Plant Ecology 169: 1–20, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.

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Spatial segregation of pines and oaks under different fire regimes in the Sierra Madre Occidental Andrew Park Groupe de Recherche en Écologie Forestiére, Université du Québec à Montréal, C.P. 8888, succ. Centre-Ville, Montréal, H3C 3P8, Québec, Canada (e-mail: [email protected]; e-mail: [email protected]; phone: (416) 925 4935) Received 29 March 2001; accepted in revised form 14 July 2002

Key words: Community segregation, Fire ecology, Neighborhood effects, Ripley’s K (t) analysis, Spatial pattern analysis Abstract Surface fire can modify spatial patterns and self-thinning in pine-oak ecosystems. Spatial pattern analyses were used to compare pattern development and interspecific spatial interactions in trees and seedlings in five Madrean pine-oak stands with different recent fire histories. Interspecific and intraspecific patterns were compared in small (< 15 cm dbh) and large (< 15 cm dbh) diameter classes of the pines (Pinus durangensis, P. teocote, and P. leiophylla) and oaks (Quercus sideroxylla, Q. crassifolia, and Q. laeta) that collectively dominated the five stands. Numbers of juvenile trees in 2.5 × 2.5 m subplots were correlated with cumulative distances to adult trees. Small pine and oak trees were intraspecifically clustered at all scales, irrespective of fire regime. Large pines were strongly clustered only in stands with longer fire-free intervals, and patterns of large versus small pine trees were regular or random in frequent fire stands. These patterns were consistent with fire-induced mortality of maturing trees under frequent fire. Large and small pines were segregated from small oaks at short and long distances in one stand with a 32-year fire-free interval, implying that two or more dynamic factors had produced regular patterns at different scales. Such regular spatial patterns at short distances were not seen in other stands. Therefore, there was little evidence for direct competition between oaks and pines. The results reported here are consistent with studies from other pine-oak ecosystems showing that different fire regime and site factors interact to influence stand development processes and relative dominance of pines and oaks. In some stands, the continued absence of fire could foster increasing tree densities and an intensification of local neighborhood effects, producing segregation of pine and oak species at longer distances. Introduction Periodic natural disturbances such as fire can structure spatial patterns among trees in forest ecosystems. For example, fire-induced mortality of Quercus laevis (turkey oak) in Florida sand hills tends to be concentrated under large Pinus palustris (longleaf pine) trees, causing post-fire clumping of surviving small oaks over short distances (Rebertus et al. 1989a). The increased segregation occurs because hot fires in pyrogenic litter of P. palustris kill smaller Q. laevis close to the pines (Rebertus et al. 1989b). A contrasting process has been suggested to generate spatial

patterns in the pine-oak forests of the Sierra Madre Occidental. Fulé and Covington (1998) found that oaks and pines over 1.3 m tall were more intraspecifically aggregated on fire-excluded sites than on a site that experienced frequent fire (Fulé and Covington 1998). They proposed that frequent fires thin clumps of juvenile and pole-stage trees, creating more random adult distributions. Pines and oaks appear to have different mechanisms for survival in ecosystems prone to frequent fire. Many pines resist fire through adaptations such as thick bark and self pruning. By contrast, oaks are fire endurers; that is, adult and juvenile oaks are eas-

2 ily killed by fire but they persist by vigorous resprouting from roots (Barton 1999). In the Sierra Madre Occidental, southwest USA, Mediterranean Europe and Florida sandhills, long fire-free intervals appear to favor root-sprouting by oaks over the germination of pine from seed (Platt et al. 1988; Fulé and Covington 1994, 1997, 1998; Barton 1995, 1999; Zavala et al. 2000). Vigorous sprouting of Quercus cambii and Q. rhyzophylla was observed following a standreplacing fire in the Sierra Madre Oriental (Esparza and Pérez (1999), Esparza personal communication). Root sprouting oaks, such as Quercus hypoleucoides (silverleaf oak) rapidly recover their pre-fire abundance in Arizona canyons (Barton 1999). Quercus laevis can gain dominance over pines in the Florida sandhills by continuous sprouting from roots (Rebertus et al. 1993). The effects of surface fires are distributed unevenly in space (Rebertus et al. 1989a; Bunnell 1995) and time (Rebertus et al. 1993; Glitzenstein et al. 1995). In the Sierra Madre Occidental, long fire-free intervals or fire suppression appear to foster dense populations of juvenile and adult trees. A greater proportion of these dense tree populations consists of oaks and less fire adapted species such as Pseudotsuga menziessii and Abies durangensis (Fulé and Covington 1997). Season of burning and variability of fire-return intervals can affect the relative dominance of P. palustris and Q. laevis in Florida (Rebertus et al. 1993; Glitzenstein et al. 1995). Site factors, such as gradients of dry season water stress, or variations in soil and topography, affect the establishment of drought-sensitive Quercus ilex and drought-tolerant Pinus halapensis in Mediterranean forests (Zavala et al. 2000). Pines in the Sierra Madre Occidental reproduce exclusively from seed (Perry 1991), but Madrean oaks are capable of regenerating from prolific root sprouts. (Fulé and Covington (1998), J. R. Bacon, personal communication). Madrean pines and oaks also have, respectively, the resister and evader characteristics noted above (A. Park, personal observation). They may therefore become segregated by firegenerated spatial mortality patterns or interspecific competition. Alternatively, spatially discrete microhabitats may favor one or the other mechanisms of regeneration. Finally, foresters in the Sierra Madre believe that the broad crowns of mature oaks limit the establishment of juvenile pines. Tests of spatial segregation have been used to investigate competitive interactions (e.g., Duncan and

Stewart (1991) and Martens et al. (1997), Moeur (1997)), and the effects of fire (Rebertus et al. (1989a, 1989b)). As noted above, differences in fire regime can affect densities, spatial patterns, and therefore, interspecific interactions of pines and oaks. Here, I attempt to clarify the role of different recent fire regimes in the development of intraspecific and interspecific spatial patterns of pines and oaks in the Sierra Madre Occidental. Five stands differing in the number of fires that had occurred since 1880, and in the time that had elapsed since the most recent fire, were chosen for study. Pine and oak populations were expected to have different spatial distributions under different fire regimes because of their contrasting mechanisms for persisting in fire-prone landscapes. Spatial patterns were also expected to differ between large and small trees because of size-specific differences in their vulnerability to the effects of fire. Therefore, spatial pattern was analyzed at multiple spatial scales on two diameter classes of mature trees, and on juvenile trees less than 3 m in height to test the following hypotheses: • H1 Frequent fires will produce random or regular spatial patterns amongst large (> 15 cm dbh) pines and oaks if fire-induced mortality (versus competitive self-thinning) disperses spatial patterns among trees as they mature. • H2 Small ( ⭐ 15 cm dbh but taller than 3 m) pines will be clustered over short distances in recent/frequent fire stands because surface fire creates a patchwork of mineral-soil microsites favoring pine germination. • H3 Regular spatial patterns between different species of large versus small trees will occur at short distances in all fire regimes if large trees inhibit the establishment of small trees through crown or root competition. • H4 Regular spatial patterns will be observed between large versus small pines, and large pines versus small oaks if frequent fire enhances juvenile tree mortality beneath large pines. Specific predictions for spatial patterns that would be observed in support or refutation of these hypotheses under different fire regimes are given in Table 1.

