The American Midland Naturalist - Kalamazoo College

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endemic to the western Great Lakes, U.S.A., by mapping individuals with a GPS. .... linear dunes (cf., McEachern, 1992), dominated by American beach grass ( .... A nearest neighbor analysis was performed for each size class (defined in Table 1) ..... suggests a trade-off for managers between reducing intraspecific resource ...

The American Midland Naturalist Published Quarterly by The University of Notre Dame, Notre Dame, Indiana

Vol. 156

October 2006

No. 2

Am. Midl. Nat. 156:213–228

Conservation Implications of Individual Scale Spatial Pattern in the Threatened Dune Thistle, Cirsium pitcheri E. BINNEY GIRDLER1

AND

THERESIA A. RADTKE

Department of Biology, Kalamazoo College, 1200 Academy Street, Kalamazoo, Michigan 49006 ABSTRACT.—For plants and other sessile organisms, the dispersion of individuals in a population can influence the strength of ecological interactions, and can have important implications for the conservation of these species. We investigated the spatial pattern in a population of the monocarpic perennial Cirsium pitcheri (Pitcher’s thistle), a dune species endemic to the western Great Lakes, U.S.A., by mapping individuals with a GPS. Using a refined nearest neighbor analysis of the mapped point data combined with Monte Carlo randomization tests, we found that individual plants were clustered on the scale of about a meter, which was smaller than expected if aggregations were caused by major habitat features such as dune height or aspect. The size of clusters was consistent with reports of relatively short-distance dispersal of seeds. We found no evidence of self-thinning via nonrandom mortality, and regression analyses indicated no density dependent effects on reproductive effort at a range of ecologically reasonable scales. However, we did find a suggestion of density dependent effects on juvenile size at several scales. The neighborhood radius that maximized the variance explained was 25 cm, roughly the radius spanned by the largest juvenile individuals in our study. Incidence of herbivory was not concentrated in denser patches of C. pitcheri; in fact, we found a trend in the opposite direction: isolated individuals were more likely to have been damaged by herbivory than those with a crowded local neighborhood. Our results show that explicit attention to such individual-scale spatial patterns can lead to increased understanding and thus more effective management of local plant populations. We call for more systematic studies examining local spatial patterns in this and other threatened plant species.

INTRODUCTION Since the recognition of Harper (1977) that interactions between individuals in plant populations (and other sessile organisms) are almost always local, ecologists have gained an increasing understanding that the spatial structure of plant populations is a key factor in plant population and community dynamics (e.g., Weiner, 1984; Mitchell-Olds, 1987; Cza´ra´n and Bartha, 1992; Levin, 1992). Spatial structure can exist at any scale, from landscape level variation (which has spawned a sub-field of population biology focusing on the study of 1

Corresponding author: Telephone: (269) 337 5977; FAX: (269) 337 7251; e-mail: [email protected]

