1 Estimating the time since fire of long-unburnt Eucalyptus salubris (Myrtaceae) stands in
2 the Great Western Woodlands
3
4 Carl R. Gosper A,B,C , Suzanne M. Prober B, Colin J. Yates A and Georg Wiehl B
5
6 AScience Division, Department of Environment and Conservation, Locked Bag 104, Bentley
7 Delivery Centre, WA 6983, Australia.
8 BCSIRO Ecosystem Sciences, Private Bag 5, Wembley WA 6913 Australia
9 CCorresponding author. Email: [email protected]
10
11 This is a pre-publication version. The definitive version of the paper has been published
12 in the Australian Journal of Botany on the CSIRO PUBLISHING website. The definitive
13 version can be found here:
14 Gosper, C.R., Prober, S.M., Yates, C.J. and Wiehl, G. (in press) Estimating the time since fire
15 of long-unburnt Eucalyptus salubris stands in the Great Western Woodlands. Australian
16 Journal of Botany doi: 10.1071/BT12212
17 http://www.publish.csiro.au/paper/BT12212.htm
18
19
1 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 20 Abstract. Establishing the time since fire in infrequently burnt, yet fire-prone,
21 communities is a significant challenge. Until this can be resolved for >50 year timeframes,
22 our capacity to understand important ecological processes, such as the periods required for
23 development of habitat features, will remain limited. We characterised the relationship
24 between observable tree growth rings, plant age and plant size in Eucalyptus salubris F.
25 Muell. in the globally significant Great Western Woodlands in south-western Australia. In the
26 context of recent concerns regarding high woodland fire occurrence, we then used this
27 approach to estimate the age of long-unburnt E. salubris stands, and the age-class distribution
28 of Eucalyptus woodlands across the region. Time since fire was strongly predicted by trunk
29 growth rings and plant size predicted growth rings with reasonable accuracy. The best model
30 estimating growth rings contained parameters for trunk diameter, plant height and plot
31 location, although simple models including either trunk diameter or plant height were nearly
32 as good. Using growth ring-size relationships to date long-unburnt stands represents a
33 significant advance over the current approach based on satellite imagery, which substantially
34 truncates post-fire age. However, there was significant uncertainty over the best model form
35 for estimating the time since fire of stands last burnt over 200 years ago. The management
36 implications of predicted age-class distributions were highly dependent on both the choice of
37 what, if any, transformation was applied to growth rings, and the theoretical age-class
38 distribution to which the actual age-class distribution was compared.
39
40
2 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 41 Introduction
42 Establishing the time since disturbance is a significant challenge in investigations of temporal
43 changes in ecosystem function and composition in infrequently-disturbed communities. Fire
44 is a common disturbance affecting vegetation dynamics across much of the world (Bond et al.
45 2005; Verdú and Pausas 2007). Individual fire events can have effects lasting for centuries
46 (Wood et al. 2010), but it is usually difficult to date fires that occurred prior to those
47 documented in contemporary sources, such as long-term historical records or remotely-sensed
48 imagery (Clarke et al. 2010). This is not a trivial problem, as many ecological processes
49 operate over long time scales (Mackowski 1984; Clarke et al. 2010), and space-for-time
50 studies based on estimated times since fire offer one of the few empirical approaches to
51 understanding these processes.
52 Researchers are thus faced with the problem of deriving a time since fire for vegetation
53 that has not been burnt since the earliest available historical records (such vegetation is often
54 referred to as ‘long-unburnt’). Historical records may include remotely-sensed satellite
55 imagery that begins in Australia in 1972, aerial photography that begins in Western Australia
56 in 1948, or written or verbal sources. One approach to deriving a time since fire for long-
57 unburnt stands is to allocate a uniform time to all, either the absolute minimum (e.g. Parsons
58 and Gosper 2011), or an estimated minimum based on the rate at which fire scars of known
59 age become less visible over successive satellite images and assuming similar rates of
60 vegetation recovery applied previously (e.g. Gosper et al. 2012). In both approaches, the time
61 since fire allocated to long-unburnt stands is likely to be substantially truncated compared to
62 their actual time since fire (Clarke et al. 2010).
63 Alternatively, efforts can be made to estimate the actual time since fire of long-unburnt
64 vegetation through dendrochronology or allometric relationships, carbon dating, and other
65 forms of evidence such as charcoal in lake, marine or bog deposits (Conedera et al. 2009;
3 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 66 Wood et al. 2010). Dendrochronology is one of the few methods of fire regime reconstruction
67 with the appropriate spatial and temporal resolution to be useful in linking with plot-based
68 chronosequence studies. Applications of dendrochronology to dating fire events have usually
69 concerned plant species in which fire scars are overgrown by living tissue (Burrows et al
70 1995; Conedera et al. 2009), allowing the reconstruction of multiple fire events. This
71 functional response to fire is rare among some communities, such as in mallee and woodland
72 in the global biodiversity hotspot of southern Western Australia. On the other hand, obligate
73 seeding plant species are abundant in some communities and offer potential for determining
74 time since the last fire (Conedera et al. 2009; O’Donnell et al. 2010). Such species would
75 need to meet a number of criteria to be suitable. These include high longevity relative to the
76 frequency of stand-replacing fires; consistent mortality after fire; rapid recruitment after fire;
77 and negligible inter-fire recruitment. Potentially suitable species in Australia include Callitris
78 (O’Donnell et al. 2010), some Allocasuarina (Burley et al. 2007) and some Eucalyptus (Rose
79 1993; Wood et al. 2010).
80 Allometric relationships between measures of plant size and age (derived from remotely-
81 sensed imagery, historical record or dendrochronology) may also allow for the ageing of
82 plants or plant parts that cannot be dated by other means (Koch et al. 2008). This has been
83 applied in Australia, with variable success, to mallee, woodland, forest and subalpine
84 Eucalyptus (Rose 1993; Schulze et al. 2006; Koch et al. 2008; Rumpff et al. 2009; Clarke et
85 al. 2010), open-forest Allocasuarina (Burley et al. 2007) and semi-arid Callitris (O’Donnell
86 et al. 2010). All of these studies found a significant relationship between trunk diameter and
87 age, although the accuracy of age predictions can decline as the trunks become older (Rumpff
88 et al. 2009) and age estimates can be less accurate than those based on dendrochronology
89 (Koch et al. 2008). The choice of any transformation applied to age is crucial: age can be
4 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 90 underestimated where untransformed, but age is also highly susceptible to minor variation in
91 plant size if square- root or log transformations of age are used (Clarke et al. 2010).
92 Eucalyptus salubris F. Muell. (gimlet) is a thin-barked tree that is killed by complete
93 canopy scorch. It is widespread across dry and semi-arid Mediterranean-climate south-
94 western Australia, including the 16M ha region known as the Great Western Woodlands
95 (GWW). The woodlands of this region are typically fire sensitive, and are at risk from
96 inappropriate fire regimes in a potentially warming and drying climate (Prober et al. 2012).