3 Table 1. Specific predictions for spatial patterns that would support or refute hypotheses. Hypothesis

Prediction if hypotheses supported

Prediction if hypotheses refuted

H1 Large pines and oaks randomly distributed in recent/frequent fire stands.

Random or regular distribution in frequent fire stands, but not in long fire-free interval stands Strong clumping of pines ⭐ 15 cm dbh in recent/frequent fire stands, but not in long fire interval stands. Regular patterns observed between oaks and pines, different oak and different pine species under all fire regimes at short distances

Expect random or regular distributions in all stands.

H2 Small pines more clumped in recent/ frequent fire stands than in stands with long fire-free intervals. H3 Large and small trees of different species adopt regular patterns at short distances under crown or root competition. H4 Fire-enhanced mortality of small pines and/or oaks beneath large pines.

Regular patterns between large pines and small pines/oaks observed in frequent fire stands only.

Pines could be clumped in all stands, be more clumped under long fire intervals, or be distributed at random. Patterns between different species could be clumped or random at short distances, or regular patterns only in frequent fire stands (see H5) Random or clumped patterns between large pines and small pines and/ or oaks in frequent fire stands.

Figure 1. Map showing Durango within Mexico and relative positions of study sites.

Methods Study sites and species The five research sites were in a pine-oak forest comanaged by an ejido (a community with collective property rights over its forests, Taylor (2000)). They were located in the Sierra Madre Occidental between latitudes 24°23⬘ – 24°36⬘ N and longitudes 105°37⬘ – 105°50⬘ W (Figure 1) at altitudes of 2460–2560 m a.s.l. The area receives 800–1200 mm per year of summer monsoon rains. Frequent surface fires, over 60 percent of which occur in the spring (Fulé and

Covington 1997, 1998) are widespread in the Sierra Madre Occidental (Fulé and Covington (1996, 1999); Park 2001). Crown fires also occur, and these can be extensive in extreme Southern Oscillation years (Fernández and García-Gil 1998; Rentería Anima and Domínguez Moreno 1999; Fulé et al. 2000). Study sites were chosen to represent a range of recent fire regimes from among 29 stands for which the dates of the most recent fires were known (Park 2001). Three types of stand were identified: stands on 20–50% slopes that had experienced recent, frequent fires (Recent Fire 1 and Recent Fire 2), (ii) stands on slopes of 10–38% in which fires occurred 24 (In-

4 Table 2. Numbers and basal areas of pines, oaks, stumps and snags in the five study sites. Numbers and basal areas (shown in brackets) ha −1 are shown to compare the different sizes of plots. All pine and oak species counted in the stand are included. Stand

Pines ha −1

Oaks ha −1

Total ha −1 (inc. stump)

Stumps ha −1 (Regen. Cut)

Snags ha −1

Recent Fire 1 Recent Fire 2 Intermediate Fire Old Fire 1 Old Fire 2

753 772 475 300 797

183 203 419 404 536

936 (23.76) 975 (22.38) 894 (32.66) 704 (21.24) 1333 (39.97)

208 133 144 176 419

58 17 69 44 31

(21.17) (18.83) (21.39) (13.61) (27.95)

(2.59) (3.55) (11.27) (7.63) (12.02)

termediate Fire) and 42 years before sampling (Old Fire 1), and (iii) a single stand (Old Fire 2) on 0–12% slopes that experienced its most recent fire 32 years before sampling (Table 2). Basal areas of mature trees varied between 21 m 2 ha −1 in Old Fire 1 to 40 m 2 ha −1 in Old Fire 2 (Table 2). All stands had recently received regeneration cuts under the Method of Silvicultural Development silvicultural system (MDS, Rodriguez et al. (1993) and Instituto Nacional de Estadistíca, G.e.I.I. (1997)). The regeneration cut is a commercial harvest that is supposed to improve the light environment for natural pine regeneration while removing 38–64% of stand basal area (Park 2001). Regeneration cuts applied to the five study sites had removed 5–13 m 2 ha −1 of stand basal area. The study sites contained 14–16 species of pines, oaks, junipers and Arbutus. However, in all stands, three pine and three oak species accounted for 76–93 percent of all mature stems, and these were the ones used for spatial analysis. The pines, Pinus durangensis Mart., P. teocote Schl. et Cham.and P. leiophylla Schl. et Cham. are Diploxylon or hard pines that reach heights of 25–40 m (Perry 1991). They have characteristics of self-pruning, thick bark and non-serotinous cones that are shared by pines that experience predictable surface and stand-thinning fires (Keeley and Zedler 1998). The oaks were Quercus sideroxylla Humboldt and Bonpland, Q. crassifolia Humboldt and Bonpland and Q. laeta Liebmann (Trelease 1924). Quercus sideroxylla is the most widespread oak in the region, reaches heights of 25 m or more and often dominates lower slopes and valley bottom sites (Park 2001). Quercus laeta and Q. crassifolia are shorter trees with spreading crowns that tend to occupy dry upland sites. All three are capable of regenerating from root sprouts as well as seed (A. Park personal observation).

(7.99) (7.56) (6.78) (6.86) (15.54)

(3.18) (0.41) (2.85) (3.54) (2.18)

Field methods A 0.36 ha plot was established in each of four study sites and one 0.25 ha. plot in the remaining site, the smaller size of this plot being dictated by topographic restrictions. Each plot was subdivided into 10 × 10 m subplots. In each plot, mature trees were mapped to the nearest decimeter with reference to the corners of the 10 × 10 m subplots. Their final positions were adjusted to plane after accounting for slope angle. Mature pines were defined as trees greater than 3 m tall. Mature oaks were either over 3 m tall or greater than 5 cm in diameter at breast height (dbh) if less than 3 m in height. All other trees, including first year seedlings, were counted as juveniles. Tree diameters were measured at a height of 1.3 m, or at 20 cm if the tree was a stump, and the presence of fire scars and charcoal staining was noted when these were present. Stem maps of juveniles were not be made because large numbers of stems were present (up to 12,000 juveniles ha −1 in frequent fire stands, see Table 3). Instead, they were sampled by counting juvenile trees less than 3 m tall within contiguous 2.5 × 2.5 m subplots. Fire history Fire history was determined from wedges cut from fire scarred live trees and complete sections taken from fire-scarred stumps (between 5 and 15 in each plot). These were sanded with belt and orbital sanders using progressively finer grit papers, and finished manually with fine-grit emery cloth. Tree ring increments were measured beneath a binocular microscope connected to a video monitor and a computerized data recording program to record the data. Locations of fire scars and possible false rings were noted. Skeleton plots and graphs were prepared to establish the locations of narrow increments used as markers in the cross-dating process. These were visually cross-dated

5 Table 3. Abundance of regenerating seedlings and saplings of dominant species in 0.36 and 0.25 ha plots, adjusted to numbers of plants per hectare for comparative purposes. Species

Pinus durangensis Pinus teocote Pinus leiophylla Quercus sideroxylla Quercus crassifolia Quercus laeta Dead Pines Other Species Totals

