*Present address and correspondence: S.C.F. Palmer, CEH-Banchory, Hill of Brathens, Banchory AB31 4BY, UK (fax 44 1330 823303; e-mail firstname.lastname@example.org).
1. Recent work has shown that the dynamics of woody and herbaceous vegetation mosaics under grazing or browsing can be strongly affected by the spatial pattern of the vegetation. A suite of models is described here to predict spatial variation in the utilization of an internationally important woody species, heather Calluna vulgaris, within heather/grass mosaics when grazed by sheep or red deer Cervus elaphus. This type of information is needed for the successful management of free-ranging herbivores grazing these extensive vegetation types.
2. The models predict: (i) heather utilization at the edge of grass patches; (ii) utilization distant from the grass edge; and (iii) the rate of change of utilization with distance from the edge of grass patches as functions of (a) the proportion by area of grass in the mosaic, (b) the length of heather/grass edge per unit area, and (c) the overall heather utilization on a site. Differences between species of grazers and seasons are also taken into account.
3. The models were fitted to data from two series of grazing experiments conducted on natural and artificial heather/grass mosaics in north-east Scotland.
4. Overall heather utilization in the experiments was estimated using a geographical information system (GIS), taking into account higher levels of utilization in proximity to grass patches.
5. A modelling approach for predicting how the heather/grass mosaic pattern will change through time under heavy grazing is proposed. As no field data are yet available on this process, this model was developed by simulation within a GIS.
6. This work demonstrates how incorporation of spatial information can improve the accuracy of utilization predictions, and thus the design of appropriate management practices. As with many other similar systems, the paucity of data on spatial variation in heather utilization by grazing ungulates, and the effects of utilization at the heather/grass edge, particularly under high grazing pressures, is highlighted. This is considered to be a major limitation to the efficacy of currently available decision support tools to aid the management of heterogeneous grazing systems.
The use of blanket non-site-specific stocking recommendations has already been shown to be inadequate in some areas, and it is clear that modifications to this type of management approach are required (Gordon & Illius 1992; Kellner & Bosch 1992; Henderson et al. 1994; Nolan et al. 1994; Pickup, Bastin & Chewings 1998; Weber et al. 1998). Armstrong et al. (1997a,b) developed a simulation model of a hill grazing system in the UK that addressed the need for site-specific predictions without requiring detailed (and often expensive and/or long-term) field measurements. This was an important and valuable step in the management of these upland vegetation types, and the model has been widely and usefully applied, both as a management and an educational tool (Milne & Sibbald 1998). Although the model considers the effects of available area and biomass of a range of vegetation types directly, it does not take into account the effects of different distributions of these vegetation types, because at the time it was developed there were insufficient data available to do this (Armstrong et al. 1997b).
This paper uses these data to develop models of changes in heather utilization with distance from grass, given data on the overall utilization of heather in an area and the spatial pattern of the heather/grass mosaic. This type of information is necessary for the successful design of management protocols for free-ranging herbivores grazing these extensive vegetation types. If heather utilization near grass is high, even in lightly grazed systems, this may have an impact on heather cover and production (Palmer 1997), with important implications for vegetation dynamics. The models presented here predict: (i) heather utilization at the edge of grass patches; (ii) utilization distant from the grass edge; and (iii) the rate of change of utilization with distance from the edge of grass patches as functions of (a) the proportion by area of grass in the mosaic, (b) the length of heather/grass edge per unit area, and (c) the overall heather utilization on a site. They were fitted to data from two series of grazing experiments conducted on natural and artificial heather/grass mosaics in north-east Scotland. These new models will contribute a further step towards predicting the longer-term impacts of herbivores on species composition, which is a crucial requirement for the use of decision support tools as management guides (Armstrong et al. 1997b). They will be used in the next stage of development of a hill grazing decision support tool, hillplan (Milne & Sibbald 1998).
Data from two experimental sites were used to construct the models presented. Both experiments were carried out at the Macaulay Land Use Research Institute's Glensaugh Research Station, Aberdeenshire, UK (56°54′N, 2°33′W; National Grid Reference NO677782). They were set up in 1991 to examine different aspects of the foraging behaviour and impacts on the vegetation of sheep and red deer within heather/grass mosaics. The moorland areas used were dominated by heather, and the grass patches were dominated by Agrostis spp., Festuca spp., and Deschampsia flexuosa L. One experiment, Finella Hill, was set up within an area fragmented by many years of grazing into a mosaic of heather and grass patches (Hester & Baillie 1998; Hester et al. 1999). The other experiment, Birnie Hill, used artificially created square grass patches of uniform sizes and distribution within a heather-dominated area (Clarke, Welch & Gordon 1995a,b; D. Welch, unpublished data).
Finella hill site
The experimental set-up is described fully in Hester & Baillie (1998). In brief, this site comprised six plots of 1 ha each, with two plots grazed by sheep only (plots 3 and 4), two by red deer only (plots 1 and 5) and two by both sheep and red deer (plots 2 and 6). All plots contained a complex mosaic of natural grass patches of different sizes, shapes and distribution, but with all plots containing approximately 20% by area of grass. Animal numbers were selected to give comparable total offtake per plot (Hester et al. 1999), and grazing regimes were applied for 8 weeks each year from 1991 to 1995. In 1991, plots were grazed in the autumn (mid-August to mid-October), in 1992 in the summer (June and July), and in 1993–95 grazing was split into two 4-week periods in the summer (June and August/September).