97 Uncertainty concerning the time since fire of long-unburnt woodlands, and hence the scale
98 over which temporal changes in woodland dynamics occur, currently constrains
99 understanding as to whether the relatively frequent recent incidence of large wildfires (DEC
100 2010; Parsons and Gosper 2011) represents a significant departure from the historical fire
101 regime or a long-term threat to mature woodland ecosystems. Towards a better understanding
102 of the fire ecology of GWW woodlands, we aimed to characterise the relationship between
103 observable tree rings, plant age and plant size in E. salubris . We then tested the viability of
104 this approach for estimating the time since fire of long-unburnt E. salubris stands and the time
105 since fire age class distribution of Eucalyptus woodlands more broadly.
106
107 Materials and Methods
108 Survey plots
109 The study was undertaken in E. salubris woodlands in three districts along the western edge
110 of the GWW, south-western Australia: Karroun Hill (30˚14 ′S, 118˚30 ′E); Yellowdine
111 (31˚17 ′S, 119˚39 ′E) and Parker Range (31˚47′S, 119˚37′E) (Fig. 1). These areas have a semi-
112 arid Mediterranean climate, with mean annual rainfall in Coolgardie and Merredin (the
113 nearest long-term weather stations) of 270.5 and 325.9 mm respectively, with the highest
114 mean rainfall months in winter. Mean monthly daily temperature maxima range from 16.1 to
5 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 115 33.3˚C (Coolgardie) and 16.2 to 33.8˚C (Merredin), and mean monthly minima from 5.2 to
116 17.0˚C (Coolgardie) and 5.4 to 18.0˚C (Merredin) (Bureau of Meteorology 2012). The region
117 supports a mosaic of mallee, scrub-heath and woodland, with vegetation type locally
118 determined by edaphic factors, and influenced by historic disturbances. While the structure
119 and understorey composition of the sampled woodlands varied substantially with time since
120 fire and other factors, all plots had a dominant crown layer of E. salubris , sometimes in
121 association with other Eucalyptus spp., most often E. salmonophloia F. Muell. (salmon gum),
122 E. yilgarnensis (Maiden) Brooker (yorrell), E. longicornis (F. Muell.) Maiden (red morrel) or
123 E. moderata L.A.S. Johnson & K.D. Hill .
124 In each district, 50 m x 50 m plots were placed in relatively uniform E. salubris woodland
125 in each of the following time since fire age classes: < 10 years (4-8 plots per district), 38-60
126 years (3-5 plots per district) and long-unburnt (> 60 years; 11-13 plots per district). An
127 additional three plots between 10 and 38 years post-fire were sampled at each of Parker Range
128 and Karroun Hill where such fires had occurred, giving a total of 72 plots. Fires < 38 years
129 ago were dated through interpretation of Landsat TM imagery (per Glen Daniel, digital image
130 processing and remote sensing at Fire Management Services, Regional Services Division,
131 Department of Environment and Conservation, WA). Distinct fire scars in the 1972 (oldest)
132 Landsat image were mapped, and allocated an indicative time since fire for the purposes of
133 this study of between 38-60 years. The year of some of these pre-1972 fires are known (e.g. a
134 fire south of Parker Range burnt in 1970; Paul Blechynden, Department of Environment and
135 Conservation, pers. comm.), while other fires lacking confirmed dates were also included in
136 the 38-60 years age class if their scars in the 1972 Landsat image were of similar appearance
137 to pre-1972 fires of known year of occurrence. The upper age limit of pre-1972 fires (60
138 years) was estimated based on patterns of vegetation recovery after fire across a series of
6 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 139 Landsat images (Gosper et al. 2012). Information on other aspects of the fire regime other
140 than time since fire (such as intensity, previous fire intervals etc), was not available.
141 Plots were spaced at least 250 m apart, and at least 500 m apart for plots of the same time
142 since fire. As fires across this landscape can be very large, exceeding 100 000 ha in size on
143 occasion (McCaw and Hanstrum 2003), it was usually necessary to place multiple samples
144 within the one fire scar in each district. This potentially creates problems in disentangling
145 location and fire event effects (Hurlbert 1994).
146 At each plot we collected tree size data by sampling 16 trees by use of a modified version
147 of the point-centred quarter method (Cottam and Curtis 1956). We measured the diameter at
148 the base of trunks and plant height of the nearest tree in each of the four compass quadrants
149 radiating from the four corners of each 50 x 50 m plot.
150 [Fig. 1 near here]
151
152 Ring counts
153 At 39 of the 72 plots, spread across all districts and time since fire age classes, we randomly
154 selected three individual E. salubris . The individuals sampled spanned a range of the sizes
155 available per plot, although unusually large or small individuals were avoided, as were those
156 with multiple basal stems. Plant height was measured using a hypsometer (Nikon Forestry
157 550), and the diameter of the sample trees was measured at their base (standard breast height
158 measurements are less useful for E. salubris as it often branches below this height). We then
159 took either a basal trunk section using a hacksaw (n = 100 trees, 34 plots) or a 12 mm
160 diameter core at ~20-30 cm from the base (using a motorised tree corer; n = 17 trees, seven
161 plots; two plots has a combination of sections and cores), depending on plant size. These
162 samples were collected in autumn and spring 2011; as the study area had a Mediterranean
7 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 163 climate, spring 2011 samples were considered to be one growing season (i.e. one growth ring)
164 older than autumn 2011 samples.
165 The application of growth ring counts for ageing trees can be constrained by the
166 development of hollow trunks in older age classes, leading to an inability to fully resolve their
167 ages (Rose 1993; Wood et al. 2010). Greater than 80% of trees that were large enough to
168 require coring (>~15 cm diameter at the base) were hollow, and of those that were not there
169 was no certainty that the core intersected the chronological centre of the tree (Burley et al.
170 2007). Hence we only scored trunk sections for rings. Only one trunk section had a hollow
171 centre, precluding accurate ring counts; this trunk was excluded.
172 Trunk sections were prepared by sanding their surface using belt and hand-held electric
173 sanders with progressively decreasing grit size, finishing with 240 grit. A binocular
174 microscope was used to assist in scoring rings. Two ring counts were completed for each
175 trunk section, one from the centre outwards, and the second from the bark inwards on a
176 different part of the section. The mean of these was taken to provide the ring number per
177 trunk used in analyses. Cross-dating growth rings, which may allow for the detection of
178 missing or false rings (Speer 2010) was beyond the scope of this study.
