribution and a much lower density of the larger size class. The mean density of seedlings <30 cm was 9865 ha−1 and for seedlings 30–150 cm 1089 ha−1. Differences in seedling density between sites were only significant among the smaller size class <30 cm (adjusted R2 = 67.4 per cent; d.f. = 13). These differences, however, did not remain significant after fitting the three-variable models (see below, Table 5).
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Table 5:
Results of multiple regression analyses investigating relationships between deer, soil and stand variables
The abundance of seedlings <30 cm was significantly related to both deer and soil and stand variables (Table 5). On their own, available water capacity and deer density were most closely related to seedling numbers, yielding similar r2 values; however, all three deer variables were significant, as were soil moisture regime, stocking density and the per cent conifers in the stand. When added to the regression models in combination, soil moisture regime, available water capacity and deer density were not included together, as they were correlated. The best model explaining 63.3 per cent of the variance included soil moisture regime, canopy cover and per cent larger deer. For larger seedlings 30–150 cm, soil moisture regime and available water capacity were significant; however, the three deer variables were the most significant. In the best model, with an R2 of 58.9 per cent, the per cent larger deer, deer density, basal area and soil nutrient regime were significant.
For seedlings in both height classes, the relationship between seedling density and deer density was curvilinear, indicating that the decline in seedling numbers was steepest at the lowest deer densities (Figures 2 and 3). Unlike deer densities, seedling densities showed neither a linear nor a quadratic relationship to the ratio of woodland: field area in each site (for seedlings <30 cm tall: F = 0.42; d.f. = 2,106; P = 0.657; for seedlings 30–150 cm tall: F = 0.53; d.f. = 2106; P = 0.590).
Figure 2.
Scatter plot of seedling density (<30 cm) vs deer density. Values on the Y axis are the density of seedlings <30 cm tall ha−1. Values on the X axis deer km−2.
Figure 3.
Scatter plot of seedling density (30–150 cm) vs deer density. Values on the Y axis are the density of seedlings 30–150 cm tall ha−1. Values on the X axis deer km−2.
Relationship between deer density and damage to seedlings
The proportion of seedlings damaged was found to be positively related to the density of deer for both smaller and large seedlings (Table 5). In these models, the per cent deer in forest and deer density were the most significant variables, the former explaining 39.8 and 42.2 per cent of the variance in seedling density for small and larger seedlings, respectively. Other variables revealed weaker relationships with seedling density and were less stable when other variables were added in combinations in the model.
Discussion
The range of deer densities recorded in this investigation is broadly comparable with densities recorded in most other studies. For example, results from 18 studies of European roe deer yielded densities between 0.9 and 76.0 km−2 (Gill, 1994) and results from seven sites surveyed by thermal imaging in the UK gave deer densities of 6.8–41.2 km−2 (Gill et al., 1997). However, extremes were not well represented. There were relatively few sites with a low deer density (<10 km−2) and none close to the highest densities (>100 km−2) which have occasionally been reported (Ward et al., 1994; Cooke et al., 1996).
The results show that higher deer densities were associated with higher rates of browsing and reduced seedling densities across the range of sites that were sampled. These results are broadly typical of many other investigations of ungulates in woodlands, which reveal a marked reduction in seedling density with increased browsing pressure (reviewed in Gill, 1992a, b, 2006; Olesen and Madsen, 2008; Ward et al., 2008). Seedling densities can be affected by ungulates both by the direct effects of browsing as well as indirectly since they can become less competitive as a result of other changes in vegetation caused by browsing (Horsley and Marquis, 1984; Stromayer and Warren, 1997). Further, deer feed heavily on seeds and fruit when available (Jackson, 1977, 1980; Danilkin, 1992), so may reduce seedling numbers of some species before browsing occurs. However, seedling densities are clearly associated with other factors, the most important of which were available water capacity and soil moisture. Although seedlings may be adversely affected by both desiccation and waterlogging (Küßner, 2003; Jinks et al., 2006), a positive association is to be expected in southern England where soils are in moisture deficit for part of the year.
The density of deer showed clear relationships to landscape characteristics. The associations between deer density, farmland type and soil conditions (with higher deer density on arable sites, and sites with drier, more fertile soils) appears not to have been reported before in Britain. However, links between soil fertility and ungulate populations are known elsewhere, for example, in North America, white-tailed deer Odocoileus virginianus exhibit higher rates of growth and reproductive performance in areas with more fertile soils, which can result in higher population density (Miller et al., 2003). In African savannas, as much as a 20-fold difference in herbivore biomass has been associated with soil fertility (Bell, 1982; Fritz and Duncan, 1994). However, some of the associations between deer density and landscape may have arisen for management, as well as ecological reasons. In the interests of reducing damage to timber, deer numbers have traditionally been kept low in publicly owned woodland, and these include the largest forests, which occur for historical reasons on poorer and wetter soils.