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metapopulations, e.g., Hanski, 1999) to variation at the scale of an individual plant and its neighbors (e.g., Mack and Harper, 1977; Silander and Pacala, 1985). Such plant-scale patterns can provide insight to ecological processes that are important drivers of population dynamics, including intraspecific and interspecific competition, and environmental heterogeneity. Much of the relevant literature concerns spatial patterns in forest communities. By analyzing spatial patterns in tropical trees, Sterner et al. (1986) found evidence of the nonrandom mortality expected from self-thinning in three of four species: adults were more uniformly distributed than juveniles. In contrast, Peterson and Squiers (1995) showed increased clumping with age in both dominant species in an aspenwhite pine forest, suggesting that the clonal aspen influenced the location and aggregation of the invading white pine. In an individual-based forest simulation model, Pacala and Deutschman (1995) demonstrated that the spatial distribution of trees played a critical role in maintaining ecosystem function. Heterogeneity in local density in the form of canopy gaps served to foster the growth of juveniles in their model; without that heterogeneity, basal area of simulated forests fell 50%. Finally, Barot et al. (1999) were able to link demographic processes of palms in a humid savannah with environmental heterogeneity using a detailed spatial analysis of adults, juveniles and nutrient patches. In herbaceous plants, most population studies addressing spatial factors focus on neighborhood density and the effects of neighbors. In a field setting, Aguilera and Lauenroth (1993) investigated the spatial pattern in a bunchgrass community, finding that plant spacing affected growing season performance, presumably through competition for spatially distributed resources. Pacala and Silander’s theoretical and greenhouse work showed that variation in local density in one and two-species systems was a significant predictor of target plant performance (Pacala and Silander, 1985, 1987; Silander and Pacala, 1985). To date, however, insights gained from such spatial pattern analyses have not been widely considered by conservation practitioners. On the one hand, managers could use analysis of spatial pattern as an assessment tool to determine if restored populations attain a ‘‘natural’’ spacing after some amount of time. On the other hand, however, if certain spatial patterns in natural populations affect population dynamics (e.g., in facilitating pollination or minimizing herbivory) then replication of natural spatial patterns might increase the effectiveness of reintroduction efforts (Primack, 1996; White, 1996). In particular, reintroduced populations will often be isolated with low initial densities of individuals, classic conditions to observe Allee effects which may inhibit positive population growth. If we can identify such tendencies in the natural variation of densities in extant populations, managers will be able to anticipate potential limiting factors in reintroductions. Pattern and scale in a threatened plant population.—Endemic to the Great Lakes region, Pitcher’s thistle [Cirsium pitcheri (Torrey ex Eaton) T. and C., Asteraceae] was listed as federally threatened in 1988 (Harrison, 1988). It is state-listed as threatened in Illinois, Indiana and Michigan, endangered in Wisconsin and rare in Ontario (Bowles and McBride, 1996). As a monocarpic perennial herb, C. pitcheri grows as a rosette for 5 to 8 y, flowers, then dies (Loveless, 1984). Colonization of new habitat patches must occur through seed production and dispersal; C. pitcheri thus exhibits a metapopulation structure (Bowles et al., 1993). The causes for the decline of Cirsium pitcheri are found at several scales. At the landscape level, sand mining, shoreline development, dune and shoreline stabilization and disruption of shoreline currents that replenish eroded shorelines have destroyed this species’ dune habitat throughout its range (U.S. Fish and Wildlife Service, 2002). At the local level, recreational impacts (e.g., hiking trails and off-road vehicle use) exacerbate the detrimental

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effects of natural ecological factors such as drought stress, and, as has been increasingly recognized, herbivory. These local factors along with the natural course of succession on dunes contribute to the loss of local populations; however, due to landscape level factors, new suitable habitats are not available for colonization. McEachern (1992) found a wide range of Cirsium pitcheri population density across successional habitats and latitude, related to local habitat quality and the frequency and intensity of disturbance. The species ranges from locally dense patches (the highest density in the literature is 40.5 plants/m2 at Sleeping Bear Dunes, Michigan; McEachern, 1992) to rare to absent within the space of a single kilometer. Using variance-to-mean ratios for subdivided transects, McEachern (1992) found that C. pitcheri had an aggregated distribution at about half the populations she studied. She attributed this variability to habitat quality and the frequency and intensity of disturbance. Differences in habitat quality may also be the cause of smaller scale variability, but there have been no published descriptions of individual-scale spatial patterns for C. pitcheri. Although several authors report having mapped sub-populations of C. pitcheri for the purposes of demographic analysis, the information was used mainly to find mapped individuals again to record mortality and fecundity, not to examine the distribution of individuals in space (Loveless, 1984; McEachern, 1992; Bell et al., 2003). The key to successful conservation of Cirsium pitcheri is facilitating metapopulation dynamics by establishing new populations (McEachern et al., 1994). Recent theoretical work has shown the importance of spatial structure in plant communities (Bolker and Pacala, 1997; Snyder and Chesson, 2004), however there has been little application to conservation. We propose that analysis of local spatial pattern in existing populations will enhance conservation efforts for threatened and endangered plant species. To that end, we mapped individuals in a typical occurrence of C. pitcheri, near the center of its range. We collected data on size and fecundity for each mapped individual to relate these fitness factors to local density. While collecting these data we noticed herbivory damage to the leaves of some juvenile plants. Herbivory by white-tailed deer and rabbits has been noted in several studies (D’Ulisse and Maun, 1996; Phillips and Maun, 1996; Rowland and Maun, 2001); insect herbivory is also of concern (Keddy and Keddy, 1984; Loveless, 1984; McEachern, 1992; Stanforth et al., 1997; Bevill et al., 1999). Although we were not able to identify the herbivore(s) responsible for the damage, we collected presence/absence data on leaf damage to ascertain whether there was a spatial component to such damage. Rates of herbivory in Cirsium pitcheri have been shown to vary at a landscape scale (i.e., between study sites: Keddy and Keddy, 1984; Bevill et al., 1999), but have not been explored at smaller scales within a local population. METHODS Most Cirsium pitcheri occurrences are in the Lake Michigan basin (U.S. Fish and Wildlife Service, 2002). Our study was conducted in August 2002 on the eastern shore of Beaver Island, in Lake Michigan (Charlevoix County, Michigan, 858309W 458419N), on the property of the Central Michigan University Biological Station. The federal recovery plan ranks the site as ‘‘good quality’’ (U.S. Fish and Wildlife Service, 2002). The habitat is typical of simple linear dunes (cf., McEachern, 1992), dominated by American beach grass (Ammophila breviligulata) on the dunes, and various sedges (Juncus spp.) in the swales and wet beach. Using a backpack mounted Global Positioning System (Trimble TSC1 Asset Surveyor, Trimble Navigation Ltd, Sunnydale, CA, published accuracy of ,50 cm with differential correction), we mapped all Cirsium pitcheri individuals (60 flowering adults, 348 prereproductive juveniles) within a 420 m2 area (Fig. 1). This area encompassed all individuals

