111 Oak Ecosystem Restoration On

111

ISLAND SCRUB OAK (QUERCUS PACIFICA) POPULATION STRUCTURE AND DYNAMICS ON SANTA CATALINA ISLAND

Roland C. de Gouvenain* and Ali M. Ansary Department of Biological Sciences, Chapman University, One University Drive Orange, CA 92866 Present address of R. de Gouvenain: Department of Biology, Rhode Island College, Providence, RI 02908 Present address of A. Ansary: University of Cambridge, Downing College, Regent Street Cambridge, UK, CB2 1DQ *Correspondent: [email protected]

ABSTRACT: The purpose of our study was to describe the demographic structure and project the demographic trend of a sample of populations of the island scrub oak (Quercus pacifica) on Santa Catalina Island, and to determine if the low regeneration observed in some populations was associated with low tree fertility or low seedling recruitment and/or survival. Matrix projection modeling using tree ring data and two different fertility estimates produced a range of population intrinsic growth rates with no conclusive association with location on the island or several environmental variables. Demographic projections differed between fertility estimates calculated from acorn production or from seedling recruitment. The discrepancy between the two suggests that acorn germination and/or seedling survival and growth are not sufficient in some populations to ensure long term population maintenance. The low recruitment observed in several populations that also have low intrinsic rates of growth is cause for concern. Further studies could determine whether this low recruitment is due to low acorn germination or low seedling survival, or both.

KEYWORDS: Canonical correlation analysis, fertility, fire, matrix model, regeneration, soil.

INTRODUCTION

Monitoring of the island scrub oak (Quercus pacifica Nixon & Muller) woodlands of Santa Catalina Island by the Catalina Conservancy suggests that several populations have experienced tree dieback and low regeneration over the last decades, for reasons yet unknown (D. Knapp pers. com.). Possible reasons for the dieback include senescence, stress due to pollution, fungal infection, and lower rain or fog precipitation (or a combination of the above). Low regeneration may be caused by impacts of introduced animals such as mule deer and American bison, competition from exotic grasses, fungal infection, decline in moisture input, and/or fire suppression.

Several species of oak have been declining throughout North America and Europe in the last decades, and a variety of causal factors have been proposed depending on the region and the species. Human-caused changes in fire regimes (Abrams 2003; Jacqmain et al. 1999; Lorimer 1980), grazing practices (Bakker et al. 2004; Kelly 2002) and drought (Faberlangendoen and Tester 1993) were all found to be possible factors, among others. In California, Griffin (1971) found that acorn germination and seedling survival for several native oak species were influenced by slope aspect, ambient temperature, and competition from grasses, seed burial activity of birds and squirrels, and seedling predation by deer and pocket gophers. Also in California, Momen et al. (1994) found that grazing history and grass density (which can co-vary), influence the success of blue oak (Quercus douglasii) regeneration.

We investigated whether the putative decline of the island scrub oak is occurring island-wide or whether it is restricted to some of the populations, and whether poor regeneration is associated with low acorn production (low fertility) and/or lack of seedling establishment and survival. We hypothesized the following:

1. If a given population of scrub oak is declining, or has experienced poor sapling survival, we should observe a population structure skewed toward older (or larger) age (or size) classes. 2. The intrinsic rate of population increase (λ) calculated from matrix population models should be <1 for declining populations. 3. If population decline is mostly connected to tree senescence, we should observe overall low tree fertility typically associated with old trees.

The purposes of our study were to: (a) describe the demographic structure of a sample of scrub oak populations from the island-wide scrub oak metapopulation, (b) project demographic trends at the population and metapopulation scale, and (c) determine whether low reproduction is due to overall tree senescence and low fertility, or low germination/seedling survival. We also examined populations for records of past fires in the tree-ring record and in the soil profile to determine if fire had been part of the disturbance regime in the past.

METHODS

Field sampling

Using a map of island scrub oak-dominated areas produced by the Catalina Conservancy, we selected 10 study areas distributed throughout Catalina Island (Table 1; Figure 1). Within each study area, populations that were clearly identifiable within the landscape from a high vantage point were numbered in the field, and one population was randomly selected. Within the selected population, we numbered five clearly identifiable Quercus pacifica trees > 10-cm diameter (10 cm above ground, since Q. pacifica often branches just above the ground) and selected one randomly as our sample starting point.