The correlation between soil moisture and seedling density may have masked some of the influence of deer density. However, the effects of deer on seedlings are nonetheless clear from our results, for two reasons. Firstly, the proportion of seedlings browsed is correlated with density and the proportion of deer in the forest, and secondly, all three deer variables showed a stronger association than any of the site variables for the larger seedlings than smaller seedlings. This is to be expected since the larger seedlings will have had more time to be affected by deer browsing and are in the height zone where deer focus most feeding and are less likely to be concealed by other vegetation or litter (Miller et al., 1982; Palmer and Truscott, 2003). In general, seedling density showed a less consistent relationship to stand variables than the deer variables. Canopy cover was positively related to small seedling density, suggesting that abundance of small seedlings is affected more by seed supply than the suppressing effect of shade, although this may have not been the case if felling coupes had been included in our sample sites. Larger seedlings, in contrast, were not correlated with canopy cover but instead revealed a weak negative relationship with stand basal area.
The decline in seedling density with increasing deer density was steepest at relatively low deer densities than higher, as indicated by the linear relationship with log seedling abundance. This suggests that seedlings are particularly sensitive to deer browsing, being among the most preferred food sources. Similar results have been reported from some other studies of deer impacts. In Eastern Canada, the impact of white-tailed deer on the density of balsam fir Abies balsamea seedlings, as well as several key understorey species (Cornus canadensis, Rubus spp. and Epilobium angustifolium), showed a non-linear response to density, declining exponentially with increasing deer density (Tremblay et al., 2006, 2007). However, there were clear differences in the responses of each of these species, with some declining more acutely than others. Further, results from some other studies indicate that deer sometimes have little effect until some threshold deer density is reached (Tilghman, 1989; Healy, 1997). Nonetheless, deer typically show marked selection for particular species of trees and shrubs, so a sharp decline in these species in response to increasing deer density may be commonplace, but differences among tree species as well as in the remaining forage species are likely to modulate the response.
The results obtained from this study suggest that a density of ∼14 deer km−2, on average, would enable almost 1200 larger seedlings ha−1 (30–150 cm tall) to survive. This is barely half the seedling density normally used in replanting woodlands but may be sufficient to maintain woodland cover. Since our study focussed on advance regeneration in mature stands, measures to actively promote regeneration, such as heavy thinning and scarification, may be successful in achieving the desired levels of regeneration at these densities (Evans, 1988; Olesen and Madsen, 2008). Our results also suggest that in Britain, higher densities can be accommodated in lowland woodlands in comparison to highland environments. Again, this result is not unexpected, given that most of the deer present are smaller than red deer (widespread in the uplands) and lowland environments are more productive.
We recorded marked differences between deer species in habitat use. Of the three most common species, fallow deer were observed making most use of fields and muntjac the least, differences that are consistent with the nutritional ecology of each species. With a larger body size, fallow deer are able to feed on less digestible forage and will graze more than the two smaller species (Jackson, 1977, 1980; Forde, 1989), which are more dependent on browse (Hofmann, 1986). Differences in deer species composition and use of fields also made a significant contribution to the models of damage and seedling density. However, although impacts were relatively lower where deer made more use of fields, they were higher where larger species were present, in spite of the fact that fallow deer made relatively more use of fields. This outcome probably arose because in several of our sites, deer density was higher in forests than adjacent fields, even where fallow deer were the main species present.
The relatively limited number of sites available in this study made it difficult to investigate the effects of deer while controlling for the influence of other variables. Within the sample of sites used in this study, the majority had an intermediate deer density (10–20 km−2 in woodlands). This meant that there were not many sites at high and low densities, which would have helped to bring the differences between deer species, and the effect of relative use of fields, into sharper focus. Secondly, the results also reveal considerable variation in seedling density between sites, some of which can be accounted for by stand and site characteristics, such as soil quality and stand characteristics—a few of the sites sampled had low deer densities and low numbers of seedlings or vice versa. This suggests that besides monitoring deer densities, it may be useful for to monitor regeneration as well and attempt to manage deer numbers according to need. It is likely that further research on deer impacts in relation to movements in mixed farm and woodland landscapes will provide more insights useful to the management of deer and their impacts.
Funding
British Forestry Commission.
Conflict of Interest Statement
None declared.
Acknowledgments
I would like to thank the members of West Oxfordshire and Cotswolds deer management groups and Gloucestershire Wildlife Trust for assistance with thermal imaging and access to woodlands to assess impacts and Alan Ockenden, Alistair Wybrow, Dave Rogers, Barbara Franzetti and Ruaraidh Milne for assistance with field work. I would also like to thank Susan Stout, Rob Fuller, Ralph Harmer, Amy Eycott and an anonymous referee for providing helpful comments on the manuscript.
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