179
180 Modelling time since fire, tree rings and plant size
181 The regression modules in Sigmaplot (Systat Software Inc. 2006) and Statistica (Statsoft
182 2005) were used to test for relationships between: (i) plant age (assumed to be equal to plot
183 time since fire, as determined from Landsat imagery; see above) and mean number of growth
184 rings per trunk; and (ii) mean number of growth rings per trunk and various combinations of
185 plant size (plant diameter at the base and/or plant height) and plot location. Linear models
186 were used for the relationship between plant age and rings, as only a linear relationship would
187 indicate that ring count could be used as a surrogate for plant age. This analysis was
8 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 188 completed using (i) only plots in which plant age is known with high accuracy (most recently
189 burnt after the 1972 Landsat image, i.e. < 38 years since fire) and (ii) also using those plots
190 with distinct evidence of fire in the 1972 Landsat image. In the latter case, all fires distinct in
191 the 1972 Landsat image were allocated a uniform 45 years since fire for this analysis. For
192 relationships between ring count and plant size and location variables, linear models were
193 tested on untransformed, and square-root and log 10 transformed ring counts. Transformation
194 was used to test if plant growth rate declined with plant age (Clarke et al. 2010; Wood et al.
195 2010). The relationship between ring count and plant size plausibly varies over the geographic
196 spread of plots sampled, due to climatic and other factors affecting productivity. A predictor
197 variable reflecting plot location was also tested in models (with and without an interaction
198 term of location x plant diameter or height). As plots are largely spread across a north-south
199 gradient, we used northing as the proxy for plot location effects. Models were compared on
200 the basis of maximising adjusted r 2 and (within transformation alternatives) minimizing AIC
201 (Akaike information criterion).
202 Using the data from the point-centred quarter measurements, we plotted the range of
203 single-trunked E. salubris plant sizes to determine if diameter at the base and plant height
204 continued to increase beyond the size of trees sampled for growth rings, and hence determine
205 if either or both size measurements were likely to be suitable for the estimation of the time
206 since fire of long-unburnt plots.
207
208 Validation of plant size models
209 The effectiveness of using plant size measurements to estimate growth rings, and then time
210 since fire, was tested using the plant size data from the modified point-centred quarter
211 measurements. At all 23 plots of known age (< 38 years post-fire) (20 at which growth rings
212 were sampled, 3 where they were not), we used all single-trunked E. salubris samples (n =
9 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 213 254) to compare plant age estimated from the growth ring-size models with known time since
214 fire using Pearson’s correlation coefficient.
215
216 Estimating the time since fire of long-unburnt Eucalyptus salubris stands
217 For E. salubris stands > 38 years post-fire without compete growth ring counts ( n = 35), we
218 calculated an estimated time since fire for each tree based on growth ring-size relationships.
219 This calculation used data from single-trunked E. salubris from the modified point-centred
220 quarter method samples ( n = 4-16 per plot). To reduce the possibility of atypically-sized trees
221 substantially skewing estimated plot age (as could occur through instances of either inter-fire
222 recruitment or adults eluding fire that killed neighbours, even though these events are
223 probably rare), the largest and smallest trunk were excluded when all trees per plot were
224 averaged to get a mean estimated time since fire per plot (n = 2-14 per plot). Estimated times
225 since fire were rounded down to nearest multiple of ten for ages > 100 years, due to slight
226 overestimation of true time since fire by ring counts (see results) and for ease of
227 interpretation. Estimated times since fire were calculated for five model options (the best
228 overall, the best two models based on diameter plus plot location and, for simplicity, the best
229 two models for diameter not including a term for location), to give an indication of the effect
230 of model choice.
231 The following rule set was applied to determine the age of stands of E. salubris for
232 determining an age-class distribution: (1) year of fire from Landsat imagery was used if this
233 was known precisely. As fire date within year was not always known, Landsat image date
234 does not always equal the number of growing seasons, so Landsat-derived time since fire was
235 rounded up one year if doing this was supported by growth ring counts; (2) the estimate from
236 growth ring counts (with the mean taken of multiple samples per plot) was used where growth
237 rings were sampled and at least two of the sampled trunks were not hollow; (3) the estimate
10 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 238 from the extrapolation of the relationship of growth rings and plant size (± plot location) was
239 used for remaining stands; (4) if rules (2) or (3) resulted in the estimated time since fire being
240 less than that possible from analysis of Landsat imagery (i.e. if a fire apparent in the 1972
241 Landsat image had an estimated time since fire from ring counts or growth ring-size
242 relationships of < 38 years), the minimum possible time since fire from Landsat was used –
243 38 years).
244
245 Creating an estimated age class distribution
246 To estimate the current age class structure of E. salubris woodlands in the GWW, we used
247 ArcGIS 9.3 in conjunction with existing fire-history mapping derived from Landsat imagery
248 (1972-2010, Fig. 1). The mapped region covered approximately the western 50%, or 79 700
249 km 2, of the Great Western Woodlands. We calculated the area that each time since fire age
250 class overlapped each of two aggregations of Vegetation Survey of Western Australia map
251 units (e.g. Beard 1972, 1976), then calculated the percentage of the total woodland area this
252 equated to. First, we used all map units listing E. salubris as one of the dominant species of
253 the vegetation association. Second, as some of our sample plots dominated by E. salubris
254 were located in vegetation map units not listing E. salubris as a dominant species, we used all
255 woodland associations including E. salubris or one of the commonly co-occurring E.
256 salmonophloia , E. longicornis and/or E. transcontinentalis Maiden (including E. moderata ).
257 Three age-class distributions were calculated: (1) using fires of known age from Landsat
258 imagery only (with fires apparent in but prior to the earliest (1972) image aged as 38-60 years
259 post-fire), (2) estimating the age-class distribution of the long-unburnt proportion (> 60 years
260 post-fire) based on the relationship between untransformed growth rings and diameter plus
261 northing (Model 2), and (3) as for (2) using the relationship between square-root transformed
262 growth rings and diameter plus northing (Model 5) (noting these were the two best
11 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 263 performing plausible models (see Results; Table 1, Supplementary Material Part A). For all
264 vegetation with no evidence of fire in the 1972 Landsat image, we assumed an age class
265 distribution reflecting that of our long-unburnt samples aged through both growth ring counts
266 and estimated by growth ring-size relationships.
267 Finally, we compared the estimated age-class distributions of E. salubris woodlands and
268 Eucalyptus woodlands more broadly to two theoretical distributions. Theoretical fire age class
269 distributions can be used to guide fire management interventions, by allowing the
270 identification of age classes that are either substantially over- or under-represented compared
271 to a theoretical ‘ideal’ (Fire Ecology Working Group 2002). First, following the method of
272 Richardson et al. (1994), a fixed proportion of the total area of woodland was allocated to
273 each age class from immediately post-fire up to the optimal mean fire interval. There are no
274 data on which to determine optimal mean fire interval, so we have used values (listed in Fig.
275 4) approximating the oldest estimated vegetation times since fire from our study for each of
276 the two alternative models. Second, a random distribution of fires may produce an age class
277 distribution approximating a negative exponential function (Johnson and Van Wagner 1985).
278 The assumption underlying this function that flammability is invariant with time since fire is
279 unlikely to be met in many real world scenarios (Clarke 2008), but this function produces
280 similar age class distributions to more complex functions lacking this restrictive assumption
281 (McCarthy et al. 2001). The negative exponential function needs to be parameterised and
282 again there is a paucity of data on which to base these values; hence we have again used
283 estimates of the fire cycles and maximum acceptable fire interval (Fig. 4) based on the oldest
284 vegetation in the two alternative models.