Heather utilization (sensuGrant 1971) was measured at the end of each year's grazing period using the method described by Grant, Hamilton & Souter (1981), which estimates the proportion of current year's growth removed from each shoot. Within each plot, heather measurements were made around 12 randomly selected grass patches: four each of small (< 6 m2), medium (6–30 m2) and large (30–400 m2) size. Measurements of heather utilization around each selected grass patch were made on four transects normal to the patch edge: one up-slope, one down-slope and one in each direction across-slope. Measurements were made at distances from the patch edge of 0, 25, 50, 75, 100, 150, 200, 250, 300, 350, 400, 450 and 500 cm, and thereafter at every 100 cm, until any measurement point came nearer to the edge of any other grass patch or path. For the purposes of the models presented here, the mean utilization across the four transects was used for each distance at each patch. In addition, ‘background’ utilization estimates were made at four randomly selected locations in heather distant from any grass patch edge (i.e. as far as possible from grass patches or animal paths).
The plots were mapped manually at the start of the experiment, and all grass patches were subsequently digitized into a geographical information system (GIS; ARC/INFO version 7, Environmental Systems Research Institute Inc., Redlands, CA 92372, USA).
Birnie hill site
At this site, a small number of large artificial patches of grass, rather than many small natural patches, were available to the herbivores. The experimental details are described in full by Clarke, Welch & Gordon (1995a,b). In brief, there were six plots of 2·5 ha, each of which contained 0·5 ha of grass within either one, four or 12 artificially created square patches. Plots 1 and 6 contained one patch of 5780 m2, plots 2 and 5 contained four patches of 1440 m2 and plots 3 and 4 contained 12 patches of 484 m2. The grazing periods were of 10 days duration. After each grazing period, numbers of grazed shoots were recorded at 0, 25, 50, 100, 150, 200, 300, 400 and 500 cm from grass patch edges. Two different experiments were carried out in 1992 (total of 60 days grazing) but we have only used the final (cumulative) measurement of heather utilization (in early September) (Clarke, Welch & Gordon 1995b). Because their first experiment (May–July) comprised alternate grazing by sheep and deer, and their second experiment (July–September) comprised grazing by sheep only (which were the utilization data we used), we categorized the data as primarily due to sheep grazing.
Additional data for plots 1 and 6 from a third experiment conducted in summer 1993 were also used (D. Welch, unpublished data). The experimental protocol was similar to that of the 1992 experiments, but with alternate grazing periods of sheep alone and sheep and deer together. In view of the regular interchange of the two herbivore species, we treated these data as mixed grazing.
In these experiments, grazing of heather was measured within zones, i.e. less than or greater than 5 m from grass patch edges. We have used only the data from within 5 m of grass patch edges. Clarke, Welch & Gordon (1995b) and D. Welch (unpublished data) simply recorded heather shoots as ‘grazed’ or ‘ungrazed’ and did not estimate proportions of growth removed. Therefore, for the purposes of our models, their data have been converted to percentage utilization (sensuGrant 1971) using the equations presented in Appendix 1 (equation A1 for the 1992 experiment and A2 for 1993).
Estimation of average heather utilization
Existing decision support tools on grazing impact (Armstrong et al. 1997a,b) and those in development (Milne & Sibbald 1998) use data on plant biomass and animal numbers to predict grazing offtake of heather, from which the overall average utilization is calculated. In order to be able to relate spatial variation in heather utilization to the overall average, our first step was to estimate, for each experimental site, the overall utilization in each plot for each of the experimental grazing periods. To do so, we first needed to estimate utilization near to and distant from grass patches, as described below.
Finella hill site
Preliminary analyses indicated that the heather percentage utilization data were positively skewed, and that there were significant differences between grazing treatments and plots (Hester & Baillie 1998). The data were therefore transformed by taking logarithms, and, as the aim of this work was to obtain the best estimate of the overall utilization within each plot in each year, and as each plot had a unique mosaic structure, the plots were modelled separately.
Heather utilization was in all cases highest at patch edges, and declined rapidly with distance from the edge (Hester & Baillie 1998). As transects were terminated when the point of measurement was nearer another grass patch, there were fewer estimates for large distances (typically beyond 300 cm on most plots), and these distances had higher standard errors. We therefore firstly identified for each plot the greatest distance at which mean transect utilization was significantly different from distant utilization (defined as the transect limit distance), taking into account yearly differences, but not patch size or slope. These transect limit distances were 100 cm on plots 1, 2, 4 and 6, 150 cm on plot 3 and 200 cm on plot 5. All utilization measurements for distances greater than these were grouped together for each patch (defined as the transect limit utilization), and the new grouped estimate was applied as at the first measurement distance beyond the transect limit distance for the plot (e.g. 250 cm for plot 5). Henceforth, utilization within transect limit distances is defined as utilization ‘near’ grass patches, and utilization beyond transect limit distances is defined as ‘distant’ from grass patches.