STAND Recent Fire 1

Recent Fire 2

Intermediate Fire

Old Fire 1

Old Fire 2

3361 994 – 839 – 219 756 951 7120

3150 1144 – 369 1489 – 31 3448 9631

178 6 842 2539 8 – 8 2136 5717

168 200 – 76 1000 924 12 1204 3584

194 153 128 1639 0 3 6 856 2978

against each other, against increment cores from dominant trees in the same stand, and with reference to master series from sites near Topia, 200 km. northwest of my study area (Fulé and Covington 1997). Fire scar records from stumps were initially dated as floating tree ring series using the COFECHA program (Grissino-Mayer and Holmes 1993). Cross-dating was also checked using COFECHA. Mean fire intervals were calculated for the periods 1880 to 1999 and their statistical qualities analyzed using the FHX2 fire analysis program (Grissino-Mayer 1995). Statistical analysis Ripley’s K(t) and K( 12t) analyses (Ripley 1977; Diggle 1983; Upton and Fingleton 1985) were used to test hypotheses 1, 2, 3, and 4. These analyses were done using computer software developed by Moeur (1993, 1997). The K(t) and K( 12t) analyses compare the distributions of all possible tree to tree distances within a species (K(t)) or between two species (K( 12t)) with their random expectation (assumed to follow a Poisson distribution) to determine whether an observed pattern is regular, random or clustered. The pattern is assessed over a range of discrete distance classes (t i–k) that may be as long as half the length of the shortest side of a plot. Distance classes t i–k represent the radii of circles and K(t) is calculated for all inter-tree distances less than the radius of each t i. If the resulting pattern is random, K(t) = ␲t 2, which is simply the area of a circle with radius t. Trees that lie outside the plot, and which are therefore not counted, nevertheless influence the patterns of trees within the sampling area. For this reason an edge correction is applied to the K(t) equation (Diggle

1983; Haase 1995; Moeur 1997). The K(t) are then subjected to a variance-stabilizing transformation: Lt i ⫽ 冪共K共t i兲/␲ ⫺ t

(1)

This transformation has an expectation of zero under a Poisson distribution and takes values greater than or less than zero for clustered and regular distributions, respectively. To test for departure from randomness, the measured L(t i–n) are measured against the expectation of L( ti-n) under the null (Poisson) distribution using confidence envelopes derived by random permutation of the actual data. Dominant pines and oaks were divided into two size classes for spatial analysis. Diameter classes were those ⭐ 15 cm dbh and those > 15 cm dbh. This division point was selected to separate pole-sized pines, which were obviously clustered in some stands, from older pines which generally appeared more isolated, and may have undergone self-thinning. The same division was applied to oaks to provide a common basis for all analyses. The former breast height diameters of pine and oak stumps were estimated using linear regression (Sokal and Rohlf (1981), r 2 = 0.97–0.99, p ⭐ 0.0001 for all species, n = 83–129). If fewer than twenty trees were present in any diameter class in a plot, the two classes were amalgamated because K(t) statistics may be less reliable when measured on too few inter-tree distances (Fulé and Covington 1998). Univariate L(t) analyses on individual diameter classes were used to test Hypotheses 1 and 2. Hypotheses 3 and 4 were tested on trees using L 12(t) on all possible intraspecific and interspecific combinations of the two diameter classes. Tests were conducted on

6 Table 4. Fire return intervals at the five study sites for all recorded fires since 1880 (from Park- in review). Statistics were calculated for all fire years, including those represented by a single scar. Stand

Recent Fire 1 Recent Fire 2 Intermediate Fire Old Fire 1 Old Fire 2 *

Number of fires

13 14 5 10 7

Time since last fire *

6 13 24 42 32

FIRE INTERVALS (years)

Mean interval (MFI)

Std. Dev.

Min.

Max.

Weibull median Interval

100% Weibull hazard

8.3 7.5 11.5 7.1 13.1

4.1 4.0 1.7 5.9 9.2

3 2 10 3 5

15 16 14 22 21

8.0 7.1 11.6 6.3 11.9

26.0 28.5 12.8 180.1 349.4

Time since fire is reported as the interval from the last fire to the year of sampling.

1 m distance classes (t i) ranging from 0–1 m to 29–30 m in 0.36 ha plots and from 0–1 to 24–25 m distance classes in the 0.25 ha plot. Two sided confidence envelopes were calculated at ␣ = 0.05 for each distance class using 200 Monte-Carlo simulations in which the largest and smallest 2.5% of values were discarded at each t. Hypothesis 4 was also tested on juvenile trees. Pearson correlation coefficients were calculated between numbers of juveniles in 2.5 × 2.5 m subplots and the cumulative distance from subplot centers to the closest five adult trees in each diameter class. To allow for edge effects, subplots from a 10 m buffer zone at the edge of each plot were excluded from analysis. Juvenile tree counts in subplots were assumed to be autocorrelated. Therefore, Clifford et al.’s (1989) modified t-test of association, as corrected by Dutilleul (1993), was used to test the significance of the correlation coefficient. In place of the N-2 degrees of freedom generally used to calculate the t-test, the modified t-test employs an estimate of “effective sample size” that accounts for autocorrelation between variables. Correlation coefficients and modified tests of significance were calculated using software developed by Legendre (2000).

Results Fire history Fire return intervals ranged from 2 to 23 years between 1880 and the date of the most recent fire (Table 4). A minimum of 6 years (Recent Fire1) and a maximum of 42 years (Old Fire 1) had elapsed be-

Figure 2. Numbers of charcoal-stained (white) and fire-scarred trees (black) found in four 0.36 ha plots and one 0.25 ha plot. Note that a different scale has been used in Recent Fire 1 for clarity.

tween the most recent fire and the year of sampling. Recent Fire1 had experienced the most widespread recent fire, as shown by the large number of charcoal stained trees in this stand (Figure 2). Fire scars penetrating the cambium were much less frequent than charcoal staining in Recent Fire 1, indicating that the widespread 1993 fire was of low intensity. Recent Fire 2 experienced more recorded fires than Recent Fire 1 since 1880, but evidence of fire in this stand was more localized. In stands where longer fire-free periods had followed the most recent fire, few trees with dateable scars were found. Statistics derived from the two-parameter Weibull distribution describe the probabilities of recurring fires (Table 4). The Weibull median interval is the time interval during which the stand has a 50% probability of burning once again. It is less influenced by large fire intervals than is the mean. The 100% Weibull hazard estimates the maximum fire-free interval before the stand is expected to burn again. Long 100% Weibull hazard intervals, such as those for Old Fire 1 and Old Fire 2 should be interpreted cautiously since skewed fire interval distributions can

7

Figure 3. Fire scar records in the five study plots. Numbers over triangles represent the number of fire-scar samples on which dating was based. Stand codes: RF1 – Recent Fire 1, RF2 – Recent Fire 2, INTF – Intermediate Fire, OF1 – Old Fire 1, OF2 – Old Fire 2.