285
286 Results
287 Growth rings for estimating plant age
12 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 288 There was a strong, positive, linear relationship between time since fire and the number of
289 growth rings. This was the case using only plants < 38 years since fire (Fig. 2) and using older
290 plants of less precisely-known age ~45 years since fire (Time since fire = -0.4516 +
2 291 0.9666(growth rings); Adj. r = 0.967, F 1,79 = 2365, P < 0.0001). The slope and intercept of
292 these were very similar, although as expected the goodness of fit declined with the inclusion
293 of the oldest, less precisely-aged plants. In both cases, there was a tendency for ring counts to
294 slightly overestimate time since fire. The magnitude of this effect was small (~5%, or ~2
295 years at 38 years since fire): the slope of the line was barely less than one; hence the predicted
296 time since fire is likely to diverge very slowly from actual time since fire. The slight
297 overestimation of time since fire may indicate a tendency for E. salubris to develop false
298 rings, or may reflect variation in the timing of germination following fire. Notwithstanding,
299 growth rings predict the age of E. salubris plants sufficiently accurately for rings to be used as
300 a proxy for time since fire without the application of a conversion factor.
301 [Fig. 2 near here]
302
303 Plant size for estimating growth rings/time since fire
304 There were strong positive relationships between growth rings and both measures of E.
305 salubris size; diameter at the base and height (Table 1; Fig. 3). This was the case in models
306 only including plant size, and remained the case when additional predictors incorporating
307 location effects were included. Differences in model performance (fit, measured by Adj. r 2)
308 between transformation options (of growth rings) and with changes in model terms were
309 generally small. The best performing model had terms for diameter, height and plot location
310 for predicting square-root transformed growth rings (Table 1). Models using tree height (±
311 plot location) tended to have slightly better fit (and lower AIC) than equivalent models using
312 diameter. Including a term for plot location always improved model performance, but in
13 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 313 contrast, including a term for the interaction of plant size and location rarely improved fit.
314 Overall, models of square-root transformed and untransformed growth rings demonstrably
315 out-performed log 10 transformation. Square-root transformation of growth rings indicates a
316 moderate decline in growth rate with increasing time since fire, and models based on square-
317 root transformation generally produced estimated stand times since fire substantially greater
318 than models of untransformed growth rings (Supplementary Material Part A).
319 Inspection of the range of E. salubris plant sizes across all plots indicated that tree height
320 reached a plateau at not much greater than the tallest plants with complete growth ring counts
321 (~ 90 years), but diameter at the base did not (Supplementary Material Part B). Consequently,
322 we believe that height would be a poor predictor of growth rings beyond the size of plants
323 used in model generation; hence we used models including a term for diameter at the base for
324 predicting growth rings at plots for which we had neither a precise time since fire value
325 derived from interpretation of Landsat imagery or complete growth ring counts. Better-
326 performing models including a term for diameter were Models 22 (square-root transformed
327 growth rings predicted by diameter + height + location), 2 (untransformed growth rings
328 predicted by diameter + location) and 5 (square-root growth rings predicted by diameter +
329 location), while well-performed models without a term for location (which may be more
330 simply applied in practice) were Models 21 (square-root growth rings predicted by diameter +
331 height), 1 (untransformed growth rings predicted by diameter) and 4 (square-root growth
332 rings predicted by diameter) (Table 1).
333 Plant size data collected from additional trees of known time since fire indicated a
334 moderate to high correlation between ages predicted through growth ring-size relationships
335 and actual times since fire. Pearson correlation using Model 2 (untransformed growth rings
336 predicted by diameter + northing; Table 1) was r = 0.79 (p < 0.01), while for Model 5 (square-
337 root growth rings predicted by diameter + northing) it was r = 0.76 (p < 0.01). Plotting this
14 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 338 relationship indicated no evidence for consistent over- or under-estimation of plant age
339 compared to actual times since fire.
340 [Table 1, Fig. 3 near here]
341
342 Estimated time since fire of long-unburnt Eucalyptus salubris stands
343 While there was little difference in the goodness of fit of relationships between untransformed
344 or square-root transformed growth rings and plant size ± location, using square-root
345 transformation increased the estimated times since fire of long-unburnt E. salubris stands by
346 an order of magnitude compared to untransformed growth rings (Supplementary Material Part
347 A). In contrast, including a parameter for plot location only slightly altered estimated times
348 since fire. The range of estimated times since fire for long-unburnt (no evidence of fire in the
349 1972 Landsat image) stands was 86-370 years using Model 1 (Table 1), 110-1440 years using
350 Model 4, 88-370 years using Model 2 and 110-1460 years using Model 5. Given the plateau
351 recorded in tree height, it is not surprising that the best-performing model overall (Model 22)
352 tended to result in lower stand time since fire estimates than other models (range 84-350
353 years; Supplementary Material Part A). Rank order of stand time since fire remained largely
354 constant between models, despite the sometimes large differences in estimated times since
355 fire.
356
357 Age-class distribution of Eucalyptus salubris woodlands
358 Based on analysis of Landsat images, the majority of E. salubris and associated woodlands
359 have not been burnt within the past 60 years (Fig. 4a).
360 Interpretation of the estimated age-class distribution of woodlands not burnt recently is
361 particularly dependent on the choice of transformation of growth rings. If Model 5 is used
362 (square root growth rings predicted by diameter + location), the woodlands have a fairly even
15 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 363 proportion of total area distributed in 50-year age brackets out to ~ 750 years post-fire, with
364 two main exceptions. A greater proportion of E. salubris and associated woodlands (but less
365 so for E. salubris woodlands solely) have been burnt recently (< 100 years ago, but
366 particularly < 60 years ago) than in other age classes, and there is a secondary peak in the
367 proportion of stands aged 400-500 years (Fig. 4c). If Model 2 is used (untransformed growth
368 rings predicted by diameter+ location), the age class distribution is substantially more
369 truncated, but the uneven distribution of age classes remains, with 0-60 (only in all
370 woodlands) and 150-250 years since fire age classes with greater representation on a fixed
371 proportion basis(Fig. 4b). Both transformation approaches result in the same general shape of
372 the age-class distribution (peaks in young and intermediate-aged vegetation), but with a
373 different temporal scale.
