Oikos 119: 179187, 2010 doi: 10.1111/j.1600-0706.2009.17793.x, # 2009 The Authors. Journal compilation # 2009 Oikos Subject Editor: Jordi Bascompte. Accepted 29 June 2009 Spatial patterns of acorn dispersal by rodents: do acorn crop size and ungulate presence matter? Carolina Puerta-Piñero, José Marı́a Gómez and Eugene W. Schupp C. Puerta-Piñero ([email protected]) and J. M. Gómez, Depto Ecologı́a, Facultad de Ciencias, Univ. de Granada, ES18071 Granada, Spain. E. W. Schupp, Dept of Wildland Resources and the Ecology Center, Utah State Univ., Logan, UT 84322-5230, USA, and Estación Biológica de Doñana (CSIC), Calle Americo Vespucio s/n, ES 41092 Sevilla, Spain. Seed dispersal is qualitatively effective when it increases recruitment probability. A poorly studied factor likely affecting recruitment is the spatial distribution of dispersed seeds. Seed-caching animals are thought to disperse seeds in a way that reduces clumping and density to impede cache pilfering. Furthermore, dispersal might differ depending on whether the seed is immediately consumed versus cached for later consumption, and might differ depending on the ecological context. The main objectives of this study were to determine: 1) the spatial pattern of seed dispersal by rodents in a heterogeneous environment; 2) whether the patterns differ among years and among acorn competitor exclosure treatments, and 3) whether rodents create different spatial patterns of dispersal for acorns that are cached versus consumed immediately following dispersal. We studied the degree of spatial aggregation of acorn dispersal by rodents using two different estimators derived from the Ripley K and the Diggle G functions. We also analyzed various metrics of dispersal distances. For both analyses we used observed acorn dispersal patterns in two years differing in crop size and inside versus outside exclosures restricting access to acorn-consuming ungulates. During 2003, a year with a larger crop size, maximum seed dispersal distances were less, and the pattern of dispersed seeds was more clumped, than in 2004, a year with a smaller crop size. Median dispersal distances did not differ between years. In the presence of ungulates, seed dispersal was marginally sparser than in their absence. Cached acorns were dispersed more sparsely than acorns eaten immediately. These results have important implications for the quality of seed dispersal for oak recruitment that are likely relevant to other systems as well. Dispersal effectiveness, the contribution of a disperser to the recruitment of a plant, has both a quantitative and a qualitative component (Schupp 1993, Jordano and Schupp 2000). Quantitatively, a disperser is effective if it disperses many seeds. Qualitatively, an effective disperser is one that increases the recruitment probability of dispersed seeds. Several aspects of the qualitative component of dispersal effectiveness have been emphasized in empirical studies. Of these, the distances seeds are dispersed (Vander Wall 1990, Jordano and Schupp 2000, Forget et al. 2005, Jordano et al. 2007, Spiegel and Nathan 2007, Gómez et al. 2008), and the microsite, microhabitat, or habitat where seeds are deposited ( Jordano and Schupp 2000, Vander Wall 2001, 2002, Wenny 2001, Hollander and Vander Wall 2004, Muñoz and Bonal 2007, Gómez et al. 2008), have probably received the most attention. In contrast, a variety of potentially important measures of the quality of dispersal have received much less consideration. Among these, the spatial pattern of dispersed seeds has only begun to be assessed quantitatively (Russo and Augspurger 2004, Moore et al. 2007), despite having important consequences for plant fate (Satterthwaite 2007). For example, seeds deposited in clumps are more likely to suffer from intraspecific competition, postdispersal seed and seedling predation, pathogen attack, and allelopathy (Augspurger and Kelly 1984, Howe 1989, Harms et al. 2000, Schupp et al. 2002). However, if the habitat is intrinsically heterogeneous in conditions and resources, clumped dispersal to favorable microsites could benefit establishment (Muller-Landau et al. 2002). Thus, the spatial pattern of the seed shadow after dispersal is potentially a critical determinant of disperser effectiveness. In addition, because the potential negative effects of clumping are driven by near-neighbour interactions and smallscale density-dependent effects, it is important to consider the distances between dispersed propagules independent of the pattern of dispersion. Seed-caching animals are thought to distribute seeds in a way that reduces clumping and local density of seeds in order to impede the pilfering of caches by other seed consumers (Stapanian and Smith 1978, 1984, Vander Wall 1990, Male and Smulders 2007, 2008). However, the spatial patterns of dispersal and the distances between dispersed seeds are not fixed characteristics of a species of disperser, but