bias estimates of the longest possible interval (Grissino-Mayer 1999). Distributions in Old Fire1 and Old Fire 2 that featured a few long fire intervals among a general pattern of short ones led to 100% Weibull hazards 25 and 27 times greater than the mean return intervals. In Old Fire 2, frequent fires between 1932– 1949 (Figure 3) led to a low mean return interval despite this stand having the longest recent fire-free period. K(t) and K( 12t) analysis The pine-oak stands in this study were characterized by complex, often contrasting, sets of spatial patterns. The character of these patterns differed between species, size classes within species, and between size classes of different species. A synopsis of the patterns and their conformity to the hypotheses is shown in Table 5. Univariate patterns used to test hypotheses 1 and 2 are reported in Table 6, and the bivariate patterns that tested hypotheses 3 and 4 are shown in Table 7. In interpreting conformity of a pattern to an hypothesis, both significant deviation from randomness and the consistency of that variation across distance classes must be considered. Patterns that depart inconsistently or at only a few points from random expectation should be interpreted more cautiously than patterns that are nonrandom across a wide range of contiguous distance

classes. The strength of departure from randomness can also be judged visually from graphs that superimpose L t lines against 95% confidence envelopes calculated by Monte Carlo simulation. Hypothesis 1 was supported by the strong clustering of big P. durangensis and P. teocote over a wide range of t i in Old Fire 2 (Figure 4a). However, large trees of these two species were also weakly clustered at 2–7 m in Recent Fire1 (Figure 4b) and (P. durangensis only) in Recent Fire 2. Large pines were clustered across a much greater range of distance classes in Old Fire 2 than in Recent Fire stands. In Figure 4a, clustered values for large P. durangensis in Old Fire 1 lie far above the upper boundary of the 95% confidence envelope. The corresponding L t pattern for large P. durangensis in Recent Fire 1 (Figure 4b) shows only weak departure from random expectation. Small pines were significantly clustered in most distance classes in all stands, irrespective of fire history. This clustering was consistent (Table 6) and pronounced (Figures 4c,d), indicating that contagious recruitment from juvenile stages to pole-sized trees has occurred under a variety of fire regimes and topographic/soil conditions. Hypothesis 2 was therefore not supported, and factors independent of recent fire regime must have contributed to observed distributions of pines ⭐ 15 cm dbh.

8 Table 5. Synopsis of main results of hypothesis testing. Hypothesis

Result/comments

H1 Large pines and oaks randomly distributed in recent/frequent fire stands.

Supported: large pines dispersed in Recent Fire 1 and 2 in comparison to patterns in Old Fire 1 and 2. However but large pines still clustered between 2–7 m. in recent fire stands. Rejected: small pines clumped at almost every scale, irrespective of stand. Rejected, except in Old Fire 2 and Intermediate Fire. In Old Fire 2, regular patterns developed between large P. teocote and small Q. sideroxylla. In Intermediate Fire, juvenile oaks and pines were less abundant close to small oaks. Supported for pines in Recent Fire 1 and Recent Fire 2 but not for oaks. Dead juvenile pines in Recent Fire 1 located closer to adults, but live juveniles generally located away from adults. Weakly supported. Weak to moderate segregation of pine and oak nearest neighbours in Recent Fire 1, Intermediate Fire and Old Fire 2 only.

H2 Small pines more clumped in recent/frequent fire stands than in stands with long fire-free intervals. H3 Large and small trees of different species adopt regular patterns at short distances under crown or root competition.

H4 Fire-enhanced mortality of small pines and/or oaks beneath large pines. H5 Potential for intraspecific competition between seedlings greater under frequent fire regimes.

Clustered patterns among small trees of all three oak species indicated contagious recruitment similar to that observed in pines. In Recent Fire 2 small Q. crassifolia were clustered at all t I, while large trees of this species were randomly distributed at all scales. In Old Fire 1, Q. laeta and Q. crassifolia were strongly clustered at all scales (Table 6). There were no consistent spatial patterns between large oaks in those stands where they were sufficiently numerous to be tested. Patterns ranged from regular (large Q. sideroxylla in Intermediate Fire, Figure 4e) through completely random (large Q. crassifolia in Recent Fire 2) to clustered (large Q. sideroxylla in Old Fire 2, Figure 4f). These patterns may have been influenced by marked differences in oak population densities in the various plots. The Q. sideroxylla in Recent Fire 1 were few in number, small and weakly clustered at shorter distances. Large Q. sideroxylla were clustered from 4–16 m in Old Fire 2 (Table 6). Hypothesis 3 was rejected for trees in 4 out of 5 stands because regular distributions of pines versus oaks did not occur consistently at short distances (Table 7). An exception was the regular pattern for large P. teocote versus small oaks in Old Fire 2 at 2–30 m (Figure 5a). Regular spatial patterns were also observed between small P. teocote and small P. durangensis versus small Q. sideroxylla at 14–30 m and 4–13 m respectively (Figure 5b). However, large P. durangensis, which were clustered with P. teocote (Table 7), were distributed at random with respect to

small Q. sideroxylla at all distances. Also in opposition to the expectations of Hypothesis 3, large and small P. teocote were significantly clustered with Q. laeta at distances greater than 4 m in Old Fire 1 (Figure 5c). Clustered patterns of Q. laeta versus Q. crassifolia were also observed in Old Fire 1, suggesting some habitat affinity between all three species. Large versus small oaks were distributed at random in all stands at short distances, but large and small Q crassifolia were clustered between 21 and 30 m in Recent Fire 2 (Table 7). Hypothesis 4 (fire-induced mortality beneath large pines) was supported by the occurrence of regular patterns between large and small pines at short distances in recent fire stands. This tendency was most pronounced in large P. durangensis versus small P. durangensis (Figure 5d) and small P. teocote (Table 7). Large versus small P. teocote did not display regular distributions at short distances in Recent Fire 1, but were significantly clustered from 19–23 m (Figure 5e). In contrast, large versus small P. durangensis were strongly clustered at 3–30 m in Old Fire 2 (Figure 5f). Large versus small P. teocote were also clustered at 1–10 m in the same stand (Table 7). Large versus small P. leiophylla were distributed at random across most distance classes. Significant clustering in scattered distance classes in small versus large P. leiophylla at 2 m in Intermediate Fire could have arisen fortuitously. Random distributions of P. leiophylla versus all other species were also observed in Old Fire 2, implying that seed dispersal

9 Table 6. Kt analysis of pines and oaks in five stands with different fire histories. Trees described as “B” were ⭓ 15 cm. dbh while those described as “Sm” were ⭐ 15 cm dbh; “St” represents stumps. Species codes are Pidu – P. durangensis, Pite – P. teocote, Pile – P. leiophylla, Qusi – Q. sideroxylla, Qucr – Q. crassifolia and Qula – Q. laeta. Statistical signicance at the 95% level is shown as follows: ‰ – clustered distribution, ˆ – regular distribution, – – not significant. Distance (m)

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Recent Fire 1 Pidu B (n = 33) Pidu Sm (n = 100) Pite B (n = 20) Pite Sm (n = 73) Qusi All (n = 32) Pinus spp. St (n = 54)

– ‰ – ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ –

‰ ‰ ‰ ‰ – –

‰ ‰ ‰ ‰ – ‰

‰ ‰ ‰ ‰ – ‰

– ‰ ‰ ‰ – ‰

‰ ‰ – ‰ ‰ –

– ‰ – ‰ ‰ –

– ‰ – ‰ – –

– ‰ – ‰ – –

– ‰ – ‰ – 䡬

– ‰ – ‰ – 䡬

– ‰ – ‰ – –

– ‰ – ‰ – –

– ‰ – ‰ – –

– ‰ – ‰ – –

– ‰ – ‰ – –

– ‰ – – – –

– ‰ – – – –

– ‰ – – – –

– ‰ – – – –

– ‰ – – – –

– ‰ 䡬 䡬 – –

– ‰ 䡬 䡬 – –

– ‰ 䡬 䡬 – –

– ‰ 䡬 䡬 – –

– ‰ 䡬 䡬 – –

– ‰ 䡬 䡬 – –

– ‰ – 䡬 – –

Recent Fire 2 Pidu B (n = 27) Pidu Sm (n = 100) Pite All (n = 69) Qucr B (n = 20) Qucr Sm (n = 45) Pinus spp. St (n = 42)