374 [Fig. 4a-c near here]
375
376 Discussion
377 Estimating the time since fire of long-unburnt stands is of great importance for understanding
378 vegetation dynamics and underpinning biodiversity conservation in infrequently-burnt fire-
379 prone ecosystems. We demonstrated that plant size can be used to predict growth rings with
380 reasonable accuracy, and that growth rings reflect time since fire in single-trunked Eucalyptus
381 salubris . This allows greater resolution of time since fire in E. salubris woodlands over the
382 globally significant Great Western Woodlands, using a relatively simple method. Further, the
383 method holds the potential for wider application in non-resprouting Eucalyptus throughout
384 Mediterranean-climate Australia, with appropriate calibration and verification.
385 Rings in Eucalyptus trunks tend to occur with changing rates of growth associated with
386 irregular rainfall, rather than an annual cycle (Schulze et al. 2006; Koch et al. 2008). This
387 presumably contributed to the tendency for time since fire to be overestimated by ring counts,
16 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 388 as has been found in other Eucalyptus species (Koch et al. 2008). Rare substantial summer
389 rainfall events or early and unsustained autumn rains may have led to the formation of
390 detectable growth rings (false) in addition to approximately annual rings associated with
391 winter rainfall in this semi-arid Mediterranean-climate region. For the purposes of this study,
392 however, the divergence between true time since fire and that estimated through ring counts
393 was acceptably low.
394 A significant source of variability in the relationship between trunk size and time since fire
395 concerns the relative dominance of different individual plants. Long-term tree growth plots
396 clearly indicate that dominant trees can grow at rates more than double that of suppressed
397 trees (Kessell and Stoate 1936; Kealley 1991), presumably in response to greater access to
398 resources. While the effect of sampling trees of different dominance status on the overall
399 estimated stand time since fire is lessened by excluding the extremes and taking the average
400 of a number of trees, it may still have had some bearing on estimates, and undoubtedly
401 contributed to the variability surrounding estimates.
402 This study clearly indicates the importance of the choice of transformation of time (growth
403 rings) in accounting for any decline in plant growth rates with age on the estimated time since
404 fire of long-unburnt stands. Both untransformed and square-root transformed growth rings
405 were adequately predicted by trunk diameter (± location) in trees up to ~15 cm diameter
406 (~100 years old), and have similar rank orders of time since fire beyond this size, but our data
407 provide little evidence supporting a choice between these transformation options for larger
408 trees. Similar to our findings, Clarke et al. (2010) do not produce conclusive evidence to
409 support the use of either untransformed or square-root transformed plant age over the
410 alternative approach in estimating the age of long-unburnt mallee. Both transformation
411 approaches have been widely applied previously (Rumpff et al. 2009; Clarke et al. 2010,
412 O’Donnell et al. 2010), and few studies examine the error associated with subsequent time
17 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 413 since fire estimates (Koch et al 2008). A longer period of growth ring records would greatly
414 increase confidence over which transformation is most appropriate. From the extrapolated
415 relationship between growth rings and trunk diameter (Fig. 3), plants of greater than 17.5 cm
416 diameter at the base (~100-150 years) would need to be sampled to resolve this issue.
417 Consequently there is higher uncertainty in accurately ageing trunks larger than this.
418 There are other forms of evidence, however, that either lend support to or discount the
419 reliability of both of the transformation options. First, in the case of using untransformed
420 growth rings, there is local evidence to suggest that growth rates decrease with age,
421 suggesting that using untransformed growth rings will underestimate true time since fire.
422 Long-term increment plot data in the Great Western Woodlands, of E. salmonophloia , shows
423 that mean annual increment over 84 years since recruitment was less than a quarter of the
424 increment over the period 19-38 years since recruitment (calculated from Kessell and Stoate
425 1936; Kealley 1991). However, it is also plausible that growth rates could reach a low point in
426 the high-density, closely-spaced regrowth stage in species regenerating after a stand-
427 replacement disturbance, when intra-specific competition may be most intense. If density-
428 dependent mortality then thins stands (probably occurring > 100 years post-disturbance), as
429 appears likely, growth rates could subsequently increase (McHenry et al. 2006). The
430 relationship between tree age and annual diameter increment would be one feasible means of
431 further investigating choice of models.
432 In estimates based on untransformed growth rings, no E. salubris stands had an estimated
433 time since fire greater than 400 years. This is a length of time approximating the estimated
434 fire interval in Eucalyptus woodlands calculated over the period 1940-2006 in the nearby
435 Lake Johnson area (405 ± a standard error of 106 years; O’Donnell et al. 2011a). O’Donnell
436 et al. (2011a) also calculated the median fire probability interval (the interval which would be
437 exceeded 50% the time) for woodlands as 310 years. While there is a high likelihood that the
18 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 438 pattern of occurrence of fire varies over time and space, in response to climatic, landscape and
439 vegetation factors (Cullen and Grierson 2009; O’Donnell et al. 2011a,b), it appears untenable
440 that none of the E. salubris stands sampled were greater than 400 years post-fire. Further, the
441 oldest E. salmonophloia and E. wandoo occurring in remnants in the adjoining Western
442 Australian wheatbelt, and Callitris in the Great Western Woodlands, were estimated to be
443 400+ years old (Rose 1993; Cullen and Grierson 2009), further suggesting that E. salubris
444 stands 400 years post-fire or older are unlikely to be exceptional. These forms of evidence
445 suggest that models using untransformed growth rings may underestimate true time since fire.
446 Second, using square-root transformed growth rings resulted in estimated times since fire
447 for the longest-unburnt E. salubris stands far exceeding 500 years. While periods of this
448 length between fires concur with findings from some other tree-dominated ecosystems
449 characterised by rare, stand-replacing crown-fires (Romme and Knight, 1981; Hemstrom and
450 Franklin, 1982), including in Australia (Turner 1984), they are rarely reported for Eucalyptus -
451 dominated communities. Mawson and Long (1994) report that hollow-bearing Eucalyptus
452 from more mesic parts of south-western Australia can possibly reach about 2000 years in age
453 (these species are resprouters, so this does not refer to time since fire), although these
454 estimates are contentious (Stoneman et al. 1997). Koch et al. (2008) estimate ages of
455 Eucalyptus species (non-resprouting) up to 735 years in Tasmanian forests. Most estimates of
456 the maximum age of tree Eucalyptus , however, fall in the range of about 400-500 years
457 (Mackowski 1984; Rose 1993; Burrows et al. 1995; Hickey et al. 1999; Whitford 2002;
458 Wood et al. 2010). Further, in Eucalyptus communities dominated by resprouting mallees,
459 such as occur in a mosaic with E. salubris woodlands, plants are yet to be found to reach ages
460 greater than 200 years, either post-fire (Clarke et al. 2010) or for lignotuber age (Wellington
461 and Noble 1985).
19 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 462 Consequently, it remains highly uncertain if E. salubris woodlands can really remain
463 undisturbed by fire (or anything else causing stand-scale mortality; Yates et al. 1994) for in
464 excess of 1000 years. Square-root transformation of growth rings results in small variations in
465 diameter having large effects on estimated age (Clarke et al. 2010) (e.g. an increase in mean
466 trunk diameter at the base of 41.6 cm to 44.7 cm would result in estimated stand time since
467 fire increasing from 700 to 800 years with Model 4; Table 1), with the consequence that the
468 oldest stands have the largest variance around estimates (Supplementary Material Part A).