Table 1. Geographic coordinates of the 10 populations sampled in this study. Three populations have no coordinates due to technical problems with GPS during sampling (refer to Figure 1).

Population No. Latitude / Longitude

1 33º 21’ 15" N / 118º 26’ 52" W 2 33º 19’ 34" N / 118º 28’ 16" W 3 No data (see map) 4 33º 23' 29.5" N / 118º 23' 49.6" W 5 33º 21' 50.2" N / 118º 27' 54.8" W 6 33º 27' 22.2" N / 118º 31' 36.5" W 7 No data (see map) 8 33º 23' 52.5" N / 118º 23' 53.1" W 9 No data (see map) 10 No data (see map)

Oak ecosystem restoration on Santa Catalina Island, California: Proceedings of an on-island workshop, February 2-4, 2007. Edited by D.A. Knapp. 2010. Catalina Island Conservancy, Avalon, CA.

Q. pacifica Population Structure and Dynamics 113

3 8

5 7 1

0 10 km Scale

Figure 1. Locations of the 10 sampled Quercus pacifica populations

We used the wandering-quarter method (Catana 1963) to collect data on 4 adult trees > 10-cm diameter and on the population. The method was modified by making the transect bearing from one tree to the next variable within a 90° window, and we selected the bearing randomly each time from a set of possible bearings with unique numbers. From each of the four trees, we collected two cores approximately 40-50 cm from the base of the tree at right angle from each other to the center of the trunk, and noted height of each core above ground.

Within a 5-m radius around each tree, we counted the number of Quercus pacifica seedlings < 50-cm tall to estimate tree fertility. We also estimated the number of acorns borne by each tree by first counting all acorns borne on a typical branch and multiplying by the number of branches; acorns on smaller branches were counted separately and added to the total. From approximately the middle of the wandering-quarter transect, we selected one additional random bearing constrained to a 90° window facing perpendicular to the transect and conducted a census of all Quercus pacific individuals within a 10×30-m belt transect in three basal diameter classes: < 5 cm (seedlings + saplings), 5-10 cm (young trees) and > 10 cm (mature trees). We repeated this procedure on the other side of the wandering-quarter transect, for a total of 600 m2 of belt transect sampling.

At each population, we dug a 50×50×50 cm soil pit and described the soil profile according to USDA (1993). We looked for evidence of charcoal in the A and B soil horizons. When dead trees were present within a population, we collected stem cross-sections for ring analysis and to look for fire scars.

Data analyses

The seedling count for population 1 was excluded from the analysis, due to an error in counting root sprouts as seedlings. All tree cores (4 trees × 2 cores × 10 populations = 80 cores total) were dried, mounted, sanded and the best core from each tree was analyzed with a Velmex® tree-ring measurement instrument under a stereo boom microscope. Tree ring increment data were measured and recorded into ring width time series (40 series total) and we charted them in Excel to cross-date (synchronize) the series among each other. When we found a fire scar, we recorded its estimated year of occurrence.

We used previously existing Quercus pacifica acorn germination and seedling growth data (Stratton, unpublished data) to determine: (a) seed germination rate (b) seedling survival rate, and (c) seedling growth rates. We then used the seedling growth rate information plus the growth rate, determined from tree ring analysis, to define a life cycle graph for Quercus pacifica which summarizes the general life history of that tree species, from seedling to mature tree (Figure 2). Stage survival rate (si) for stage 1 was estimated from our analysis of Quercus pacifica seedling survival data (Stratton, pers. comm.), and set as a constant for all 10 populations. We estimated si for stage 2 and 3 individually for each population from our census of living trees in each of the size classes corresponding to stage 2 through 4 in each -7 population. We set si for the terminal stage 4 at 110 (≈0) for all populations.