– ‰ ‰ – ‰ ‰

‰ ‰ ‰ – ‰ ‰

‰ ‰ ‰ – ‰ –

‰ ‰ ‰ – ‰ ‰

‰ ‰ ‰ – ‰ ‰

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

䡬 ‰ ‰ – ‰ –

䡬 ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

䡬 ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

– ‰ ‰ – ‰ –

䡬 ‰ ‰ – ‰ –

䡬 ‰ ‰ – ‰ –

䡬 ‰ ‰ – ‰ –

䡬 ‰ ‰ – ‰ –

䡬 ‰ ‰ – ‰ –

䡬 ‰ ‰ – ‰ –

Intermediate Fire Pile B (n = 97) Pile Sm (n = 49) Qusi B (n = 40) Qusi Sm (n = 106) Pinus spp. St (n = 48)

– – – ‰ –

– – – ‰ –

– – – ‰ –

‰ ‰ – ‰ ‰

‰ ‰ – ‰ ‰

‰ ‰ – ‰ –

‰ ‰ – ‰ –

‰ ‰ – ‰ –

– ‰ – ‰ –

– ‰ – ‰ –

‰ ‰ – ‰ –

– ‰ – ‰ ‰

– ‰ – ‰ –

‰ ‰ – ‰ –

‰ ‰ 䡬 ‰ –

– ‰ 䡬 ‰ –

– ‰ 䡬 ‰ –

– ‰ 䡬 ‰ –

– ‰ 䡬 ‰ –

– ‰ – ‰ –

– ‰ – ‰ –

– ‰ 䡬 ‰ –

– ‰ 䡬 ‰ –

– ‰ – – –

– ‰ – – –

– ‰ – – –

– ‰ – – –

– ‰ – – –

– ‰ – – –

– ‰ – – –

Old Fire 1 Pite B (n = 20) Pite Sm (n = 24) Qucr All (n = 42) Qula All (n = 59) Pinus spp. St (n = 23)

– – ‰ ‰ –

‰ ‰ ‰ ‰ –

‰ ‰ ‰ ‰ –

‰ ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰

Old Fire 2 Pidu B (n = 22) Pidu Sm (n = 31) Pile B (n = 38) Pile Sm (n = 62) Pite B (n = 38) Pite Sm (n = 20) Qusi B (n = 50) Qusi Sm (n = 137) Pile St (n = 47) Pinus spp. St (n = 135)

– ‰ – ‰ – ‰ – ‰ ‰ ‰

– ‰ – ‰ ‰ – – ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ – – ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰

– ‰ ‰ ‰ ‰ ‰ ‰ ‰ – ‰

– ‰ ‰ ‰ ‰ ‰ – ‰ – ‰

– ‰ ‰ ‰ ‰ ‰ – ‰ – ‰

– ‰ ‰ ‰ ‰ ‰ – ‰ – ‰

– ‰ ‰ – ‰ ‰ – ‰ – ‰

– ‰ ‰ – ‰ ‰ – ‰ – ‰

– ‰ ‰ – ‰ ‰ – ‰ – –

– ‰ ‰ – ‰ ‰ – ‰ – –

– ‰ ‰ – ‰ ‰ – ‰ – –

– ‰ ‰ – ‰ – – ‰ – –

– ‰ ‰ – ‰ – – ‰ – –

– ‰ ‰ – ‰ – – ‰ – –

– ‰ ‰ – ‰ – – ‰ – –

– ‰ ‰ 䡬 ‰ – – ‰ – –

patterns in this species occurred independently from the dispersal of other species. Stem maps were used as aids in interpreting differences in spatial patterns in Old Fire 2 (Figure 6)

and Recent Fires 1 and 2 (Figure 7). These stem maps showed that four abundant species in Old Fire 2 were concentrated in different map quadrants. Small and large P. durangensis were concentrated in the north-

10

Figure 4. Example plots of distance vs. L(t) that compare and contrast intraspecific spatial patterns. Solid line is L(t) while dotted lines represent upper and lower 2.5% limits of the 95% confidence interval.

east quadrant (Figure 6a). Small Q. sideroxylla were strongly clustered in the northwest quadrant (Figure 6b). Large and small P. teocote were concentrated in the south and east (Figure 6d). This contrasts with both recent fire stands, where clusters of small trees appeared to occupy less space than those in Old Fire 2, and large trees were distributed more evenly (Figure 7).

Correlations Correlations between juvenile tree counts and the cumulative distance to the five closest trees in each diameter class were generally low (from 0.00 to +0.34 and −0.28, Table 8). Almost all correlations had Type I error probabilities higher than ␣ = 0.05 because autocorrelation had reduced effective degrees of freedom. However, the distribution of negative and posi-

11

Figure 5. Example plots of distance vs. L( 12t) that compare and contrast interspecific and between-diameter-class spatial patterns in different stands. Solid line is L( 12t) while dotted lines represent upper and lower 2.5% limits of the 95% confidence interval.

tive correlations (Table 8) was consistent with spatial patterns in large versus small adult trees that supported Hypothesis 4. In Recent Fire 1, plots with more dead juvenile pines tended to be closer to adult pines. Live juvenile pines in both recent fire stands tended to be located further away from adult trees, or had no specific spatial associations. In Intermediate Fire and Old Fire 1,

correlations showed that juvenile pines were growing somewhat apart from adult pines. In contrast, juvenile pines tended to grow closer to adult pines of all species in Old Fire 2. Juvenile Q. sideroxylla were more numerous at greater distances from adult pines in several cases, but displayed no tendency to grow closer to adult oaks. By contrast, Quercus crassifolia showed a gen-

12 Table 7. Bivariate K( 12t) analyses of species and diameter classes in five stands with different fire histories. Trees described as “B” were ⭓ 15 cm. dbh while those described as “Sm” were ⭐ 15 cm dbh. Species codes are Pidu – P. durangensis, Pite – P. teocote, Pile – P. leiophylla, Qusi – Q. sideroxylla, Qucr – Q. crassifolia and Qula – Q. laeta. Statistical signicance at the 95% level is shown as follows: ‰ – clustered distribution, 䡬 – regular distribution, – – not significant. Distance (m)

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Recent Fire 1 Pidu B vs Pidu Sm Pidu B vs Pite Sm Pidu Sm vs Pite B Pite B vs Pite Sm Pite B vs Pidu B Pite Sm vs Pidu Sm Pidu B vs Qusi All Pidu Sm vs Qusi All Pite B vs Qusi All Pite Sm vs Qusi All

– – – – – ‰ – – – –

– – – – ‰ ‰ – – – –

䡬 – – – ‰ ‰ – – – –

䡬 – – – ‰ ‰ – – – –

䡬 – – – ‰ ‰ 䡬 – – –

䡬 – – – ‰ ‰ 䡬 – – –

䡬 䡬 – – ‰ ‰ – – – –

䡬 䡬 – – ‰ ‰ 䡬 – – –

䡬 䡬 – – ‰ ‰ – – – –

䡬 䡬 – – – ‰ – – – –

䡬 䡬 – – – ‰ – – – –

䡬 䡬 – – – – – – – –

䡬 䡬 – – – – – – – –

䡬 䡬 – – ‰ – – – – –

䡬 䡬 – – ‰ – – – – –

䡬 䡬 – – – – – – – –

䡬 䡬 – – – – – – – –

– – – – – – – – – –

– – – ‰ – – – – – –

– – – ‰ – – – – – –

– – – ‰ – – – – – –

– – – ‰ – – – – – –

– – – ‰ – – – – – –

– – – – – – – – – –

– – – – – – – – – –

– – – – – – – – – –

– – – – – – – – – –

– – – – – – – – – –

– – – – – – – – – –

– – – – – – – – – –

Recent Fire 2 Pidu B vs Pidu Sm Pidu B vs Qucr B Pidu B vs Qucr Sm Pidu Sm vs Qucr B Pidu Sm vs Qucr Sm Pite All vs Pidu B Pite Sm vs Pidu B Pite Sm vs Pidu Sm Pite Sm vs Qucr B Pite Sm vs Qucr Sm Qucr B vs Qucr Sm