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FIG. 1.—Map of Cirsium pitcheri individuals in a population on Beaver Island, Charlevoix County, Michigan, whose coordinates were obtained via a GPS system. Open circles are uneaten juveniles (rosettes); filled circles are juveniles with herbivory damage; stars are reproductive individuals. Hatched areas indicate back slopes of dunes, with west-facing aspect. Dashed lines represent trails. The northsouth trail runs along the primary dune ridge; the water’s edge runs roughly north-south about 27 m to the east of the study plot

in the dune-swale system from the shoreline to the treeline (east to west). The northern and southern boundaries were arbitrarily defined by a foot trail to the north, and by a property line to the south; the population of C. pitcheri extended well to the north and south of this sample area with the same apparent (but unsampled) density. A rudimentary foot trail ran north-south along the primary dune ridge. GPS coordinates for each plant were determined by straddling the plant as the researcher faced north. To increase the accuracy of our GPS coordinates, we logged a minimum of 10 positions for each individual over a minimum time span of 30 s. After post-processing, we calculated a mean standard deviation for all points of 0.073 m. Loveless (1984) found regression of longest leaf length on total biomass to be a highly significant predictor of whole-plant biomass, therefore, we used this measure as a proxy for size of rosette for juvenile individuals. Leaf lengths were measured to the nearest cm; we found no individuals with longest leaves smaller than 2 cm. For 293 of the juvenile plants, we also recorded presence or absence of herbivory, as ascertained by visual inspection. Herbivory was defined as any portion of any leaf missing, and could range from a few square mm to a completely defoliated rosette with just the base left; we made no distinction among levels of damage. Reproductive plants had already begun to senesce, and most of their leaves had dried out almost completely, therefore, leaf length and herbivory could not be recorded for these individuals. Analysis of spatial pattern.—There are several methods available for analyzing spatial pattern using mapped point data (Pielou, 1977; Ripley, 1981; Diggle, 1983; Upton and Fingleton, 1985; Hamill and Wright, 1986). We chose a refined nearest neighbor analysis for its relatively straightforward interpretation and its ability to reveal the scale or grain of spatial pattern (Getis and Franklin, 1987). To analyze the pattern of dispersion of Cirsium pitcheri individuals we used the x-y coordinates of the 408 mapped individuals to calculate the distance to the nearest neighbor for each plant. The cumulative distribution of distances F(d) was calculated as the proportion of plants in the P population of n plants that had a nearest neighbor distance di within d: F(d) ¼ (1/n) di(d ), where di(d ) ¼ 1 if di  d and 0 if di . d.

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TABLE 1.—Incidence of herbivory on juvenile rosettes of Cirsium pitcheri in a population on Beaver Island, Charlevoix County, Michigan, by size class. The overall rate of herbivory (125 out of 293 individuals were damaged) was 0.4266 Size class