Utilization near grass patches was modelled by fitting a general linear model (GLM) to log-transformed percentage utilization for each plot as a function of year (entered as a factor) and the interaction between year and the distance from the grass patch edge (entered as a covariate):
logU = YEy + ky.d + ε(eqn 1)
where U is the percentage utilization of heather; YEy is the effect of year (y = 1–5 for 1991 to 1995); ky is the rate of change of logU with distance from the edge in year y (cm−1); d is the distance from the edge of the grass patch (cm); and ε is a normally distributed error term. Parameter values obtained by fitting the equation are given in Table 1.
Table 1. Fitted parameters (with standard errors in parentheses) for equation 1, which describes percentage utilization of heather (log-transformed) around the edge of grass patches on the Finella Hill plots as a function of year and the interaction of year with distance from the edge (data: Hester & Baillie 1998)
Plot Grazing species
2 Deer + sheep
6 Deer + sheep
Utilization distant from grass patches was estimated for each year in each plot as the combined mean of the four background utilization sample locations (as far from grass as possible) and the transect limit utilization for each patch (i.e. up to 12 values, depending on the transect lengths around each patch):
logU = YDy + ε(eqn 2)
where U is the percentage utilization of heather; YDy is the effect of year (y = 1–5 for 1991 to 1995); and ε is a normally distributed error term. Parameter values obtained by fitting the equation are given in Table 2.
Table 2. Fitted parameters (with standard errors in parentheses) for equation 2, which describes percentage utilization of heather (log-transformed) distant from grass patches on the Finella Hill plots, as a function of year (data: Hester & Baillie 1998)
Plot Grazing species
2 Deer + sheep
6 Deer + sheep
The overall utilization for each year within each plot was estimated by creating a series of zones around the grass patches, using GIS buffering routines, and applying the utilization estimates to these zones.
The zones were each 25 cm wide, and extended to one zone beyond the transect limit distance. Thus there were five zones created for plots 1, 2, 4 and 6, seven for plot 3 and nine for plot 5. The utilization within an edge zone was estimated using equation 1, and for all distant zones using equation 2. The overall utilization for each year in each plot was calculated as the mean of all zones (back-transformed) weighted by area (Table 3):
Table 3. The values of UPLOT in equation 3, which estimates overall percentage utilization of heather on the Finella Hill plots, derived from area-weighted zonal means
Plot Grazing species
2 Deer + sheep
6 Deer + sheep
where UPLOT,y is the overall percentage utilization of heather for the plot in year y; ai is the area of the ith edge zone; aj is the area of the jth distant heather zone; Uiy is the utilization in the ith edge zone in year y derived from equation 1; and UDy is the utilization in all distant zones in year y derived from equation 2.
Birnie hill site
The calculation of utilization at the edge, utilization distant from the edge and the rate of change with distance was simpler than that for the Finella Hill plots, as all grass patches within each plot were exactly the same size and distance apart. As the grazing treatments differed between years, the two years were treated separately. Plots with different arrangements of patches were modelled separately (Table 4). The overall utilization within each plot was estimated as above using 25 cm zones.
Table 4. Estimated overall utilization of heather (UPLOT) on the Birnie Hill plots, and the parameters from which this was derived
Plot No. of patches
where UE is the percentage utilization of heather at the grass edge; k is the rate of change of logU with distance d from the edge, such that logU = logUE + kd + ε; UD is the percentage utilization of heather distant from the grass edge, such that logU = logUD + ε; UPLOT is the overall percentage utilization of heather within the plot.
The effect of grass edge on utilization declined rapidly with distance from the edge in the four- and 12-patch plots: only the utilization at 25 cm or less and at the patch edge, respectively, was significantly less than the utilization distant from the edge. The four- and 12-patch plots were included in models of utilization at the grass edge and distant from the edge. However, they were omitted from the model of the rate of change of utilization with distance (equation 9 below), because the edge effects were detectable over only a short distance, resulting in misleadingly high values of k (Tables 1 and 4).
The effects of spatial heterogeneity on utilization
Having estimated the overall heather utilization within each plot for each year, the next step was to identify how the spatial variation in utilization was related to the overall utilization, given the known pattern of the vegetation. Thus, within a decision support tool, if the spatial vegetation pattern can be described, the effects of grazing on heather cover and production, and hence on vegetation dynamics, can be predicted. The effects of spatial heterogeneity on heather utilization were modelled for the Finella Hill data alone (the natural mosaics only) and for the combined set of Finella Hill and Birnie Hill data (the natural and artificial mosaics together).
The spatial characteristics of each plot were summarized as the proportion by area of grass (pg) and the length of heather/grass edge per unit area (E) (Table 5). The Birnie Hill plots covered a similar range of proportion of grass to the Finella Hill plots, but the individual grass patches were larger. Therefore the inclusion of Birnie Hill data in the model greatly increased the range of edge per unit area (Fig. 1).