– – – – – – – ‰ – – –

䡬 – – – – – – ‰ – – –

䡬 – – – – – – ‰ – – –

– – – – – – 䡬 ‰ – – –

– – – – – – 䡬 ‰ – – –

䡬 – – – – – 䡬 ‰ – – –

䡬 – – – – – 䡬 ‰ – – –

䡬 – – – – – 䡬 ‰ – ‰ –

䡬 – – – – – 䡬 ‰ – ‰ –

䡬 – – – – – – ‰ – ‰ –

䡬 – – – ‰ – – ‰ – ‰ –

– – – – ‰ – – ‰ – ‰ –

– – – – ‰ – – ‰ – ‰ –

– – – – ‰ – – ‰ – ‰ –

– – – – ‰ – – ‰ – ‰ –

– – – – ‰ – – ‰ – ‰ –

– – – – ‰ – – – – ‰ –

– – – – ‰ – – – – ‰ –

– – – – ‰ – – – – ‰ –

– – – – ‰ – – – – ‰ –

– – – – ‰ – – – – ‰ ‰

– – – – ‰ – – – – – ‰

– – – – ‰ – – – – – ‰

– – – – ‰ – – – – – ‰

‰ – – – – – – – – – ‰

‰ – ‰ – – – – – – – ‰

‰ – ‰ – – – – – – – ‰

‰ – ‰ – – – – – – – ‰

‰ – ‰ – – – – – – – ‰

‰ – ‰ – – – – – – – ‰

Intermediate Fire Pile B vs Pile Sm Pile Sm vs Qusi B Pile B vs Qusi Sm Pile B vs Qusi B Pile Sm vs Qusi Sm Qusi Sm vs Qusi B

– – – – – –

‰ – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

‰ – – – – –

‰ – – – – –

‰ – – – – –

‰ – – – – –

Old Fire 1 Pite B vs PiteSm Pite B vs Qucr All Pite Sm vs Qucr All Pite B vs Qula All Pite Sm vs Qula Sm Qucr All vs Qula All

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – ‰ ‰

– – – – ‰ ‰

– – – – ‰ ‰

– – – – ‰ ‰

– – – – ‰ ‰

– – – – ‰ ‰

– – – ‰ ‰ ‰

– – – ‰ ‰ ‰

– – – – ‰ ‰

– – – – ‰ ‰

– – – ‰ ‰ ‰

– – – ‰ ‰ ‰

– – – ‰ ‰ ‰

– – – ‰ ‰ ‰

– – – ‰ ‰ ‰

– – – ‰ ‰ ‰

– – ‰ ‰ ‰ ‰

– – ‰ ‰ ‰ ‰

– – ‰ ‰ ‰ ‰

– – ‰ ‰ ‰ ‰

– – ‰ ‰ ‰ ‰

Old Fire 2 Pidu B vs Pidu Sm Pidu B vs PileB Pidu B vs Pile Sm Pidu Sm vs PileB Pidu Sm vs Pile Sm Pidu B vs Pite B Pidu B vs Pite Sm Pidu Sm vs Pite B Pidu Sm vs Pite Sm Pidu B vs Qusi B Pidu B vs Qusi Sm Pidu Sm vs Qusi B Pidu Sm vs Qusi Sm Pile B vs Pile Sm Pile B vs Qusi B Pile B vs Qusi Sm Pile Sm vs QusiB Pile Sm vs Qusi Sm Pite B vs Pite Sm Pite B vs Pile B Pite B vs Pile B Pite B vs Pile Sm Pite Sm vs Pile B Pite Sm vs PileSm Pite B vs Qusi B Pite B vs Qusi Sm Pite Sm vs Qusi B Pite Sm vs Qusi Sm Qusi Sm vs Qusi B

– – – – – – – – – ‰ – – – – – – – – ‰ – – – – – – – – – –

– – – – – – – – ‰ – – – – – – – – – ‰ – – – – – 䡬 䡬 – – –

‰ – – – – – – – ‰ – – – – – – – – – ‰ – – – – – – 䡬 – – –

‰ – – – – – – – ‰ – – – 䡬 – – – – – ‰ – – – – ‰ – 䡬 – – –

‰ – – – – – – – ‰ – – – – – – – – – ‰ – – – – – – 䡬 – – –

‰ – – – – – – – ‰ – – – 䡬 – – – – – ‰ – – – – – – 䡬 – – –

‰ – – – – – – – ‰ – – – 䡬 – – – – – ‰ – – – – – – 䡬 – – –

‰ – – – – – – – ‰ – – – 䡬 – – – – – ‰ – – – – – – 䡬 – – –

‰ – – – – – – – ‰ – – – 䡬 – – – – – ‰ – – – – – – 䡬 – – –

‰ – – – – – – – ‰ – – – 䡬 – – – – – ‰ – – – – – – 䡬 – – –

‰ – – – – – ‰ – ‰ – – – 䡬 – – – – – – – – – – – – 䡬 – – –

‰ – – – – – ‰ – ‰ – – – 䡬 – – – – – – – – – – – – 䡬 – – –

‰ – – – – – ‰ – ‰ – – – 䡬 – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – – – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – – – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – ‰ – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

‰ – – – – – – – ‰ – – – – – – – – – – – – – – – – 䡬 – 䡬 –

13

Figure 6. Stem maps for dominant pine and oak species in RF1 (A/B), and RF2 (C/D). Codes: black circles = small trees; open circles = large trees; triangles in B = Q. laeta.

eral tendency to grow closer to adult conspecifics and adult P. teocote in Old Fire 1. Juvenile Q. crassifolia also tended to be associated with adult Q. laeta in Old Fire 1, but Q. laeta juveniles were negatively correlated with both Q. crassifolia and adult conspecifics. Juvenile Q. sideroxylla tended to grow away from small conspecific adults and P. leiophylla in Intermediate Fire. Juvenile P. leiophylla displayed the same tendency in Intermediate Fire, but the opposite tendency in Old Fire 2. Juvenile Pinus teocote tended to be more numerous in plots that were close to adult oaks in recent

fire stands. Juvenile P. durangensis were also associated with short distances to adult Q. sideroxylla in Recent Fire 1. In Old fire 2, no such correlations were observed, and in Old Fire 1, P. teocote was more numerous away from adult Q. laeta, and was not associated with adult Q. crassifolia. Taken together, these observations suggest that fire regime, species composition and site characteristics interact to produce contrasting intraspecific and interspecific interactions between juvenile and mature trees.

14

Figure 7. Stem maps for dominant pine and oak species in DF2. Codes: black circles = small trees; open circles = large trees.