Length of longest leaf

Sample size

Proportion with herbivory

1 2 3 4 5 6 7

2–5 cm 6–8 cm 9–11 cm 12–14 cm 15–18 cm 19–22 cm 23–33 cm

34 41 46 38 48 47 39

0.2059 0.2195 0.3261 0.6579 0.5833 0.5745 0.3590

Nearest neighbor analyses in the literature usually compare a plot of the cumulative distribution of observed nearest neighbor distances to the expectation of spatial randomness: a ‘‘Poisson forest’’ with the same overall density as the study population (Upton and Fingleton, 1985; Barot et al., 1992; Moeur, 1993). These analyses usually include a correction for edge effects because the nearest neighbor for a given plant may be outside the study area. Because plant locations are not independent observations, the use of traditional statistics such as a Kolmogorov-Smirnov test to compare the observed distribution with the random expectation is not appropriate. However, it is straightforward to generate confidence intervals for F(d) using Monte Carlo randomizations. Use of the Monte Carlo method has the added benefit of eliminating the need to correct for edge effects since the randomly generated points will have the same bias as the mapped plants (Ripley, 1981; Baddeley et al., 1993). We followed the procedure for Monte Carlo randomization outlined in Moeur (1993). We generated 1000 sets of 408 random coordinates (the sample size of the observed population) and calculated Fsim(d) for each set (the subscript indicates a simulated value). For each value of d in 10 cm increments, ranging from zero to 2.5 m, the 1000 values of Fsim(d) were ordered, and the largest and smallest 2.5% were discarded. The function F(d ) was equal to one for all values of d greater than 2.5 m for both empirical and simulated data. The remaining minimum and maximum values from the set of random simulations defined the boundaries of a two-sided 95% confidence envelope. The empirical distribution F(d ) was then inspected for all values of d; the null hypothesis of spatial randomness was rejected for points at which F(d) fell outside the confidence envelope. This analysis can detect departures from a random pattern that are both clustered, F(d) . Fsim(d) and regular, F(d) , Fsim(d ), as well as indicate the scale of the pattern, i.e., the approximate ‘‘size’’ of the clumps, or spacing in a regular pattern (Ripley, 1981; Upton and Fingleton, 1985; Moeur, 1993). A nearest neighbor analysis was performed for each size class (defined in Table 1) to indirectly test the hypothesis that the degree of aggregation will decrease as a cohort matures and individuals exhibit nonrandom mortality due to intraspecific competition. One thousand random replicates were simulated for each size class to generate 95% confidence intervals for the cumulative F(d) functions. Testing for density dependence.—To determine whether rosette size was affected by neighborhood density, we tested whether the size of juvenile individuals (as assessed by length of longest leaf) was dependent on the number of neighbors for a range of circular neighborhood sizes (1.0 m, 0.5 m, 0.25 m and 0.20 m radius), using linear regression. Independence assumptions for linear regression were not met for these tests, because plants within a given distance of each other could be both a focal plant (dependent variable) and

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a neighbor (the explanatory variable) and, thus, would show up twice in the analysis for a given neighborhood size. To test whether this double counting affected significance estimates, we used an algorithm that allowed a given plant to be used only once in the analysis: as a focal plant or as a neighbor, but not both. This algorithm reduced sample size by approximately 36%, but in ten trials, gave similar results to the full analysis, so only the latter is presented here. A similar series of regression analyses were run on reproductive individuals, with number of capitula as the dependent variable. Analysis of herbivory incidence.—For 293 juvenile individuals, incidence of herbivory was noted as present or absent. We asked whether a given plant was more or less likely to have been damaged if its local density was higher or lower than average, i.e., we tested whether the incidence of herbivory was density dependent. We first estimated local density for each juvenile individual by determining the number of neighbors (both juvenile and reproductive) within a circle with radius of 1 m centered on the target individual (this radius was suggested by analyzing the scale of aggregation of all mapped individuals). The null hypothesis was that the observed pattern of herbivory was random with respect to local density. To test the null hypothesis, we again used a randomization approach: holding local density constant, we randomly assigned herbivory incidence to individuals at the same overall rate as the study population (0.4266 of individuals had evidence of herbivory, n ¼ 125 out of 293 individuals). We generated 100 of these random populations. Logistic regression is useful for situations in which the dependent variable is dichotomous, such as our herbivory data. Therefore we examined the slope coefficient of a binary logistic regression of herbivory incidence (zero or one) on number of neighbors (zero to 15) in order to test whether the likelihood of herbivory was greater for more isolated or more crowded individuals. To test the significance of the empirically derived slope we calculated binary logistic regression slope coefficients for the 100 simulated populations with random herbivory; the P-value was obtained by inspecting the ranked randomly-generated coefficients to find how many of them were larger (more positive, indicating positive density dependence) or smaller (more negative, indicating negative density dependence) than the value for the empirical population. A subsequent analysis involved combining the extremes of the density classes into two groups with similar sample sizes: plants with zero to two neighbors within 1 m (n ¼ 69), and plants with nine or more neighbors (n ¼ 68). In this case, the proportion of herbivory was calculated for both groups and the significance of the difference between them was assessed by comparing it to ranked differences in 1000 randomly generated populations. RESULTS A map of the study area showing locations of Cirsium pitcheri individuals is shown in Figure 1. The mean density of mapped individuals in the study plot, obtained by dividing the number of plants by plot area, was 0.92 individuals/m2. Nearest neighbor distances for the 408 C. pitcheri individuals in the plot ranged from 0.01 to 1.83 m, with a mean of 0.41 m. By taking the inverse of the mean nearest neighbor distance, one can obtain a measure of perceived density. The mean value for perceived density was double the overall estimate, at 1.85 individuals/m2, with the highest perceived density (inverse of the smallest nearest neighbor distance) being 1624.03 individuals/m2 and the lowest perceived density (inverse of the largest nearest neighbor distance) being 0.10 individuals/m2. Dispersion.—By comparing the empirical cumulative distribution of nearest neighbor distances to those obtained from sampling 1000 random populations using Monte Carlo simulations, we found that Cirsium pitcheri individuals in the study plot were aggregated