469 Overall, there are viable arguments in support of and contradicting both of the
470 transformation options, and in all likelihood a more accurate range of estimated times since
471 fire lie between the two. Due to the length of time required for mature communities to
472 develop, combined with the lack of feasible management options to increase the rate of
473 community development, it is arguable that in infrequently-burnt communities it is
474 precautionary to use a method that may overestimate stand time since fire, compared to one
475 that may underestimate stand time since fire. If stands are aged using square-root transformed
476 growth rings (Models 4 and 5), however, we suggest that it may be prudent to place an upper
477 limit on stand time since fire (perhaps ~650 years; within about two standard errors of the fire
478 interval estimate of O’Donnell et al. 2011a), for analysis purposes until further data become
479 available.
480 Validation of stand time since fire through other methods would help resolve the issue of
481 alternative transformation options, and further contribute to understanding past fire regimes
482 across the GWW. Eucalyptus salubris would appear mostly unsuited to one frequently-used
483 alternative method, radiocarbon dating (e.g. Turner 1984), due to the ubiquity of hollows in
484 older trunks. While it would be preferable to have greater confidence in the real time since
485 fire of the longest-unburnt E. salubris , the fire-age distribution from the models is a
20 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 486 substantial improvement over the current state of knowledge based on remotely-sensed
487 imagery.
488 In addition to the uncertainty in ageing large trees due to choice of transformation of
489 growth rings, there is also error in predicting the time since fire of trees of any size due to
490 variation in tree size within ages (Fig. 3). While such variation is not unexpected given our
491 samples were spread across dominance classes (Kessell and Stoate 1936; Kealley 1991), it
492 suggests the need for caution in estimating stand time since fire from a small sample of trees.
493 The prediction intervals for Model 1 (Fig. 3) at 10 cm diameter at the base were ± ~ 17 years.
494 This potential error in age estimates is not negligible, yet even with this level of variation the
495 models still represent a significant advance in understanding of times since fire of E. salubris
496 woodlands compared to that able to be derived from remotely-sensed imagery. In
497 communities like E. salubris , where many important ecological processes are likely to operate
498 over periods of hundreds of years post-fire, we argue that the levels of error of our models are
499 acceptable in many cases in the study of post-fire ecological processes.
500 A number of factors are likely to affect the long-term susceptibility of particular plots to
501 fire, including landscape features such as proximity to salt lakes, granite outcrops and other
502 vegetation communities with fuel structures more conducive to fire (O’Donnell et al. 2011a).
503 While some of the plots of the greatest estimated time since fire were close to a chain of salt
504 lakes, others were not. Many of the oldest plots were located in the northern half of the survey
505 area, although due to the design of the study, it is not possible to determine the cause of this.
506 The apparent lower fire incidence in woodlands in the north is supported by the occurrence of
507 more and larger fires in the southern part of the study area over the period of Landsat
508 imagery. This difference in fire occurrence between northern and southern areas also explains
509 the relatively higher estimates of total woodlands recently burnt compared to E. salubris
510 woodlands only, as the latter communities are mapped as being less widespread in the south.
21 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 511 As would be expected for a community with a mean fire-return interval of ~400 years
512 (O’Donnell et al. 2011a), most of the E. salubris and associated woodlands have not been
513 burnt over the ~60 year period for which contemporary records are available. The highly
514 truncated age-class distribution resulting from analysis of Landsat imagery, however,
515 contributes little to understanding the real age-class distribution of such infrequently-burnt
516 ecosystems, or for providing guidance for fire management interventions.
517 Estimated age-class distributions can be compared to theoretical distributions based on
518 known or estimated parameters of the fire regime (Richardson et al. 1994; Gill and McCarthy
519 1998; McCarthy et al. 2001). Substantial deviations of the actual age-class distribution from
520 theoretical ones might then be used to guide management interventions, such as by applying
521 prescribed fire to over-represented older age classes or prioritising the exclusion of fire from
522 certain areas if younger age-classes are over-represented. As the underlying ecological
523 knowledge that is required to support estimates of fire regime parameters (such as maximum
524 fire intervals and fire cycles) is lacking in E. salubris and associated woodlands, comparisons
525 with theoretical distributions should be viewed with caution. Further, fire events are likely to
526 be non-randomly distributed over time, due to the effects of variable climate and fuel
527 distribution (Cullen and Grierson 2009; O’Donnell et al. 2011a,b), so some variation in the
528 distribution of post-fire ages around the theoretical function might be expected.
529 Our results suggest that the comparison of actual and theoretical age class distributions is
530 fraught with difficulty. First, given the ready availability of remotely-sensed imagery and the
531 challenges of dating fires prior to 1972, many applications of theoretical age-class
532 distributions are likely to use actual distributions derived solely from Landsat imagery. If fire-
533 return intervals for the community under consideration frequently exceed 38 years, then
534 comparisons using Landsat-derived data will often mistakenly give the impression that older
535 age classes are over-represented (Clarke et al. 2010; Fig. 4a c.f. b and c) due to the
22 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 536 compression of a diverse age class structure into a truncated one. Second, the form of the
537 function to which the actual age class distribution is compared is important. Irrespective of
538 the model used to estimate the actual age-class distribution, comparison with the approach of
539 Richardson et al. (1994) suggested that there has been an undesirable increase in recent fire
540 (Parsons and Gosper 2011), whilst using a negative exponential function (Johnson and Van
541 Wagner 1985; Gill and McCarthy 1998) provided less compelling evidence for over-
542 representation of the youngest age class.
543
544 Supplementary material
545 Supplementary material with details regarding the estimated times since fire from alternative
546 models for plots which were not sampled for growth rings and the frequency distribution of
547 sizes (diameter at base and tree height) of Eucalyptus salubris is available from the Journal’s
548 website.
549
550 Acknowledgements
551 This study was supported by the Department of Environment and Conservation’s (DEC)
552 Great Western Woodlands Conservation Strategy, CSIRO Ecosystem Sciences (CES) and the
553 Great Western Woodlands Supersite, part of the Australian Government’s Terrestrial
554 Ecosystem Research Network. The spatial distribution of sampling and analysis of age class
555 distribution was based in part on remote sensing data derived from the research of Glen
556 Daniel, in digital image processing and remote sensing at Fire Management Services,
557 Regional Services Division, DEC. We thank Gary Ogden, Nat Raisbeck-Brown (both CES),
558 Matthew Williams and Ian Steward (both DEC) for assistance with the tree corer, GIS
559 analyses, statistical advice and GIS layers respectively. Lachie McCaw and two anonymous
560 reviewers provided helpful comments on drafts of the manuscript.