Table 5. Spatial characteristics of plots: proportion of grass by area and length of heather/grass edge per unit area
Finella Hill 1991–95
Proportion of grass
Edge per unit area (m−1)
Birnie Hill 1992–93
No. of patches
Proportion of grass
Edge per unit area (m−1)
For each year within each plot, the spatial effects on utilization are represented by UE (the utilization at the patch edge), ΔlogU[the rate of change of log utilization with distance from the edge (cm−1), i.e. ky] and UD (the utilization of distant, i.e. non-edge, heather). In order to be able to predict the spatial distribution of heather utilization, we need to know how these three variables vary with UPLOT, pg and E, and also whether the relationships vary with season or species of grazer. However, there are also certain boundary conditions that must be satisfied, which make regression models unsuitable.
Utilization at the patch edge
The boundary conditions that must be satisfied for a predictive model to make reasonable extrapolations in extreme cases are:
UE→ UPLOT as UPLOT→ 0% and as UPLOT→ 100%(eqn 4a)
UE→ UPLOT as pg→ 0 and as pg→ 1(eqn 4b)
otherwise UE > UPLOT(eqn 4c)
The condition of equation 4a as UPLOT→ 100% may not actually hold true, as edge utilization could well be greater than 100%, i.e. removal of some of the previous year's growth on all shoots present, but as we have no data for such high levels of utilization, and this would be unlikely to happen even in winter under the normal ranges of sheep densities in moorland areas (Armstrong et al. 1997b; Palmer 1997; S.C.F. Palmer and A.J. Hester, unpublished data), we assumed a symmetrical relationship.
where f1and f2 are functions that satisfy the boundary conditions of equations 4a and 4b, respectively; α, βE, βD, βS and βA are fitted parameters; and Deer, Sheep and Aut are dummy variables to represent grazing by deer, sheep and during autumn, respectively.
For simplicity, we applied the further constraint that f1= f2= f, and tried three possible functions:
sine f(y) = sine(π *y)
quadratic f(y) = (y - y2)
semi-circle f(y) = (0·52 - (y - 0·5)2)0·5
where y = UPLOT/100 or y = pg.
The models were fitted numerically (Microsoft Excel 97 Solver) to the 5 years of plot data (n = 30 for Finella Hill only; n = 38 for Finella and Birnie Hill combined). As the quadratic and sine functions gave very similar results, we show only those for the sine and semi-circle functions. The goodness-of-fit to the data was assessed by comparing the root mean square error (RMSE, %) of each fitted model (Table 6).
Table 6. Goodness-of-fit to the data (RMSE, %) of difference (equation 5a) and ratio (equation 5b) models of utilization at the patch edge
Finella + Birnie Hill
Finella + Birnie Hill
Clearly the difference model of equation 5a fitted the data considerably better than the ratio model of equation 5b. The two f functions gave similar results for Finella alone, but the semi-circle function performed better than the sine function for the two sites combined. Moreover, the semi-circle difference model gave by far the most realistic values of UE at high overall utilization (UPLOT) for a realistic range of pgand E (Fig. 2). The parameter solutions for the best-fitting semi-circle difference models are given in Table 7.
Table 7. Parameter solutions for the best-fitting semi-circle difference models (equation 5a) of utilization at the patch edge
Finella + Birnie Hill
Utilization distant from the patch edge
The boundary conditions are similar to those for utilization at the edge, namely:
UD→ UPLOT as UPLOT→ 0% and as UPLOT→ 100%(eqn 6a)
UD→ UPLOT as pg→ 0 and as pg→ 1(eqn 6b)
otherwise UD < UPLOT(eqn 6c)
As the difference model with semi-circle function was clearly the best option for the edge utilization, we fitted a similar model for the distant utilization:
where f is defined as above for the semi-circle (Fig. 3). The parameter solutions for the fitted models are given in Table 8.
Table 8. Parameter solutions and goodness-of-fit to the data (RMSE, %) for the best-fitting semi-circle difference models (equation 7) of utilization distant from the patch edge
Finella + Birnie Hill
Rate of decrease of utilization with distance from the edge
It is not intuitively obvious what the boundary conditions for the rate of decrease of utilization with distance from the edge should be as the proportion of grass approaches 0 or 1 or the overall plot utilization approaches 0% or 100%. In order to examine whether there were any apparent relationships in the data, we fitted stepwise multiple regression models. Quadratic terms in pg and E were included, to allow for strongly non-linear relationships. Data for the Birnie Hill plots 2–5 were omitted from these analyses, as they had much greater rates of decrease of utilization than on other plots (Table 4) due to the short transect limit distances used.
For the Finella Hill plots alone, the best fitting model with all terms significant at P < 0·05 incorporated the spatial parameters and the overall plot utilization only:
adj. r2 = 0·53, n = 30, P < 0·001.
In contrast, when the two Birnie Hill single grass patch plots (1 and 6) were also included, main and interaction terms relating to the grazers were also significant:
adj. r2 = 0·58, n = 34, P < 0·001.
Clearly, the effects of the spatial characteristics, pg and E, on the rate of change of utilization with distance from grass were non-linear over the range of available data.