Discussion Spatial pattern analysis revealed patterns that supported Hypothesis1 (random distribution of large pines and oaks), and spatial correlations provided weak support for Hypothesis 4 (enhanced mortality under large pines; see Table 1 and Table 5). Hypotheses 2 (small pines more clumped in recent fire stands) and hypothesis 3 (root competition between different species) were rejected. Significant clustering among small pines in every stand, and regular patterns of pines versus oaks in Old Fire 2 implied eco-

logical causes not tested in hypotheses 2 and 3. The ability to infer the causes of the observed patterns was limited, however, by the unreplicated treatments and retrospective nature of the analysis. Interpretations in this study should therefore be considered most relevant to the unique combinations of stand history and species composition represented by the sites (see Platt et al. (1988)). Results also cannot be extended beyond the maximum scale of measurement. Nonetheless, scales of analysis used in this study accord with results of other temperate forest studies that report significant spatial interactions up to about 30 m (Bon-

Pidu Pite Pile Qusi

−0.14 −0.25 −0.17 −0.01

129 54 50 64

0.108 −0.10 181 0.07 −0.22 68 0.227 −0.11 64 0.939 0.08 94

df

r

p

r

df

Pidu > 15

Pidu ⭐ 15

Old Fire 2

0.118 0.27 34 0.190 0.17 65 0.17 −0.22 34

0.27 33 0.16 64 −0.23 34

Pite Qula Qucr

df

r

p

r

df

Pite > 15

Pite ⭐ 15

0.34 28 0.24 49

Old Fire 1

0.273 0.22

0.22 26 0.18 47

df

r

r

df

Qusi ⭐ 15 p

0.825 −0.03 45 0.920 −0.02 51 0.330 0.02 70

Pile (All)

−0.04 34 −0.01 44 0.13 52

df

Pile Qusi

Int. Fire

Pidu Pite Qucr

p

r

df

r

38 68 79 113

Pidu > 15

−0.06 −0.03 −0.18 −0.02

Pidu ⭐ 15

0.330 0.430 0.811 0.685

Recent Fire 2

104 79 82 114

−0.10 0.09 −0.02 −0.04

df

r

p

r

df

Pidu > 15

Pidu ⭐ 15

Pimt Pidu Pite Qusi

Recent Fire 1 r

df

0.01 39 0.02 44 0.10 60

df

0.00 32 0.02 59

df

r

df

Qula (All)

r

Qusi > 15

r

r

df

0.187 −0.15 140 0.074 −0.24 53 0.361 −0.24 51 0.445 0.03 78

p

Pite ⭐ 15

0.119 0.33 32 0.182 0.13 67 0.188 −0.33 31

p

0.067 0.088

p

0.853 0.906 0.840

p

Pite (All)

0.731 −0.17 39 0.770 0.06 76 0.080 0.11 65 0.800 0.14 127

p

Pite ⭐ 15 r

df

0.10 43 0.06 48 0.09 40

df

r

df

Qucr (All)

r

r

df 0.068 0.04 192 0.073 0.04 133 0.086 −0.19 64 0.787 0.09 86

p

Pite > 15

0.063 −0.01 38 0.289 0.20 63 0.065 −0.28 37

p

0.99 0.879

p

0.951 0.895 0.430

p

Qucr ⭐ 15

0.290 −0.19 45 0.652 0.01 94 0.380 0.00 94 0.127 0.01 138

p

Pite > 15 r

df

r

df

r

df

Pile ⭐ 15

0.540 −0.07 160 0.674 −0.07 81 0.134 −0.22 67 0.419 0.07 80

p

0.954 0.106 0.081

p

0.509 0.09 59 0.683 −0.15 44 0.559 −0.15 52

p

Qucr > 15

0.27 0.07 47 0.961 −0.15 66 0.961 −0.26 68 0.903 0.03 155

p

Qusi (All) r

df

r

df

Pile > 15

0.314 0.04 207 0.514 0.16 76 0.072 −0.13 73 0.520 0.08 254

p

0.460 0.32 0.28

p

0.627 −0.19 41 0.228 0.24 63 0.030 −0.02 82 0.692 0.15 113

p

r

df

All pine > 15

r

df 0.598 −0.01 142 0.173 0.01 59 0.27 −0.15 52 0.314 0.08 94

p

Qusi ⭐ 15

0.221 −0.11 39 0.056 0.00 59 0.87 −0.18 82 0.118 0.00 162

p

All pine ⭐ 15

r

df

Qusi > 15

0.920 0.01 167 0.455 0.09 59 0.28 −0.09 58 0.435 0.08 125

p

0.508 0.993 0.098 0.960

p

0.874 0.460 0.489 0.390

p

Table 8. Correlation coefficients between numbers of juveniles in 2.5 × 2.5-m subplots and distance to the nearest five trees in each diameter class. Effective degrees of freedom and p-values were calculated using Dutilleul (1993) modified t-test. Species acronyms are as in Table 6 and Table 7. Sample sizes were 256 for 0.36 ha plots and 144 for the 0.25 ha plot.

15

16 nicksen and Stone 1981; Kenkel 1988; Platt and Rathbun 1993; Biondi et al. 1994; Peterson and Squiers 1995). Univariate spatial pattern analysis supported a role for fire in determining differences in tree distributions in recent fire versus old fire stands. The stronger clustering of small and large pines in old fire stands compared to the small fire stands suggested that different fire regimes had modified juvenile survival, thinning of maturing pine cohorts, and interspecific interactions among adult trees. Dispersed patterns of large pines in frequent fire stands versus strongly clustered patterns in Old Fire 2 were consistent with fire-induced mortality of maturing trees under frequent fire (Hypothesis 1). Regular distributions of large versus small pines in frequent fire stands supported the possibility that pyrogenic litter enhances young tree mortality beneath large pines (Hypothesis 4). The tendency for dead and living juvenile pines to be located, respectively, closer to and further away from adult pines in Recent Fire 1 was also consistent with the expectations of Hypothesis 4. Living P. teocote juveniles tended to be closer to adult Q. sideroxylla, implying that fire temperatures could be cooler beneath oaks, as is the case for Q. laevis in Florida (Platt et al. 1991). Juvenile oaks were not consistently less abundant in plots that were closer to mature pines, however, in contrast to juvenile oak distributions in P. palustris-Q. laevis stands (Rebertus et al. 1989a, 1989b). Small pines and oaks were clustered over all except the shortest distance classes in every stand. Differences in fire regime do not, therefore, provide a complete explanation for the distribution patterns of small trees (Hypothesis 2). However, different fire regimes may have affected the distribution of large trees. Clustering among large pines and large oaks in Old Fire 2 may have arisen because infrequent fires allowed more young trees to survive into larger size classes than in frequent fire stands. This result agrees with Fulé and Covington (1998) finding of greater intraspecific tree aggregation at sites without a recent history of frequent fires. There was no evidence that high tree densities in Old Fire 2 had led to increased mortality because few standing dead trees were present (Table 2). Mortality rates of adult trees in pine-oak ecosystems are generally low (Biondi 1996; Platt et al. 1988). If fire remains infrequent, tree densities may therefore continue to increase in old fire stands and Intermediate Fire. These conditions would encourage stands to