23 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 561
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678 Table 1. Alternative linear models for the relationship between Eucalyptus salubris growth rings (= time since fire) and plant size
679 (diameter at base and/or plant height) and plot location
680 All regressions were significant ( P < 0.01). Northing was used as a proxy for plot location. AIC = Akaike information criterion. Model terms: y1,
681 untransformed growth rings (years); y2, square-root transformed growth rings (years); y3, log 10 transformed growth rings (years); x1, diameter at
682 base (cm); x2, plant height (m); x3, northing (northing/10000). Shading indicates Models used for estimating stand time since fire (Supplementary
683 Material Part A). n = 99
2 Numbered Model a a(se) b b(se) c c(se) d d(se) adj. r AIC
Diameter at base
1. y1 = a + bx1 -4.549 1.59 6.288 0.24 0.877 427.7
2. y1 = a + bx1 + cx 3 244.8 70.7 6.437 0.23 -0.383 0.11 0.890 417.6
3. y1 = a + bx1 + cx 3 + dx 1x3 251.0 156 5.452 22.0 -0.392 0.24 0.0015 0.03 0.889 419.6
4. y2 = a + bx1 1.718 0.15 0.595 0.02 0.882 -44.1
5. y2 = a + bx1 + cx 3 19.94 6.68 0.606 0.02 -0.028 0.01 0.890 -49.5
6. y2 = a + bx1 + cx 3 + dx 1x3 10.05 14.7 2.180 2.08 -0.013 0.02 -0.0024 0.00 0.889 -48.1
7. y3 = a + bx1 0.691 0.03 0.110 0.00 0.839 -342.1
28 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 8. y3 = a + bx1 + cx 3 2.509 1.53 0.111 0.01 -0.003 0.00 0.842 -341.5
9. y3 = a + bx1 + cx 3 + dx 1x3 -2.770 3.31 0.952 0.47 0.005 0.01 -0.001 0.00 0.843 -342.8
Plant height
10. y1 = a + bx2 -7.396 1.77 8.261 0.33 0.870 432.0
11. y1 = a + bx2 + cx 3 261.0 73.0 8.469 0.31 -0.412 0.11 0.885 420.7
12. y1 = a + bx2 + cx 3 + dx 2x3 335.2 178 -5.590 30.8 -0.536 0.27 0.022 0.05 0.884 422.5
13. y2 = a + bx2 1.363 0.13 0.799 0.02 0.916 -78.3
14. y2 = a + bx2 + cx 3 22.02 5.54 0.815 0.02 -0.032 0.01 0.926 -90.0
15. y2 = a + bx2 + cx 3 + dx 2x3 17.82 13.5 1.610 2.34 -0.025 0.02 -0.0012 0.00 0.925 -88.1
16. y3 = a + bx2 0.609 0.03 0.151 0.01 0.906 -397.0
17. y3 = a + bx2 + cx 3 2.942 1.16 0.153 0.01 -0.004 0.00 0.909 -399.1
18. y3 = a + bx2 + cx 3 + dx 2x3 -2.106 2.78 1.109 0.48 -0.004 0.00 -0.0015 0.00 0.912 -401.2
Diameter at base and plant height
19. y1 = a + bx1 + cx 2 -6.522 1.59 3.553 0.72 3.774 0.96 0.895 411.4
20. y1 = a + bx1 + cx 2 + dx 3 268.8 64.0 3.610 0.66 3.915 0.88 -0.423 0.10 0.912 395.4
21. y2 = a + bx1 + cx 2 1.411 0.13 0.198 0.06 0.549 0.08 0.924 -87.9
29 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 22. y2 = a + bx1 + cx 2 + dx 3 22.46 5.19 0.203 0.05 0.560 0.07 -0.032 0.01 0.935 -102.0
23. y3 = a + bx1 + cx 2 0.612 0.03 0.013 0.01 0.135 0.02 0.906 -396.1
24. y3 = a + bx1 + cx 2 + dx 3 2.970 1.16 0.013 0.01 0.136 0.02 -0.004 0.00 0.909 -398.4
684
30 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 685
686
687 Fig. 1. Map showing the location of the Great Western Woodlands and coverage of fire
688 history mapping
689
40 2 (Adj. r = 0.992, F 1,55 = 7158, P < 0.0001) Time since fire = -0.890 + 0.9695(growth rings) 95% Confidence Band Expected relationship (y = x) 30
20
Timesince (years) fire 10
0 0 10 20 30 40 690 Mean growth rings per plant
691 Fig. 2. Relationship between Eucalyptus salubris time since fire and growth rings, compared
692 with the expected relationship if each ring is equivalent to one year. The strong positive
693 relationship indicates that growth rings can be used to estimate plant age.
31 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 200
150
100
50 Time sinceTimefire/growth rings
0 0 5 10 15 20 25 694 Diameter at base (cm)
695 Fig. 3. Relationship between years since fire/growth rings and diameter at the base in
696 Eucalyptus salubris , showing the effect of choice of transformation of growth rings on
697 estimated times since fire of long-unburnt plots. x = samples of known age (from Landsat); ▲
698 = samples dated by growth ring counts; solid line, Rings = -4.549 + 6.288(Diameter)
699 (untransformed growth rings, Model 1; Table 1); dashed line, Rings = [(1.718 +
700 0.595(Diameter)]2 (square-root transformed growth rings, Model 4). The dotted lines show
701 95% prediction intervals for Model 1.
702
32 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm (a)
100
80
Eucalyptus salubris vegetation associations 60 Plus additional aligned vegetation associations
40
Percentagewoodlandof area 20
0 0-5 6-10 11-15 16-20 21-25 26-30 31-37 38-60 >60 703 Age class (years)
(b) 30 Eucalyptus salubris vegetation associations Plus aligned vegetation associations y = 21.29e -0.0025x 25
20
15
10 Percentage of woodland area woodland of Percentage 5
0 0-60 61-99 100-149 150-199 200-249 250-299 300-349 350-399 704 Age class (years)
33 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm (c) 25
20 Eucalyptus salubris vegetation associations Plus aligned vegetation associations y = 8.564e -0.0011x
15
10
Percentage of woodland area woodland of Percentage 5
0 0 60 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 >1001 705 Age class (years)
706 Fig. 4. Age-class distribution of Eucalyptus woodlands in the Great Western Woodlands,
707 derived from: (a) known age class distribution from fire boundaries mapped from Landsat
708 imagery (Glen Daniel, Fire Management Services, DEC, unpublished data); (b) predicted age-
709 class distribution based on the assumption that the age of unburnt woodlands (> 60 years post-
710 fire) is proportional to that of the 36 plots whose age was estimated through growth ring
711 counts or growth ring-size relationships in E. salubris using Model 2 (untransformed growth
712 rings predicted by diameter + location,Table 1; Supplementary Material Part A); and (c)
713 predicted age-class distribution calculated as above using Model 5 (square-root transformed
714 growth rings predicted by diameter + location). Note that some columns cover different time
715 spans than the majority, due to the irregular timing of earlier Landsat imagery, and that age-
716 class scales differ between Fig. a and b-c. Percentages were calculated for two aggregations of
717 mapped vegetation units: (i) those listing E. salubris as a dominant species; and (ii) these and
718 additional units with the frequently co-occurring E. salmonophloia , E. longicornis and/or E.