F4 F3

G G G 1 1 2 2 3 3 4

P1 P2 P3 P4 Seedlings Saplings Young trees Mature trees Age (years) 0-6 7-20 21-40 41-80 Diameter (cm) 0 - 1 1.1 - 5.0 5.1-10 10.1-25

Figure 2. Quercus pacifica life cycle graph

The life cycle graph (Figure 2), stage graduation rates, and fertility rates (see below) were then used to build a Lefkovich matrix A for each of the 10 modeled populations as:

 P1 0 F3 F4  G P 0 0  A =  1 2   0 G2 P3 0     0 0 G3 P4 

where Gi is the yearly probability of surviving and growing to the next stage, Pi is the yearly probability of surviving and remaining in the same stage, and Fi is the number of seedlings produced per tree per year in each fertile stage (see below). We set our projection time interval for matrix A equal to 1 year. We then used the matrix to project population growth for each of the 10 modeled populations for ten time intervals (ten years) using the linear equation:

n(t+1) = An(t) where n(t) is a vector of stage abundance at time t and n(t+1) is the projected vector of stage abundance at time t+1.

We calculated the rate of population increase () at the population and at the metapopulation scales as follows, assuming a post-breeding census model: we estimated each stage duration Ti as the number of years an oak tree would typically spend in a given stage through a regression analysis of tree age with tree diameter (Figure 3). We calculated i, the probability of survival of an individual in stage i per projection 1/Ti interval, as: i = (stage i survival) . Pi (the probability of surviving and staying in stage i), and Gi (the probability of surviving and growing from stage i to stage i+1), were calculated as per (Caswell 2001):

Gi = i  i Pi = i  (1  i)

where i is the probability of graduating = P(growth from i to i+1 | survival).   ( i )Ti  ( i )Ti -1 We estimated  =   by using the iterative calculation of  suggested by i  ( i )Ti -1  Caswell (2001), where  is the dominant eigenvalue of A and also the rate of increase of the modeled population.

For stages 3 and 4, average tree fertility (m) was estimated for each of the 10 sampled populations in two ways: (a) from the number of seedlings recorded around each of the four sampled trees and (b) from the number of acorns recorded for each of these trees times the germination success rate calculated from acorn/seedling trials (Stratton, pers. comm.). Stage fertility was then calculated as: Fi = Pimi + Gimi+1, where mi is the estimated fertility (number of seedlings produced per tree of stage i per year). We assumed that Fi = 0 for juvenile trees in stages 1 and 2. To determine to which life stage λ was most sensitive to, and therefore which stage would respond most to conservation efforts, we calculated elasticities (the proportional contribution of each matrix element to λ) (Caswell 2001).

Given the small size of Santa Catalina Island, the dynamics of the island-wide metapopulation of Quercus pacifica may be more relevant to the conservation of the species on the island than the individual population-level dynamics. We assumed that gene flow occurs among these population through cross- pollination and seed dispersal due to windy conditions and high habitat connectivity on the island. Populations growing in harsher habitats (possibly with low λ) may benefit from dispersal from populations with high λ growing in more productive habitats (Hanski 1999). We therefore estimated an island-wide metapopulation λ by pooling the demographic data across the sampled populations (excluding population 1) and by calculating an average seedling count and acorn crop per mature tree to estimate fertility.

120

100

Age (years) Age 40

0 0 5 10 15 20 25 Tree diameter (cm)

Figure 3. Relationship age-diameter for Quercus pacifica across all 10 populations, using data from 38 cored trees, 9 sapling cross-sections and 6 seedling data points from seedling trials (trials data provided by Lisa Stratton). Diameter is a significant predictor of age (p << 0.05, R2 = 0.56)) but data are heteroschedastic (variance is a function of diameter), so regression model must be interpreted with caution. For the seedling-sapling stages, the diameter-age relationship appears non-linear, probably because tree seedlings typically increase preferentially in height at a young age, and only later start growing in girth.

At the population level, we analyzed the overall relationship between intrinsic population attributes (λ, RGR, # trees < 5 cm diam, # trees 5-10 cm diam., number of trees > 10 cm diam., average number of acorns per tree and average number of seedlings per tree, presence of dieback and oldest tree age) and environment-related variables (soil horizon thickness, presence of charcoal in soil profile and presence of fire scar in tree cores) using Canonical Correspondence Analysis (CCA) (Gauch 1982; Jongman et al. 1995).