Prediction of changes in edge per unit area
In order to predict grazing impacts on heather fragmentation and the feedback effects of fragmentation on subsequent herbivore grazing impacts, it is necessary to estimate likely changes in heather/grass boundaries as a result of grazing, so that these, too, can be used in the creation of a dynamic decision support tool (Armstrong et al. 1997b; Milne & Sibbald 1998). The spread of grass within a heather/grass mosaic under high grazing pressure (and its converse under low or no grazing pressure) will cause a change in the length of heather/grass edge per unit area. The direction and magnitude of the change will depend on the initial conditions (the proportion of grass and the length of edge) and on the magnitude of the change in area (or its surrogate, the new proportion of grass). In this section we examine how best to create an appropriate algorithm based on the available data.
We used a series of GIS coverages each representing a 1-ha square block of heather/grass mosaics. These comprised: (i) the Finella Hill plots described above; (ii) ‘complements’ of the Finella Hill plots, i.e. with heather and grass patches interchanged; (iii) a set derived by ‘clipping’ 1-ha squares from a digitized aerial photograph of part of a heather-dominated area of Invercauld Estate, Aberdeenshire (S.C.F. Palmer, unpublished data), which was grazed by low densities of free-ranging sheep, mountain hares Lepus timidus L. and red grouse Lagopus lagopus scoticus Lath. This photograph was digitized at lower resolution than the Finella Hill plots, and therefore had ‘less’ edge per unit area. In order to cover the full range of possible values of edge per unit area against proportion of grass, additional squares were created within the GIS by either removing small patches from copies of the Finella squares or adding patches to copies of the Invercauld squares.
A total of 62 different heather/grass mosaics in the GIS was created in this way.
The proportion of grass in each mosaic was then increased by expanding every grass patch outwards by 25 cm using GIS buffer routines. This operation was repeated eight times, i.e. until the grass patches had expanded outwards by 2 m, and at each distance the proportion of grass and length of edge was recorded for each 1-ha square.
Each successive patch expansion by 25 cm gave values of the proportion of grass and length of edge per unit area both before and after the operation. If the proportion of grass was less than 0·01 or greater than 0·99 then the observation was discarded, leaving a total of 469 observations. The new length of edge was fitted by the method of residual maximum likelihood as a linear multiple regression model with site (i.e. Glensaugh or Invercauld) and plot (nested within site) entered as random effects:
where En is the new edge per unit area (m−1); Eo is the old edge per unit area (m−1); pgo′ is the old proportion of grass by area (arcsine transformed); and pgn′ is the new proportion of grass by area (arcsine transformed).
The coefficient for the old edge per unit area was significantly less than unity, indicating that the relationship between En and Eo was not linear.
The converse operation (the expansion of heather at the expense of grass) was not modelled directly, but could be modelled approximately by replacing the proportion of grass in equation 10 by its complement, the proportion of heather. The constraint outlined above would not apply in this case, as heather is considered unlikely to invade grass readily except by spread at existing edges (Marrs, Bravington & Rawes 1988; Hill, Evans & Bell 1992).
Spatial heterogeneity in vegetation and herbivore use has been shown to affect the impacts of given densities of herbivores in different areas, for a range of different vegetation types, as well as the specific communities described in this paper (Clarke, Welch & Gordon 1995b; Coughenour 1991; Hester & Baillie 1998; Pickup, Bastin & Chewings 1998; Weber et al. 1998). The potential for increased accuracy in predicting herbivore impacts through the incorporation of spatial data has already been well demonstrated for a range of other rangeland systems (Senft, Rittenhouse & Woodmansee 1983; Pickup & Chewings 1988; Pickup, Bastin & Chewings 1998; Weber et al. 1998). The models described in this paper predict changes in heather utilization in relation to grass proximity, as functions of the proportion by area of grass, the length of heather/grass edge per unit area and the overall heather utilization of an area. Here we consider in turn the various steps made in this process, and discuss the value of our models, together with any data limitations, in the context of requirements for the development of appropriate management prescriptions in areas of fragmenting heather moorland. The wider applicability of these techniques and the practicalities of appropriate data collection are discussed in relation to the potential benefits from the refinement of management prescriptions within areas of heterogeneous vegetation.
Estimation of whole-plot heather utilization
The first step in our model development was to calculate whole-plot heather utilization from the site data available, to enable the subsequent model fitting. For this step, the most likely source of error in relation to the Finella Hill plot estimates was the identification of the transect limit distance, which differed slightly between plots and was affected by the declining sample sizes at increasing distances from the grass/heather boundary. However, in view of the fact that critical levels of heather utilization will normally be very close to the heather/grass boundaries (Grant et al. 1982; Hester & Baillie 1998), we do not consider this to be a problem as it should not greatly influence the whole-plot estimates. For all Finella Hill plots, equation 2 for the utilization distant from grass patches was a poorer fit than equation 1 for the utilization within the transect limit distance. This was as expected, not only because there were fewer samples further from grass, but also because grazing of heather away from grass edges was unevenly distributed: many measurements were zero, but others relatively high. It appears that the animals tended to graze a small patch of heather fairly heavily before moving somewhere else, rather than graze lightly and uniformly across the whole area of heather. This could result in isolated patches of heavily used heather far from grass, but even with more data it would be very hard to model this phenomenon.