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FIG. 2.—The cumulative distribution of nearest neighbor distances, F(d), for Cirsium pitcheri individuals (n ¼ 408) in a population on Beaver Island, Charlevoix County, Michigan. Empirical data are represented by the heavy solid line; dotted lines are 95% confidence envelopes for 1000 randomly generated populations

at all distances less than approximately 1 m (i.e., the observed curve was outside the 95% confidence envelope, Fig. 2). That is, more plants had nearest neighbors less than 1 m away than one would expect by chance given a random dispersion of plants on the study plot. There was no evidence of a uniform dispersion at any scale (i.e., within clumps). Density dependence.—When size classes (see Table 1 for classifications) were considered separately, we saw no evidence that the degree of clumping decreased with the size (and presumably, age) of the plant (Fig. 3). The smallest size class had a cumulative distribution of nearest neighbor distances that was the most deviant from the 95% confidence interval, but clumping was seen to varying degrees in all other size classes, as well as in the reproductive plants. The size of juvenile individuals was negatively correlated with number of neighbors within 0.5 m and within 0.25 m. In Figure 4 we show the 0.25 m radius neighborhood because it explained the most variation in plant size, although the amount of variation explained by this relationship was minimal (n ¼ 348, R2 ¼ 0.02, P ¼ 0.008). In a similar analysis, we used nearest neighbor distance as a proxy for degree of isolation, and found a positive relationship (not shown, n ¼ 348, R2 ¼ 0.01, P ¼ 0.05), indicating more isolated plants tended to be larger than more crowded individuals. The number of capitula produced by reproductive individuals was independent of the number of neighbors within a range of neighborhood radii (1.5, 1.0, 0.5, 0.25, 0.2 m) (Fig. 4b). Similarly, a regression of number of capitula on nearest neighbor distance was insignificant (not shown, n ¼ 60, R2 ¼ 0.002, P ¼ 0.68). Herbivory.—The overall herbivory rate was about 43%, with larger individuals being more likely to suffer damage than smaller individuals. The distribution of herbivory incidence by size class deviated significantly from expectation (v2 ¼ 19.45, df ¼ 6, P , 0.005), with more herbivory than expected in three of the four largest size classes (Fig. 5). However, the trend

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FIG. 3.—Cumulative distribution of nearest neighbor distances, F(d), for Cirsium pitcheri individuals in a population on Beaver Island, Charlevoix County, Michigan, for (a) through (g) size classes 1 through 7, respectively (size classes given in Table 1); and for reproductive individuals (h). For all panels, solid lines are empirical distributions and dashed lines are the 95% confidence intervals given by 1000 Monte Carlo simulations

did not hold for the largest size class; individuals spanning a large range of longest leaf lengths—from 22 to 33 cm—were not more likely to be eaten than expected. For descriptive purposes, we show the proportion of herbivory vs. each neighborhood density in Figure 6, with the sample sizes indicated for each data point. These data do not conform to the assumptions of linear regression since the ‘‘data points’’ are averages of groups with differing number of observations, so we plot the regression line merely to point out the negative trend in the data. The binary logistic regression on the full data set considered whether or not an individual plant was damaged, depending on density. The slope coefficient b was 0.043, indicating