RESULTS

The demographic structure varied across the 10 sampled populations (Table 2). Average relative growth rate (RGR) of cored trees for the last 50 years varied slightly from one population to the next, between 1.52 and 1.69 mm per mm-year (Table 2). Regeneration varied substantially across populations, from 0 to 12 seedlings per tree ≥ 10 cm diameter on average (Table 2). Fertility (and thus potential regeneration), as measured by average acorn crop per mature tree within a given population, also varied among populations, with populations located on the east and south of the island exhibiting higher acorn crop (53 to 363 acorn per tree ≥ 10 cm diameter on average) than populations located on the west or north side of the island (20 to 83 acorns per tree ≥ 10 cm diameter, P < 0.05). This may be related to a trend toward thicker O and A soil horizons eastward and southward on the island, with western populations growing on less fertile soils with shallower O and A horizons (Figure 4). There appears to be a positive association

Table 2. Environmental, population and tree characteristics of 10 sampled populations of Quercus pacifica on Santa Catalina Island.

Population 1 2 3 4 5 6 7 8 9 10 Attribute General location on the island W W C E W N E E E S Aspect (˚) 360 n/a n/a 65 335 50 20 60 30 320 Slope (˚) 20 0 0 30 35 20 20 12 20 30 Presence of tree “dieback” no no yes no yes no yes no yes yes # trees < 5cm diam.§ 5 12 6 12 15 1 57 0 1 3 # trees 5.1 – 10 cm diam.§ 9 27 19 6 18 2 22 11 0 20 # trees > 10 cm diam.§ 6 37 39 1 11 8 82 35 5 30 Diam. of largest tree sampled (cm) 19.2 18.1 22.4 24.2 16.6 23.8 22.8 21.2 24.5 19.6 Age of oldest live tree cored (yrs) 98 72 103 39 73 66 81 85 98 85 Presence of fire scars in no no no no no no yes no yes no core/cookie Thickness O horizon (cm) 1 2 8 6 2 3 1 2 4 11 Thickness A horizon (cm) 7 8 12 14 6 9 8 8 10 14 Thickness B horizon (cm) 22 25 15 15 12 18 36 11 21 25 Presence of charcoal in soil profile yes no no no no no no no no no (Horizon) (A) Average RGR§§ (mm mm-1 year-1) 1.67 1.52 1.65 1.62 1.52 1.64 1.64 1.69 1.62 1.65 Total # of seedlings in four 5-m 47 0 0 12 4 2 3 2 26 10 radius samples around cored tree Average # of seedlings per 11.75 0 0 3 1 .5 .75 .5 6.5 2.5 sampled tree > 10 cm diam. (SD) (19.7) (0) (0) (3.4) (1.2) (1.0) (1.5) (1.0) (8.2) (1.3) Average # of acorns per sampled 20 35 43 338 83 53 53 343 363 281 tree > 10 cm diam. (SD) (40) (28) (85) (390) (117) (70) (66) (375) (363) (388)

§ In two 10 x 30 m belt transects = 600 m2 sample within each population §§ RGR = relative growth rate (of diameter)

P3 P3 P5

P10

P8 OhorOhor

AAhorhor

Axis 2 P7 BBhorhor

P4 P9

Axis 1

Figure 4. CCA ordination of intrinsic population (P) attributes (as “pseudospecies”) and environmental attributes. Environmental vectors (Ohor, Ahor, Bhor for O, A, and B horizon thickness, respectively) point away from the centroid of the ordination in directions of increasing value for these variables. Other environmental variables (presence/absence of charcoal in soil profile and of fire scar in tree cores) did not significantly contribute to the CCA ordination and are therefore not represented as vectors.

6 cm diam

10 10 5

Mean Mean # seedlings per tree > 0 0 100 200 300 400 Mean # acorns per tree > 10 cm diam

Figure 5. Association between mean # of acorns per tree > 10 cm diameter and mean # of seedlings produced by a tree > 10 cm diameter (R2 = 0.51) across 9 populations (population 1 excluded).

between average # of acorns per tree > 10 cm diameter and the average # of seedlings produced by trees > 10 cm diameter (Figure 5), but this association is not statistically significant (P > 0.05, R2 = 0.51) because of very high variance in seedling production for trees with high acorn crops.