For the Birnie Hill plots, derived values of the overall utilization UPLOT differed little from utilization distant from the edge, UD (Table 4). These two values would be expected to be closer to each other than on the Finella plots, because of the much lower edge per unit area. However, as there were only on average 91 sample points with observations of heather utilization per plot within 5 m of the grass edge on each plot in 1992, compared with an average of 366 per plot for the Finella experiments, and as the grazing periods were only 10 days each, the true extent of the edge effect may have been underestimated in the individual treatment analyses. At the end of the first experiment, a combined analysis of all plots, rather than pairs of plots (as here), suggested that the transect limit distance might be as high as 100 or 150 cm (see figure 4 in Clarke, Welch & Gordon 1995b), which is comparable to that of the Finella plots. It is likely that, even in individual plots, the edge effects would have been significant over greater distances had the grazing periods been longer and/or a larger number of measurements made per plot at each distance from the edge.
The effects of spatial heterogeneity on utilization
The proportion of grass present and the edge per unit area are considered to summarize the spatial characteristics of the plots reasonably well for the purposes of this model. Both these parameters have been shown to influence herbivore foraging and heather utilization (Clarke, Welch & Gordon 1995a, b; Hester & Baillie 1998; Hester et al. 1999) and should be relatively easy to measure or estimate at different sites, if necessary from aerial photographs or satellite imagery (cf. data inputs for the semi-arid range use models of Pickup, Bastin & Chewings 1998). Further simple parameters that might increase the accuracy of predictions include the number of paths to or from a grass patch (Hester & Baillie 1998) and the proximity of other patches. However, it is not yet known to what extent these parameters influence heather utilization around a patch. In view of this, and for the purposes of simplicity, we used the two parameters likely to have the most influential effects on spatial variation in heather utilization. For management purposes, clearly the spatial data required to run a model should be as simple to collect as possible, or the model becomes impractical for many land managers to use (Armstrong et al. 1997a,b; Milne & Sibbald 1998).
As the ranges of available data on the proportion of grass, the edge per unit area and the overall plot heather utilization were restricted, a statistical approach (e.g. by multiple regression) to developing predictive models of spatial variation in heather utilization was not possible if extrapolations were to fall within reasonable bounds. Instead, a number of possible functions were examined that met the boundary conditions defined for the system, and which could be fitted to the experimental data available for intermediate conditions. Of these, the semi-circle function gave the most reasonable extrapolations. However, it is possible that an asymmetrical function would actually be more appropriate to use at a future date, if data were to become available to parameterize it at high ratios of grass : heather and at high overall utilization levels.
Whichever function was applied to either the difference (equation 5a) or ratio model (equation 5b) of the utilization at the patch edge, the model fit was substantially better (lower RMSE) for the Finella Hill plots alone than for the Finella Hill and Birnie Hill plots combined. However, for the difference model of the utilization distant from the patch edge (equation 7), the fit was slightly better for the combined data. As the same explanatory variables were included in each model, this suggests that there was some unknown difference between the two sets of data in the estimates of the utilization at the patch edge. It is possible that the different methods of sampling and utilization estimation contributed to this result (Clarke, Welch & Gordon 1995b; Hester & Baillie 1998). In addition, as the grass patches had been artificially created on the Birnie Hill plots, there was no ‘historical’ impact of grazing, unlike on the Finella plots (and the open hill), where the height of the heather decreased towards grass patch edges (Hester & Baillie 1998).
The predicted utilization at the patch edge and distant from the edge (Figs 2 and 3, respectively) both give realistic predictions for overall utilization up to about 70% for a range of values of the proportion of grass and edge per unit area. However, the model for utilization distant from the edge is clearly deficient at very low values of the overall utilization, as it predicts utilization to be less than zero. It is theoretically possible, although unlikely (Armstrong et al. 1997b; S.C.F. Palmer and A.J. Hester, unpublished data), for utilization at the patch edge to be greater than 100%, if all the heather shoots present were grazed into the previous year's growth. However, the models are not expected to be reliable at very high values of overall utilization owing to the lack of available data for heavily grazed situations.
Spatial differences in heather utilization are predicted to be slightly greater under sheep grazing than under deer grazing, and considerably greater in autumn than in summer, as we would expect. Interpretation of the effect of edge per unit area, however, is not straightforward. The correlation between edge per unit area and proportion of grass for the six Finella plots suggests that these two spatial parameters are likely to be correlated for natural mosaics where the proportion of grass is less than half. As the proportion of grass increases to above 50%, the edge per unit area will decline, and over the full range of proportion of grass, no correlation would be expected. The contribution of edge per unit area to the models is therefore rather speculative, and it may be that a non-linear function would be more appropriate. More data are required from areas with greater proportions of grass to refine these parameters. Data on the proportions by area of all main vegetation types are already required for the non-spatial prediction of utilization (Armstrong et al. 1997a,b). It is clearly important that the additional requirement for an estimate of edge per unit area is relatively easy to satisfy. This could be achieved by establishing good relationships between proportion of grass and edge per unit area for a wide range of typical situations, so that if required the option of using default values in a decision support system could be explored, based on fragmentation indices rather than quantitative data.