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FIG. 4.—Effects of local density on fitness of Cirsium pitcheri individuals in a population on Beaver Island, Charlevoix County, Michigan. (a) Juvenile plant size (n ¼ 348, R2 ¼ 0.02, P ¼ 0.008); (b) Number of capitula (n ¼ 60, R2 ¼ 0.03, P ¼ 0.18)

that plants with fewer neighbors were more likely to have suffered herbivory than plants with more neighbors, and was not significantly different from b’s derived from Monte Carlo simulation data (P ¼ 0.10). Given that we were interested in the extremes of the relationship, i.e., we wanted to know whether relatively isolated or more crowded individuals were more likely to suffer herbivory, we investigated the negative trend found in Figure 6 in an ad hoc analysis that combined the extreme density classes into two groups with approximately equal sample sizes. Thirty-three

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FIG. 5.—The number of Cirsium pitcheri individuals with herbivory present by size class in a population on Beaver Island, Charlevoix County, Michigan. Solid bars are empirical data; open bars are values expected if overall herbivory rate of 0.4266 was applied equally to all size classes. v2 ¼ 19.45, df ¼ 6, P , 0.005

of the 69 (47.8%) juvenile Cirsium pitcheri individuals with zero to two neighbors within 1 m were recorded as having incidence of herbivory, whereas 21 of the 68 (30.9%) individuals with nine or more neighbors were recorded as having incidence of herbivory. The difference in herbivory rates between these two groups (isolated minus crowded) was 0.169. We found a difference this large in only 16 of 1000 randomly simulated (Monte Carlo) populations (P ¼ 0.016). To assess at what size herbivory risk to isolated individuals increases, we compared herbivory rates for only those plants with two or fewer neighbors within 1 m (n ¼ 69). We found no deviation from expectation among the seven size classes (v2 ¼ 5.89, df ¼ 6, P . 0.1), although the trend was similar to that seen in Figure 5, with medium-sized individuals between 12 and 22 cm experiencing higher than expected herbivory. DISCUSSION Individuals of Cirsium pitcheri in our study plot were distributed nonrandomly. This is not surprising; all populations are aggregated at some scale, although whether this is because of underlying environmental heterogeneity or is generated endogenously is not always clear (Levin, 1992). The scale of aggregation of about 1 m can be interpreted as the approximate size of the ‘‘patches’’ of individuals on the dunes (Upton and Fingleton, 1985). Based on visual inspection of the mapped individuals, we had expected to find some clustering at a larger scale: the densest areas appear to be on the ridge of the dune. We found no evidence of aggregation on the scale of 4–5 m. This may be due to the north-south orientation of the dune; the nearest neighbor analysis we used is not sensitive to the differential angular dispersion of neighbors (i.e., it fails to distinguish between neighbors to the north versus neighbors to the west; see Mack and Harper, 1977). It is also likely that too few of these larger scale clusters were present in our plot; a larger sample area would have been necessary to detect these larger patches. The scale of clumping that we did detect is consistent with previous findings of a clumped distribution of seedlings in this species. Previous researchers have attributed aggregated

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FIG. 6.—Herbivory rate for Cirsium pitcheri individuals in a population on Beaver Island, Charlevoix County, Michigan, grouped by the number of neighbors within 1 m of target plants. Labels for each point indicate the sample size within each density group. The dotted regression line is shown only to indicate the negative trend in the data

distributions in Cirsium pitcheri to the fact that dispersal of seeds often consists of intact capitula falling from the parent plant without the scattering of individual seeds. Keddy and Keddy (1984) and Loveless (1984) determined that most seedlings were found within 4 m of the parent plant. Such a pattern will effectively increase the density perceived by an individual (Bolker and Pacala, 1997). For plants and other sessile organisms, this localized density determines the likelihood and strength of ecological interactions that impact population dynamics, such as competition, herbivory and reproductive strategy via pollinator behavior. Clumped seedlings would be expected to compete intensely and exhibit nonrandom mortality and therefore self-thinning as they grew into larger size classes. In the nearest neighbor analysis for each size class, we did not find the decreasing aggregation with plant size (and presumably age) that we would expect if intraspecific competition were driving nonrandom mortality and self-thinning. However, a size class based analysis is not equivalent to a true cohort analysis and all the standard caveats of static population studies apply: each cohort sampled in our ‘‘snapshot’’ will have integrated a different temporal sequence of changing climate and disturbance factors (Clark and Clark, 1984; Sterner et al., 1986). A more direct test of density dependence and intraspecific competition is to ask whether neighborhood density affects individual plant fitness. Without experimental evidence, it is difficult to assign causation to the admittedly weak density dependence shown in Figure 4. Number of neighbors may be a good predictor of the size of a focal plant for two reasons. First, conspecific neighbors may compete with a focal plant for resources, most likely soil nutrients, and reduce its growth. This same pattern could also arise, however, simply from the fact that smaller individuals are aggregated: small plants have many neighbors which are also small plants, pulling the right hand side of the regression in Figure 4 down. Alternatively, the larger lone plants may be those few remaining individuals of a cohort that have not yet