The intrinsic rate of population increase (λ) was different depending on whether fertility was estimated using seedling or acorn counts, with the latter yielding higher λ estimates except for population 1, where seedling counts were probably inflated (as explained earlier). Mean λ estimates (from seedling and acorn counts) were higher overall for populations 4 and 8 (east side), and 10 (south side) (λ ≥ 1.05), suggesting these three populations are growing (Table 3), despite the fact that we observed some dieback in population 10. Mean λ estimates for populations 2, 3, 7, and 9 were all < 1.0, suggesting these populations are not growing, while mean λ estimates for populations 5 and 6 are both 1.01, suggesting these two populations are stable. Because of the relatively small sample size at each population, these population- level λ estimates should be interpreted with caution. The metapopulation-level λ estimate differed depending on whether seedling counts (λ = 1.07) or acorn counts (λ = 1.15) were used, with an average λ greater than 1.10, suggesting that the island-wide metapopulation is growing. For all populations, elasticity matrices (Appendix 1) suggested that changes in number of stage 3 trees (young adult trees with diameter between 5.1 and 10 cm and a 21-40 years-old age range) would have the most influence on λ, followed closely by stage 2 (saplings with diameter between 1.1 and 5 cm, and a 7-20 years-old age range).

Table 3. Finite rate of increase (λ) for populations 1 through 10, calculated using two estimates of tree fertility: from seedling counts under sampled adult trees and from acorn counts on sampled adult trees at each population. Populations are ranked by decreasing average λ. “Loc” column indicates general location of the population on the island.

Fertility Fertility Population Loc estimated from estimated from Mean seedling acorn production

4 E 1.03 1.10 1.07 10 S 1.01 1.09 1.05

8 E 0.97 1.10 1.04

§ 1 W 1.06 1.00 1.03 5 W 0.98 1.04 1.01 6 N 0.97 1.04 1.01 §§ 7 E 0.96 1.02 0.99

3 C 0.81 1.03 0.92 9§§ E 0.93 0.98 0.96 2 W 0.81 1.03 0.92 §§§ Metapopulation - 1.07 1.15 1.11

Of the environmental variables we measured, the CCA analysis suggested that only the thickness of the O and A horizons may have an association (albeit non-significant) with λ, and the 3 populations with the highest λ (populations 4, 8 and 10) are also those located in areas with thick top (O and A) soil horizons (Figure 4). Higher fertility of these three populations may be related to better soil development and thus higher soil fertility, although population 3, with relatively thick O and A horizons (Table 2), displayed a low λ (Table 3). B horizon thickness is less informative in this study since soil pit depth was limited to 50 cm, thus possibly truncating the actual thickness of that horizon at each population. We did not find any association between our estimate of λ and other population attributes or environmental variables, or with location of the population on the island (Table 2).

For two populations located on the eastern slopes of the island (populations 7 and 9), we found fire scars within tree cores and/or cross-sections collected on dead trees. In population 7, the fire scar indicated fire activity 31 years prior to the death of the tree, which we estimated to have occurred in 1995. This would place that fire event approximately in 1964. In population 9, fire scars we found in tree cores indicated that fires may have occurred around 1955 and 1972. In addition, charcoal was found in the A horizon at population 9, supporting the hypothesis that fire occurred in that stand, without necessarily killing trees. We did not find evidence of any fire activity (fire scars of soil charcoal) in any of the other 8 populations.