The rate of decrease in utilization with distance from the edge depends critically on the width of the edge zone in which utilization is higher than the background level. As utilization tends to be variable away from the edge, large sample sizes would be required to identify this edge zone distance with accuracy, and especially to identify significant differences between herbivores, seasons and grass patch sizes. The data from the experiments presented here indicate that the edge zone was generally 100–150 cm wide, but these data are really only sufficient to model the rate of decrease approximately. However, we consider this to be adequate for most management purposes, because even at high herbivore densities most, if not all, critical damage to heather (i.e. causing the death of the plant and its replacement by grasses) is likely to fall within the first metre or two of the boundary with grass. Thus precise prediction of the width of the edge zone and rate of decline in utilization should not be critical in the prediction of patterns and rates of heather fragmentation and loss (Grant et al. 1982; Palmer 1997; Hester & Baillie 1998; S.C.F. Palmer and A.J. Hester, unpublished data).
Prediction of changes in edge per unit area
In view of the lack of data on grass patch expansion under heavy grazing, the model predicting changes in edge per unit area is unavoidably the most speculative. However, from current understanding of the processes involved, we consider the assumptions made to be robust. Testing of this model requires long-term data on changes in vegetation at the heather/grass interface under known levels of grazing pressure. The model constrains the expansion of grass to occur only at existing edges. In reality, this is where the greatest effects will usually be apparent. However, less commonly, new grass patches may be created within heather-dominated areas under conditions of heavy grazing, trampling or burrowing (Hester & Baillie 1998; A.J. Hester and G.R. Iason, unpublished data). Incorporation of ‘new patch creation’ would require a much more sophisticated model (e.g. using cellular automata) in which new grass patches could arise at random under given conditions.
Comparison with non-spatial model predictions
To assess the potential value of the models presented here to improve upon non-spatial predictions of heather utilization under different herbivore densities, let us consider a simple scenario. Consider a hypothetical 1000-ha area dominated by building heather (Watt 1955) in eastern Scotland at 300 m altitude, containing 20% Festuca–Agrostis-dominated grass by area (i.e. 200 ha in total). For a density of 3 sheep ha−1 (of average weight 50 kg and present throughout the year), the non-spatial prediction of Armstrong et al.'s (1997a,b) model gives an overall heather utilization of 30%, which would be considered not seriously damaging (Grant et al. 1978, 1982). If we incorporate simple spatial data as in the models presented here, the predictions of utilization will differ at the edge compared with the distant heather. For example, if the grass is distributed as 10 patches of approximately equal size (20 ha), the length of edge will be approximately 18 000 m, giving an edge per unit area of 0·0018 m−1. This results in a prediction of 46% heather utilization at the edge of grass patches (i.e. a 50% increase) and only 22% distant from grass. The higher predicted utilization at the edge would certainly result in reduced heather shoot production (Palmer 1997), and in management terms this would not be considered a sustainable level of heather utilization. From this simple comparison, it is clear that heather utilization at grass patch edges may well reach critically damaging levels that a non-spatial prediction of overall heather utilization would fail to highlight. Thus, we concur with the views of Coughenour (1991), Pickup, Bastin & Chewings (1998) and Weber et al. (1998) that the importance to management of even the most simple addition of spatial data cannot be understated.
Conclusions and recommendations
In view of the fact that spatial differences in heather utilization have been shown to be of fundamental importance in the prediction of heather utilization, the models presented here represent a key step in the process of developing fully spatially explicit models of herbivore impacts on upland vegetation dynamics. As illustrated here and fully recognized by Armstrong et al. (1997a,b), this type of additional detail is needed for the successful management of heather moorland. Incorporation into a decision support tool (hillplan; Milne & Sibbald 1998) will substantially improve the accuracy of predictions of critical levels and distribution of heather utilization under different grazing regimes. The full modelling sequence will be as follows: (i) prediction of overall heather utilization at the end of winter using a foraging algorithm (Milne & Sibbald 1998); (ii) use of spatial data on the proportion of grass and edge per unit area to predict utilization in the edge zone (this paper); (iii) a vegetation dynamics submodel, which will calculate whether there will be any change in composition of the edge zone and hence derive a revised proportion of grass (C.P.D. Birch and B. Werkman, unpublished data; Milne & Sibbald 1998); then (iv) the new proportion of grass is used to calculate a new edge per unit area (this paper). The heather/grass system considered here provides a good example of discrete boundaries between vegetation types that lend themselves to this type of modelling approach. This approach should be equally applicable, with appropriate parameterization, to any major boundary between discrete vegetation types, not just between woody and herbaceous species. The main requirement for ease of management use is that the input data are relatively easy to collect (Senft, Rittenhouse & Woodmansee 1983; Pickup, Bastin & Chewings 1998).
With regard to the importance of accuracy in estimation of heather utilization and the errors involved in conversion of more simple measures of grazing (see the Appendix), we recommend that future field studies use the scoring method of Grant, Hamilton & Souter (1981) wherever possible. From our own experience, the additional time required is small compared to driving/walking to study sites, setting up transects, and so on. As demonstrated in the Appendix, season of data collection further confounds the problem of converting simple measures of grazing to utilization estimates.