instead depend on the ecological context in which dispersal occurs. Since caching incurs both costs and 179 benefits, optimal hoarding should vary depending on the ecological context. Thus, the spatial pattern of seed dispersal might vary depending on the abundance and composition of the community of competitors potentially pilfering caches (Muñoz and Bonal 2007). Spatial patterns of dispersal can also vary depending on whether the seeds will be immediately consumed or will be cached for later consumption (Vander Wall 1990, Li and Zhang 2003, Jansen et al. 2004). Finally, it is predicted that with increasing seed crop size, seeds will be dispersed further before caching in order to maintain a low cache density and reduce pilfering (Stapanian and Smith 1978, Vander Wall 2002, Jansen et al. 2004, Moore et al. 2007). However, increasing seed dispersal distances does not guarantee reduced local small-scale density and cache isolation since long-distance caches can still be quite clumped. Plant spatial patterns result from many processes that can operate simultaneously and even interact with each other (Nathan and Muller-Landau 2000). Seed dispersal is the first process that creates the template for plant spatial distributions (Schupp and Fuentes 1995, Schupp et al. 2002, Russo and Augspurger 2004). After seed deposition, intra- and interspecific competition, post dispersal predation, secondary dispersal, herbivory, pathogens, and more can restructure this primary spatial distribution (Jordano and Herrera 1995, Schupp and Fuentes 1995, Muller Landau et al. 2002). Many of these interacting processes can lead to substantially similar final observed spatial patterns. Thus, it is important to consider the mechanisms actually shaping spatial patterns. The seed dispersal kernel, a measure of the frequency distribution of seeds as a function of distance, has been extensively investigated in a wide variety of systems (Nathan and Muller-Landau 2000, Jordano and Godoy 2002, Nathan et al. 2002, Kwit et al. 2004, Nathan 2007). However, spatially-explicit approaches focused on the actual point patterns of seed dispersal provide a more powerful tool for investigating the processes creating plant spatial patterns (Nathan and Muller-Landau 2000). Nonetheless, to date there has been little success linking the spatial pattern of the seed shadow with the spatial distribution of the plants (but see Russo and Augspurger 2004). In this study we analyze the dispersal distances and the spatial patterns of acorn dispersal by rodents under different ecological contexts: 1) two years that differed in acorn crop size and 2) with and without ungulate competitors for acorns. We discuss the implications of our results for rodent caching behaviour, for plant recruitment, and for seed dispersal effectiveness. In particular, the objectives of this study were to determine: 1) the spatial pattern of seed dispersal by rodents in a heterogeneous oak woodland; 2) whether dispersal distances and spatial patterns differ among years which differed in crop sizes, and among exclosure treatments that alter the community of competitors for acorns, and 3) whether rodents create different spatial patterns of dispersed acorns depending on whether the dispersed acorns are cached or consumed immediately following dispersal. For analyses of spatial patterns, we used spatially-explicit models considering two functions simultaneously. First, Ripley’s K function (Ripley 1981) tests the spatial distribution by counting the number of points within an area (density) at different radii from the origin. 180 Second, the Diggle’s G function (Diggle 1979) considers the distance between each point and its nearest neighbour. Methods Study species and sites As a model system, we used a heterogeneous landscape composed of oak woodland patches (Quercus ilex, the holm oak) intermingled with pine woodlands (Pinus spp.) and shrubland patches (Gómez 2003). The study site is located in the Sierra Nevada protected area, southeastern Spain (3785?N, 3828?W), between 1550 and 1800 m a.s.l. Climate is continental Mediterranean, with cold winters, hot summers, and severe summer drought. Mean annual temperature is 11.58C. Precipitation, mostly as rain in autumn and spring, totals 825 mm year 1. Oak woodland patches, the focus of this study, are internally heterogeneous with Q. ilex clumps or clones mixed together with different species of shrubs, pines, and open spaces. Quercus ilex is a masting evergreen tree abundant in the Mediterranean region. Acorns are dispersed from late October through early December by rodents, mainly the woodmouse Apodemus sylvaticus (Muñoz and Bonal 2007, Gómez et al. 2008), and by the Eurasian jay Garrulus glandarius (Gómez 2003). Acorns at the site are also consumed by ungulates, especially wild boars Sus scrofa, and to a lesser extent Spanish ibex Capra pyrenaica (Gómez and Hódar 2008); these ungulates are acorn predators