719 transcontinentalis . Alternative theoretical age-class distributions are superimposed on these
720 estimated age-class distributions: (i) a fixed proportion per age class using the method of
34 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 721 Richardson et al. (1994) based upon optimal mean fire intervals of 400 (Fig. 4b) and 1050
722 (4c) years (dashed line); and (ii) a negative exponential distribution (solid line; Johnson and
723 Van Wagner 1985) based upon fire cycles of 250 (Fig. 4b) and 600 (4c) years, and maximum
724 fire intervals of 400 (Fig. 4b) and 1050 (4c) years.
725
35 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 726 Supplementary Material
727
728 Estimating the time since fire of long-unburnt Eucalyptus salubris (Myrtaceae) stands in
729 the Great Western Woodlands
730
731 Carl R. Gosper A,B,C , Suzanne M. Prober B, Colin J. Yates A and Georg Wiehl B AScience
732 Division, Department of Environment and Conservation, Locked Bag 104, Bentley Delivery
733 Centre, WA 6983, Australia.
734 BCSIRO Ecosystem Sciences, Private Bag 5, Wembley WA 6913 Australia
735 CCorresponding author. Email: [email protected]
736
36 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 737 Supplementary Material Part A . Estimated time since fire for plots not sampled for
738 growth rings .
739 Estimated time since fire (years ± SE of single-trunked E. salubris from modified point-
740 centred quarter samples; see Methods) was calculated by extrapolation of the relationship
741 between (i) untransformed growth rings and diameter (Model 1; Table 1, Fig. 3); (ii) square-
742 root transformed growth rings and diameter (Model 4; Fig. 3); (iii) untransformed growth
743 rings and diameter + northing (Model 2); (iv) square-root transformed growth rings and
744 diameter + northing (Model 5); and (v) square-root transformed growth rings and diameter +
745 height + northing (Model 22).
Model number (Table 1) Evidence
of fire in
Plot 1 4 2 5 22 1972
GIM01 24 ± 2.3 20 ± 2.0 26 ± 2.4 22 ± 2.1 33 ± 1.9 Yes
GIM02 39 ± 2.9 35 ± 3.2 42 ± 3.0 38 ± 3.4 40 ± 2.9 Yes
GIM04 140 ± 13 250 ± 40 140 ± 13 260 ± 41 150 ± 22 No
GIM08 250 ± 27 740 ± 135 A 260 ± 28 770 ± 140 A 280 ± 41 No
GIM13 180 ± 15 400 ± 55 190 ± 15 420 ± 57 200 ± 25 No
GIM17 120 ± 11 190 ± 33 120 ± 11 200 ± 34 100 ± 11 No
GIM18 230 ± 12 590 ± 53 230 ±12 610 ± 54 240 ± 24 No
GIM22 150 ± 11 270 ± 36 150 ± 11 280 ± 37 120 ± 12 No
GIM23 48 ± 3.6 45 ± 4.9 48 ± 3.7 46 ± 5.1 56 ± 3.7 Yes
37 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm GIM27 200 ± 12 470 ± 50 200 ± 12 490 ± 52 170 ± 12 No
GIM28 240 ± 15 630 ± 66 240 ± 15 650 ± 68 230 ± 21 No
GIM29 240 ± 23 690 ± 131 A 240 ± 23 690 ± 134 A 230 ± 29 No
GIM31 230 ± 33 690 ± 176 A 230 ± 34 690 ± 180 A 220 ± 38 No
GIM34 200 ± 15 470 ± 60 200 ± 15 470 ± 61 170 ± 18 No
GIM35 180 ± 14 410 ± 54 180 ± 14 410 ± 55 160 ± 18 No
GIM36 29 ± 2.7 24 ± 2.6 24 ± 2.8 21 ± 2.4 31 ± 2.9 Yes
GIM38 180 ± 25 430 ± 97 180 ± 25 420 ± 98 160 ± 26 No
GIM40 140 ± 17 260 ± 56 140 ± 17 260 ± 56 120 ± 17 No
GIM43 170 ± 19 350 ± 74 160 ± 19 350 ± 75 130 ± 17 No
GIM45 160 ± 5.1 320 ± 18 160 ± 5.2 320 ± 18 120 ± 7.3 No
GIM46 210 ± 30 530 ± 131 210 ± 31 550 ±136 200 ± 35 No
GIM48 35 ± 2.6 30 ± 2.6 35 ± 2.6 30 ± 2.7 38 ± 3.2 Yes
GIM49 86 ± 11 110 ± 24 88 ± 12 110 ± 25 84 ± 7.5 No
GIM50 210 ± 24 530 ± 99 220 ± 24 550 ± 103 230 ± 20 No
GIM52 200 ± 12 450 ± 49 200 ± 13 470 ± 51 230 ± 14 No
GIM53 110 ± 6.9 160 ± 17 100 ± 7.0 150 ± 17 100 ± 11 No
GIM55 230 ± 20 620 ± 95 230 ± 20 620 ± 96 220 ± 24 No
38 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm GIM57 210 ± 27 550 ± 125 210 ± 27 550 ± 127 160 ± 23 No
GIM58 370 ± 20 1440 ± 143 A 370 ± 21 1460 ± 146 A 350 ± 33 No
GIM61 170 ± 17 370 ± 71 170 ± 18 390 ± 73 160 ± 24 No
GIM68 180 ± 16 400 ± 57 190 ± 16 420 ± 59 200 ± 21 No
GIM69 200 ± 5 480 ± 22 210 ± 5.5 500 ± 23 230 ± 18 No
GIM70 290 ± 36 940 ± 187 A 300 ± 37 970 ± 194 A 310 ± 41 No
GIM71 250 ± 21 700 ± 105 A 250 ± 21 710 ±108 A 240 ± 22 No
GIM72 270 ± 43 800 ± 225 A 270 ± 43 820 ± 232 A 200 ± 91 No
746 APlots with a more uncertain estimated time since fire, due to small changes in trunk diameter
747 causing large changes in estimated time since fire with square- root transformation of
748 growth rings (Clarke et al. 2010). Until more information on the time since fire of the
749 longest-unburnt plots becomes available, it may be prudent to regard these plots as having
750 an age of > ~ 650 years.
751
39 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm 752
(a) 350
300
250
200
150
Numbertrees of 100
50
0 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 65-70 >70 753 Diameter at base size class (cm)
(b) 120
100
80
60
40 Number of trees Number of
20
0 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 >13 754 Height size class (m)
755 Supplementary Material Part B. Frequency distribution of sizes of single-trunked
756 Eucalyptus salubris : (a) diameter at the base; (b) tree height. The arrow indicates the largest
757 individual sampled with a complete growth ring record. The proportion of individuals larger
758 than the maximum of any trunk with a complete growth ring record was 35.4% for diameter
759 at the base, and 16.1% for plant height. The maximum of any trunk with a complete growth
760 ring record was 12.3% of the largest trunk diameter measured, and 56% of the tallest tree
761 measured.
762
40 For the definitive version of this paper, go to: http://www.publish.csiro.au/paper/BT12212.htm