DISCUSSION

Our results show no clear association between population intrinsic growth and location on the island. Eastern populations, while exhibiting more “dieback” than other populations on the island, have the potential for good regeneration from higher acorn production (Table 2). The discrepancy between estimated fertility rates based on acorn production and germination and survival rates on one hand, and

Oak ecosystem restoration on Santa Catalina Island, California: Proceedings of an on-island workshop, February 2-4, 2007. Edited by D.A. Knapp. 2010. Catalina Island Conservancy, Avalon, CA. Q. pacifica Population Structure and Dynamics 121 fertility rates based on seedling count on the other hand, suggests that, if there is lack of regeneration overall, it is not due to low fertility rates of adult trees. Low seedling counts may reflect natural mast- seeding cycles, common among oak species (Healy et al. 1999; Sork 1993) and/or ecosystem conditions that negatively affect acorn germination and/or seedling survival, such as low acorn burial activity by birds or rodents, high seedling predation by herbivores, or competition from grasses. Low seedling regeneration rates may also be an artifact of including only seedlings in the regeneration stage. This may not be appropriate when describing the demographic structure of Quercus pacifica populations, for which much of the regeneration appears to occur from root sprouting. By including only seedlings, we may have underestimated overall regeneration on the island and thus the rate of population increase as well.

If poor ecosystem conditions are to explain the discrepancy between estimated population growth from fertility estimates and from seedling counts, lambda estimates from seedling counts are probably more realistic and are cause for concern in populations that have both low recruitment and low intrinsic rate of growth (populations 6 and 9 for instance). Exotic grass cover on the eastern side of the island may contribute to a reduced acorn germination and/or survival of oak seedlings. Grass removal experiments within scrub oak population, either mechanically or with prescribed burning, may help test this hypothesis (see Stratton, this volume). While fire is a difficult tool to use for several reasons, adult Quercus pacifica trees have survived ground fires on the eastern side of the island in the past, suggesting that some types of fires are not fatal to scrub oak populations, and may possibly improve ground conditions for acorn germination and seedling survival. Timing of prescribed burns and pre-burn site preparation would be critical in protecting existing seedlings and/or saplings.

Careful management of bison grazing could be attempted as well to keep grass cover down on the eastern side of the island. While continued heavy bison use in one area would damage oak seedlings (see Manuwal, this volume), rapid bison pasture rotation could reduce grass cover, and thus competition from grass roots, with little damage to oak seedlings and possible long-term benefit to oak regeneration. In any case, elasticity analyses suggest that maximizing survival of saplings and young adult trees would benefit population growth. Any management action that would put Quercus pacifica saplings or young adult trees at risk should thus be avoided. Mechanical protection of saplings might be needed in some areas prone to browsing. Grass cover reduction programs would also reduce the risk of losing saplings to fires.

Overall, our study suggests that adult tree fertility is sufficient to ensure sustained regeneration of the island-wide metapopulation of island scrub oak, but inadequate biotic and/or abiotic ecosystem conditions in some parts of the island are impacting acorn germination and/or seedling and sapling survival. This is likely responsible for the low regeneration and declining trend we observed in some of the oak populations.

ACKNOWLEDGEMENTS

We thank Denise Knapp and Frank Starkey for their help and collaboration, and Cheryl Mantia for help with field work. We thank Lisa Stratton for providing us with acorn germination and seedling trials data and for helpful suggestions. The draft of this paper benefited from the comments of two anonymous reviewers. This research project was supported by a Faculty Scholarly Grant from Chapman University and a matching in-kind grant from the Catalina Island Conservancy.