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flowered. Such demographic thinning need not be density related; spatially random mortality that occurs as individuals flower would maintain the aggregated dispersion present in older size classes, but would result in fewer neighbors for those remaining individuals. Whatever the cause of the density dependence, it is apparently not strong enough to effect self-thinning: the population as a whole is strongly aggregated, and the size class analysis showed no trend toward random or regular spacing in the larger size classes. The departure from random herbivory that we found in our study population—increased prevalence on larger and more isolated individuals—could have implications for conservation and management of this species. Our assessment of herbivory was admittedly coarse; the presence of herbivory indicated anything from a few square millimetres of leaf missing to the near-complete defoliation of the rosette. We did not attempt to differentiate among different possible herbivores (e.g., mammals vs. phytophagous insects); however, there are sizeable populations of both white-tailed deer and rabbits at the study site, and we found fresh evidence of both species in the study plot. We did not observe any insects feeding on the leaves of Cirsium pitcheri, although it was near the end of the growing season, and the damage we observed could have occurred earlier in the summer. In Figure 1, herbivory appears to be more frequent along the rudimentary foot trail on the primary dune ridge. Rabbits and deer use foot trails, behavior that would expose nearby plants to greater herbivory risk. A larger sample area would be necessary to confirm this trend. Stanforth et al. (1997) found that the probability of insect herbivory in Cirsium pitcheri increased with juvenile size, although this pattern was confounded with landscape-level variation in the size of individuals at different sites. More southern and more inland sites in their study were at later stages in succession, with larger juveniles. Thus, the higher rates of herbivory on larger juveniles in their study may have had more to do with successional stage of the population than with size per se. In our study on a single dune, the increasing likelihood of herbivory with plant size may be explained simply as the search image effect of the herbivore: very small plants may be easily overlooked, so larger plants are eaten more often—they offer a larger target. However, the very largest individuals in our study plot were not more likely to have been damaged by herbivory, perhaps due to toughness, secondary compounds, or good luck. Larger individuals may also tend to experience different kinds of herbivory, such as root crown damage, or leaf mining along the leaf mid-vein (Stanforth et al., 1997), which we did not take into account when we scored herbivory damage. Our second finding with respect to herbivory amounts to an Allee effect: more isolated individuals—those having only one or two neighbors within 1 m—were more likely to suffer herbivory than relatively more crowded ones—those individuals with nine or more neighbors within 1 m. This nonrandom pattern of herbivory means that reintroduced individuals established at a low density may be relatively more likely to suffer damage from grazers, imposing a barrier to successful establishment of a new population. In reporting results of a reintroduction of Cirsium pitcheri in Illinois, Bowles et al. (1993) initially suggested that herbivory was not an important factor affecting thistle survival: they found no difference in survivorship between fenced and nonfenced transplants. However, after following that cohort for several more years, Bowles and McBride (1996) found that one of the two individuals that reproduced in its fourth year was severely damaged by animal herbivory, prompting these authors to caution that such herbivory could be a ‘‘critical factor affecting growth of this small population.’’ From the description of the reintroduction protocol, it is difficult to reconstruct the local density for the transplanted individuals, however, it is likely that the local neighborhood (which we are defining as within 1 m) included fewer than eight individuals, and probably as