As is always the case for models of this sort (Armstrong et al. 1997a,b; Palmer 1997), in addition to increasing the predictive accuracy of the system under study (Coughenour 1991), they also serve to illustrate areas where data are currently deficient (cf. Weber et al. 1998). There is a clear requirement for more data on heather utilization patterns and boundary changes under heavy herbivore use. In addition, most of the currently available data relate only to summer (and some autumn) grazing (Palmer 1997), yet it is well established that heather utilization is often heaviest during winter when other forage is scarce (Grant et al. 1978, 1982; Bakker et al. 1983; Hester & Baillie 1998). There is also a need for data from sites with a wider range of proportions of grass and heather present, as the vegetation mosaics on Birnie Hill and Finella Hill both contained only about 20% grass. Some of these data deficiencies are being addressed by current work (S.C.F. Palmer and A.J. Hester, unpublished data; S. Oom and A.J. Hester, unpublished data). Furthermore, in both sets of experiments used here, the study animals were confined within fairly small plots (1 ha or 2·5 ha), and further work is needed to establish how well these models apply to free-ranging sheep and red deer. Preliminary analysis of data from the Cairngorms, Scotland (S.C.F. Palmer and A.J. Hester, unpublished data), indicates that patterns of free-ranging herbivore use on open moorland throughout the year are actually very similar to those modelled here. Finally, the models presented here are also only parameterized for dry heather moorland, and we do not know of comparable data for wetter moors, on which heather does not usually attain such dominance over graminoids and other dwarf shrubs (Rawes & Welch 1969; Grant et al. 1976; Marrs, Bravington & Rawes 1988).
The ‘ideal’ balance between accuracy of model predictions and ease of data collection for model use is not easy to define for any system (cf. Coughenour 1991; Weber et al. 1998). From the Finella Hill data, for example, it is clear that there was also year-by-year variation in utilization, even under the same herbivore densities. For this first step in introducing spatial models to the prediction of heather utilization, we have opted for a simple approach by selecting only the most significant and easy to collect parameters. The benefit of even these simple models in increasing the accuracy of utilization predictions has been demonstrated. There is clearly great potential to develop more complex models for detailed study to increase our understanding of the system further, as new data become available. However, the value to land managers will still be strongly dependent on the ease of collection of the data required.
We are grateful to Sander Oom for assistance in preparing the GIS data and to David Welch for access to unpublished data. Robin Pakeman, John Milne, Florian Jeltsch and two anonymous referees gave useful comments on the manuscript. This work was supported by awards under the Scottish Office Agriculture, Environment and Fisheries Department's Flexible Fund Scheme and the Joint Agriculture in the Environment Programme (JAEP).
Received 6 April 1999; revision received 25 February 2000
Conversion of percentage of heather shoots grazed to utilization
In order to combine data from the Finella Hill and Birnie Hill experiments, it was necessary to express the level of browsing on heather in the same units. Although it would have been straightforward to convert heather utilization (sensuGrant 1971), as recorded on the Finella Hill plots (Hester & Baillie 1998), into the more simple measure of percentage of shoots grazed or ungrazed, as was recorded on the Birnie Hill plots (Clarke, Welch & Gordon 1995b; D. Welch, unpublished data), that option was rejected because utilization is a much more useful measure than percentage grazed when modelling the biomass offtake by grazing herbivores.
Hester & Baillie (1998) derived a single equation (Fig. 4) for the prediction of utilization from the percentage of shoots grazed from all the data collected on the Finella Hill plots. However, as the Birnie Hill plots were grazed during the summer only, we derived new relationships omitting data from the autumn, and based on data for the grazers concerned. Separate regression relationships were derived for the 1992 and 1993 Birnie Hill experiments. Zero values were omitted. Logarithmic transformation of both percentage of shoots grazed and percentage utilization yielded residuals that were not normally distributed but were a better approximation to a normal distribution than untransformed or arcsine-transformed data.
For the 1992 experiments, data for sheep and deer grazing alone were combined:
U = 0·378G1·094(eqn A1)
r2 = 0·74, n = 1957, P < 0·001
For the 1993 experiment, data for sheep grazing alone and mixed grazing were combined:
U = 0·390G1·089(eqn A2)
r2 = 0·75, n = 1969, P < 0·001
where U is the percentage utilization of heather; and G is the percentage of heather shoots grazed.
In both relationships, the exponent was significantly different from unity. The non-linearity presumably reflects the occurrence of shoots grazed for a second time at high utilization.
For comparison, under autumn grazing, the degree of non-linearity was more marked. For sheep grazing alone:
U = 0·236G1·189(eqn A3)
r2 = 0·81, n = 1038, P < 0·001
And for deer grazing alone:
U = 0·236G1·222(eqn A4)
r2 = 0·81, n = 1038, P < 0·001
Armstrong & MacDonald (1992), using data collected during the spring, i.e. at the time of maximum heather utilization, derived a linear relationship between the two measures. Their equation yields higher estimates of utilization for a given percentage of shoots grazed than the non-linear relationship of Hester & Baillie (1998) (Fig. 4). This may be because, by the spring, a greater proportion of long shoots has been grazed more than once. A further consideration is that the data used both by Hester & Baillie (1998) and in the present paper are dominated by summer grazing. If autumn grazing alone is considered, e.g. equation A3, the discrepancy with the predictions of Armstrong & Macdonald (1992) is even greater (Fig. 4).