REFERENCES

Abrams, M. D. 2003. Where has all the white oak gone? BioScience 53:927-939. Bakker, E. S., H. Olff, et al. 2004. Ecological anachronisms in the recruitment of temperate light- demanding tree species in wooded pastures. Journal of Applied Ecology 41:571-582. Caswell, H. 2001. Matrix population models. Sunderland, Sinauer, Sunderland, MA. Catana, H. J. 1963. The wandering-quarter method of estimating population density. Ecology 44:349-360. Faberlangendoen, D., and J.R. Tester. 1993. Oak mortality in sand savannas following drought in east- central Minnesota. Bulletin of the Torrey Botanical Club 120:248-256. Gauch, H.G., Jr. 1982. Multivariate analysis in community ecology. Cambridge University Press, Cambridge, UK. Griffin, J.R. 1971. Oak regeneration in the upper Carmel Valley, California. Ecology 52:862-868. Hanski, I. 1999. Metapopulation ecology: Ecology and evolution. Oxford University Press, Oxford, UK. Healy, W.M., A.M. Lewis, et al. 1999. Variation of red oak acorn production. Forest Ecology and Management 116:1-11. Jacqmain, E.I., R.H. Jones, et al. 1999. Influences of frequent cool-season burning across a soil moisture gradient on oak community structure in longleaf pine ecosystems. American Midland Naturalist 141:85-100. Jongman, R.H. G., C.J.F. ter Braak, et al. 1995. Data analysis in community and landscape ecology. Cambridge University Press, Cambridge, UK. Kelly, D.L. 2002. The regeneration of Quercus petraea (sessile oak) in southwest Ireland: A 25-year experimental study. Forest Ecology and Management 166:207-226. Lorimer, C.G. 1980. Age structure and disturbance history of a southern Appalachian virgin forest. Ecology 61:1169-1184. Momen, B., J.W. Menke et al. 1994. Blue oak regeneration and seedling water relations in four sites within a California oak savanna. International Journal of Plant Sciences 155: 744-749. Sork, V.L. 1993. Evolutionary ecology of mast-Sseeding in temperate and tropical oaks (Quercus spp). Plant Ecology 108:133-147.

Appendix 1. Lefkovitch and elasticity matrices for populations 1-10

Population Lefkovitch matrix Elasticity matrix

1 0.745 0 0.050 0.650 0.095 0 0.008 0.025 0.099 0.909 0 0 0.033 0.322 0 0 0 0.091 0.921 0 0 0.033 0.378 0 0 0 0.059 0.764 0 0 0.025 0.081

2 0.751 0 0.086 1.137 0.096 0 0.009 0.026 0.092 0.921 0 0 0.035 0.306 0 0 0 0.079 0.942 0 0 0.035 0.391 0 0 0 0.058 0.764 0 0 0.026 0.076

3 0.753 0 0.101 1.397 0.097 0 0.009 0.027 0.091 0.924 0 0 0.036 0.305 0 0 0 0.076 0.945 0 0 0.036 0.387 0 0 0 0.055 0.764 0 0 0.027 0.076

4 0.766 0 0.477 11.094 0.109 0 0.014 0.033 0.078 0.946 0 0 0.047 0.294 0 0 0 0.054 0.967 0 0 0.047 0.349 0 0 0.000 0.033 0.764 0 0 0.033 0.075

5 0.754 0 0.144 2.712 0.104 0 0.011 0.029 0.090 0.926 0 0 0.040 0.318 0 0 0 0.074 0.935 0 0 0.040 0.349 0 0 0 0.041 0.764 0 0 0.029 0.081

6 0.754 0 0.119 1.726 0.098 0 0.010 0.027 0.090 0.926 0 0 0.037 0.304 0 0 0 0.074 0.947 0 0 0.037 0.382 0 0 0 0.053 0.764 0 0 0.027 0.076

7 0.748 0 0.148 1.750 0.103 0 0.009 0.028 0.096 0.883 0 0 0.037 0.246 0 0 0 0.051 0.935 0 0 0.037 0.427 0 0 0 0.065 0.764 0 0 0.028 0.085

8 0.766 0 0.481 11.274 0.109 0 0.014 0.033 0.078 0.946 0 0 0.047 0.294 0 0 0 0.054 0.967 0 0 0.047 0.348 0 0 0 0.033 0.764 0 0 0.033 0.075

9 0.735 0 1.419 11.915 0.117 0 0.008 0.030 0.108 0.714 0 0 0.038 0.105 0 0 0 0.006 0.909 0 0 0.038 0.523 0 0 0 0.091 0.764 0 0 0.030 0.109

10 0.765 0 0.416 9.245 0.108 0 0.014 0.032 0.079 0.944 0 0 0.046 0.295 0 0 0 0.056 0.966 0 0 0.046 0.352 0 0 0 0.034 0.764 0 0 0.032 0.075

Metapop. 0.774 0 1.461 52.306 0.116 0 0.019 0.037 0.069 0.959 0 0 0.056 0.283 0 0 0 0.041 0.979 0 0 0.056 0.321 0 0 0 0.021 0.764 0 0 0.037 0.074