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few as four. The overall density of Cirsium pitcheri at the Illinois reintroduction site might have been low enough (only 78 plants dispersed over approximately 670 m2, an overall density of 0.12 individuals/m2) that herbivores simply did not encounter transplanted individuals. Unfortunately, information on the spatial pattern of other reintroduction efforts (e.g., Rowland and Maun, 2001) has not been reported. In the population of Cirsium pitcheri we studied on Beaver Island, relatively isolated individuals may have been more likely to suffer herbivory than conspecifics in nearby patches because the patches attract grazers to the general vicinity and then protect members of the patch (through ‘‘predator dilution’’), leaving isolated plants vulnerable because they are obvious. This does not necessarily imply that widely spaced individuals, such as transplants in a reintroduction, would be equally vulnerable. Indeed, isolation may be beneficial when the larger area a plant occupies is rather sparse, because herbivores will not have discovered it, as—perhaps—in the initial stages of the Illinois reintroduction. In that population, the transplanted rosettes may simply have grown large enough to have been noticed by grazers, similar to the size effect that we found in our study. It is worth pointing out that the two factors which seem to partially explain the incidence of herbivory in this study population—size and degree of isolation of the individual—may not be independent, as discussed above in terms of density dependence. The apparent Allee effect, wherein sparsely distributed individuals suffer greater herbivory, may be a result of the fact that the more isolated plants tend to be the larger ones (a density dependent effect, perhaps due to intraspecific competition), and the larger the plant, the more leaf area is available to be eaten. Among only isolated plants, the size effect was not significant; larger isolated plants were not more likely to be damaged than smaller isolated plants. This result may have been due to a loss of statistical power with such a small sample; the degree to which herbivory risk increases with size independent of the degree of isolation in this species remains an open question. Finally, although both effects are relatively weak—i.e., number of neighbors explains only a fraction of the variation in plant size and incidence of herbivory— we believe they are noteworthy given that we have not accounted for a host of other potentially relevant factors, such as proximity and identity of individuals of other species and habitat heterogeneity, that are contributing noise to the data set. Floral herbivory in Cirsium pitcheri would have obvious consequences for population growth by directly decreasing fecundity (Louda, 1994; Stanforth et al., 1997). Leaf herbivory might also affect population dynamics by increasing the likelihood of mortality and delaying reproduction. Phillips and Maun (1996) suggest that because the flowering ability of monocarpic perennials such as C. pitcheri is dependent upon stored root reserves, high levels of herbivory might prolong the juvenile stage of growth by delaying flowering (see also Hirose and Kachi, 1982). In terms of reproductive potential, initiation of flowering in C. pitcheri appears to be size-dependent (D’Ulisse and Maun, 1996). Repeated bouts of herbivory, therefore, might lead to an extension of the juvenile phase even if it does not affect annual mortality rates. Thus, slight differences in resource allocation could multiply over the lifetime of an individual; herbivory would have an impact on the population dynamics of C. pitcheri by extending the generation time for these individuals. This extension of the juvenile stage would lower the intrinsic rate of population growth by itself, but would also have the concomitant effect of increasing the period of vulnerability to herbivory, sand burial and other environmental stresses (Rowland and Maun, 2001). Implications for conservation and management.—Regardless of the causative factor, the indication that variation in density within a single population can affect the size of plants and herbivory rates points out the need to take spatial patterns into account when attempting to restore and manage local populations of Cirsium pitcheri. Although patterns of

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dispersion at the scale of an individual and its neighbors are being increasingly recognized in general ecological theory, to our knowledge, this is the first study to apply such analysis to a threatened or endangered plant species. Understanding such localized spatial patterns may turn out to be critically important for the management of local populations, just as our recognition of the temporal patterns of disturbance has helped us to understand the dynamics and persistence of metapopulations (Pavlovic, 1994). We realize that drawing such global conclusions from such a small study may not be warranted. Different populations of Cirsium pitcheri, and the same population in different years, may have different spatial patterns. For example, we see temporal variation in growth rates in C. pitcheri due to the dynamic dune environment (Bell et al., 2003; M. Bowles, pers. comm.). Therefore, for this particular species, future field studies should examine spatial patterns in several different populations, across the range of habitats (simple linear dunes, isolated blowouts, perched dunes) and successional stages that make up its regional metapopulation. The impact of spatial patterns on pollination biology, and inflorescence-feeding insect herbivory, are also worth pursuing. Future reintroductions of C. pitcheri should be designed so as to test hypotheses suggested by such field studies, so that management teams can continue to adapt their strategies to take increasing knowledge of species biology into account. In particular, the Allee effect that we detected in this study suggests a trade-off for managers between reducing intraspecific resource competition by planting transplants sparsely, and reducing herbivory risk, by clustering individuals. Acknowledgments.—We would like to thank the staff at the Central Michigan University Biological Station for their hospitality, especially the director Jim Gillingham. Tim Kailing suggested mapping a rare species with a GPS in the first place and was extremely helpful in framing the analysis. We thank Steve Pacala and Ben Bolker for helpful comments on spatial statistics, and Marlin Bowles, Timothy Bell, and two anonymous reviewers for insightful comments on an earlier draft. This work was supported by Kalamazoo College start-up funds made available to E.B.G.

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ACCEPTED 13 APRIL 2006