shift towards conditions characterized by slow growth, stagnating nutrient cycles, and increased crown fire hazard, as seen in ponderosa pine stands in the US southwest (Covington and Moore 1994; Covington et al. 1997; Fulé and Covington 1997). Proportions of adult oaks and juveniles were higher in stands with longer fire-free intervals. Longterm research in P. palustris-Q. laevis ecosystems shows that irregular fire intervals offer a “survival window” allowing oaks to grow out of the small size classes that suffer high mortality rates during frequent fires (Rebertus et al. 1993). Fire return intervals were more variable in old fire than in frequent fire stands, suggesting that Q. sideroxylla populations may be similarly favored by longer, less predictable fire intervals. Fire variability may also help to explain the nearrandom patterns among large pines in recent fire stands. Although 1–3 year interval fires in P. palustris stands cause mortality among juvenile pines (Rebertus et al. 1993), few P. palustris ⭓ 10 cm dbh are killed by fire (Platt and Rathbun 1993). In my study sites, fire scars generally affected no more than 1.5 m of the bowl of any fire-scarred tree. Charcoal staining was also three times more common than fire scarring in Recent Fire 1 (Figure 2). These observations imply that fire-induced mortality of small (polesized) trees is rare in these stands, and that only occasional intense fires could thin clusters of pole-sized trees sufficiently to produce random patterns. Such fires occur in ponderosa pine ecosystems (Fischer and Bradley 1987; Barnes et al. 1998), and in Mexico during Southern Oscillation extremes (Fulé et al. 2000; Fernández and García-Gil 1998). Stochastic variations in timing and intensity of fires may therefore be integral to maintaining the open character of warm-temperate pine and pine-oak ecosystems. There was little evidence for interspecific crown or root competition between large and small trees (Hypothesis 3). Exceptions were the regular patterns at short distances of large and small P. teocote and P. durangensis versus small Q. sideroxylla in Old Fire 2. Regular spatial patterns of P. teocote versus Q. sideroxylla also occurred at distances of up to 30 m in Old Fire 2, suggesting that two or more dynamic factors may have produced regular patterns at different scales. Regularity at short distances in Old Fire 2 may have been produced by the combined effects of crown and root competition. Niche partitioning and/or dispersal limitation are more likely, however, to have

17 produced regularity across longer distance classes in Old Fire 2. Different fire regimes, abetted by different site environments, may have influenced the scale and quality of interactions within and between species in Old Fire 2. Spatially explicit Markov models, (Frelich et al. 1998) show that 2–5 species exerting strong neighborhood effects can segregate into spatially distinct communities, even starting from random distributions in a uniform environment. Patches of high and low fire intensity (Rebertus et al. 1989a; Waldrop and Brose 1999; Platt et al. 1991) could have imposed small-scale patchworks of exposed mineral soil, residual litter, and live and dead trees (especially juveniles) across frequent fire stands. These patterns, imposed repeatedly and frequently, may have produced the discrete clusters of small trees, intermingling of species, and dispersed adult tree patterns seen in Figure 6. In contrast, deep, extensive litter layers that build up in the absence of fire would limit successful pine germination (Cain and Shelton 1998; Farmer 1997; van der Wall and Joyner 1998). The few seeds that did germinate under these circumstances would likely do so near to adult trees because most seeds fall at short distances from the parent tree (Rudis et al. 1978; Farmer 1997; Lanner 1998), perhaps leading to a concentration of the local species neighborhood. Increased neighborhood strength among small Q. sideroxylla may have developed because more root sprouts survived in the more variable fire regime. In Florida sandhills, small Q. laevis produce more sprouts than do large ones (Rebertus et al. 1993). A similar tendency in Madrean oaks might explain the large clusters of small trees in Old Fire 2, and the absence of spatial interactions between large and small Q. sideroxylla in Old Fire 2 and Intermediate fire. The spatial relationships and abundance patterns reported here support results from other pine-oak ecosystems where fire interacts with site characteristics to influence the quality of species relationships. In particular, strong clustering of large and small trees in Old Fire 2, and the dominance of oaks in Intermediate Fire and old fire stands support observations that infrequent fires favor oak accession and denser tree populations overall. In the pine-oak stands studied here, this generalization is complicated by the occurrence of different spatial patterns in different species/ size-class combinations, which themselves may have been modified by site character. Fire frequency is partly a function of site character and regional climate. Therefore these variables tend

to be confounded. A general model proposed to explain the role of regional climate predicts that establishment will be limited by available soil moisture on xeric sites, but that light will be the limiting resource in mesic environments (Holmgren et al. 1997; Callaway and Walker 1997). This model is supported in Mediterranean pine-oak systems, where drought-tolerant P. halapensis and shade-tolerant Q. ilex respectively dominate dry and wet ends of a regional drought gradient (Zavala et al. 2000). Barton (1992, 1993) found that the germination and survival of pine species, including P. leiophylla and P. ponderosa, were better in shaded microsites beneath nurse trees in Arizona’s Chiricahua Mountains. Pinus resinosa and P. strobus have also been found to establish preferentially beneath large Quercus robur (Kellman and Kading 1992). In my study, the tendency for P. teocote juveniles to be closer to oaks in recent fire stands could reflect cooler fire temperatures beneath oaks or the creation of more favorable soil moisture conditions in the generally coarse soils of recent fire stands. By contrast, the tendency of both juvenile P. leiophylla and Q. sideroxylla to be segregated from small Q. sideroxylla trees in Intermediate Fire may indicate root competition from dense clusters of small oak trees in this stand. Root competition from adult conspecifics is cited as restricting the distribution of Pinus palustris juveniles at distances beyond the radii of adult pine crowns (Brockway and Outcalt 1998), and as a competitive mechanism between large and small ponderosa pine in the Gus Pearson Natural Area, Arizona (Biondi 1996). Where fire has permitted tree densities to increase, root competition, detectable by spatial pattern analysis, may be more likely. Two qualitative models have been proposed to support the generalization that oaks experience a relative advantage where fire intervals are longer (Barton 1999; Rebertus et al. 1993). In both models, pine establishment from seed is favored under intermediate fire frequencies. In Barton’s model, derived from observations in mixed stands of Pinus engelmanii, P. leiophylla, Quercus hypoleucoides, Q. arizonica, Q. emoryi and Q. rugosa in Arizona, oaks are favored at very short and longer fire intervals. This speculation may be true for the extensive sprouting of Quercus cambii and Q. rhyzophylla after a rare stand-replacing fire in the Sierra Madre Oriental (Esparza and Pérez 1999). In Rebertus and colleagues’ model, P. palustris is favored by intermediate fires and low variance of the fire-return interval, but oaks were only

18 favored under long return intervals or shorter average intervals with high variance. In my study, fire frequency and variability appeared to be related to site. Fires were less frequent in low-ling sites with fine-textured soils. Oak dominance may therefore be inherent in Madrean pine-oak stands with this combination of fire regime and site quality (see also Barton (1999)). On the other hand, dominance by pines, especially P. durangensis and P. teocote, may be assured on more steeply-sloping sites with coarse soils as long as frequent fires continue. Understanding the interplay between fire regimes, site characteristics and species composition in pine-oak stands is therefore likely to be an essential precondition to the institution of improved forestry management in Madrean forests.

Acknowledgements I am grateful to the directorate and staff of Forest Conservation and Development Unit No. 4, and to the people of a Durango ejido for permission to study their forest, and for accommodation and friendship during my fieldwork. Thanks also to Nick Moss, who ably assisted in gathering the field data. In Durango, Lidia Orrante and her family provided friendship, company and good food. Jeff Bacon of Juarez University identified tricky oak specimens and provided insights into life and research in Mexico. I owe many thanks to Pete Fulé and Richard Joos, Dr William Platt (editor of Plant Ecology), and two anonymous reviewers for reviewing and greatly improving earlier drafts of this manuscript. Field work was partially supported by a Canada-Latin America Research Links Fellowship from the International Development Research Center, and a University of Toronto Open Fellowship.

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