that compete with rodents. This study was conducted during 2003 and 2004, years differing in acorn production. Acorn production was estimated each year on 50 Q. ilex trees within the study plots. Using a semi-quantitative scale ranging from 0 (no acorns) to 4 (more than 90% of the branches full of acorns), acorn production (n 50 trees) was 1.8391.28 (mean9 SD) in 2003 and 0.8290.52 in 2004 (Levene F 85.84; pB0.0001). Experimental design Experimental acorns were placed on the ground and covered with a 0.51.0 0.1 m (w l h) metal cage with 1-cm2 mesh which was open on two opposing sides to allow the entrance of rodents but not ungulates or jays (supply point, hereafter). Acorns were individually numbered and attached to a metal wire (8 cm long, 0.6 mm ø) with a flag (see Gómez et al. 2008 for a complete description of the methods). This marking method does not appear to affect seed dispersal by rodents (Xiao et al. 2006). Experimental acorns were set out in November during the natural dispersal period, and censused periodically to determine fate. All supply points were located beneath Q. ilex adult trees, the microhabitat in which rodents naturally encounter acorns. When rodents cached acorns in the soil or beneath leaf litter, the flagging was exposed on the surface making relocation easy (Xiao et al. 2006). We began censuses at supply points and searched outwards in expanding circles. As in Gómez et al. (2008), we considered an acorn to be dispersed only when it was moved at least 50 cm from its initial location, independent of the fate of the acorn (cached vs consumed immediately). When a dispersed acorn was found, we recorded the distance (in cm) and direction (in degrees) from the supply point and the fate of the acorn (eaten or cached). Note that the number of surviving caches at the end of the season was too small for the spatial statistical analyses; therefore, our analyses use data from the first census as it was the one with the highest number of cached acorns. In 2003, we monitored a total of 450 acorns in 18 supply points (25 acorns/supply point), 10 located inside a 12-ha exclosure constructed in 1982 with a 2-m tall fence that excludes ungulates but allows the passage of rodents, and eight located outside the exclosure. In 2004, we monitored 1500 acorns in 50 supply points (30 acorns/ supply point), 20 inside the exclosure and 30 outside the exclosure. Overall, we relocated 70% of the acorns dispersed from supply points (Gómez et al. 2008). Quantification of spatial patterns of dispersed acorns We first determined the Cartesian coordinate position of each dispersed acorn within a circular plot centered on the supply point (n 68 supply points) that acorn came from (see Fig. 1 for an example and Supplementary material Appendix 1 for all the maps). Each plot had a radius equal to the maximum dispersal distance for the relocated acorns from that supply point, so each plot had a different radius and area. Thus, each plot included all dispersed acorns that were relocated in the field. As the observed dispersal patterns showed evident lack of stationarity (i.e. the probability distribution varies in space), we then fit the spatial trend of each supply point (see Fig. 1 on the right for an example of this trend) and used this trend to compute the inhomogeneous Ripley’s K and Diggle’s nearest neighbor G for the total observed acorns dispersed from each supply point (Diggle 1979, Ripley 1981, Baddeley and Turner 2005). The tests involve two complementary functions based on: (1) the average number of points located within an area for a given distance from the supply point (Ripley’s K function, K(d), hereafter) and (2) the distance between each point of the observed sample and its nearest neighbour (Diggle’s G function, G(w)). Deviations between the empirical and theoretical curves give insight into the spatial dispersion of the points. The two tests have different sensitivities to different types of spatial distributions (Diggle 1979); for example, G(w) is a better detector of regularity while K(d) has the advantage of being density-independent (Barot et al. 1999). Therefore, using various methods simultaneously, as we have, is highly recommended (Diggle 1979, Ripley 1981). Finally, as we considered all relocated acorns per supply point, we did not compute an edge correction for either the inhomK(d) or the G(w) functions (Wiegand et al. 2007). The Ripley’s K function, K(d), is a second order measure of spatial association. The K(d) function is defined so that lK(d) equals the expected number of additional points of the spatial pattern resulting from a random point process, X, within a distance d of a point of X, where l is the intensity (expected number of points per unit area), as in the equation: K(d)p d2 where d is the distance between any two points of the sample. To attain constant variance and easier interpretation of the results, K(d) is often transformed (Fortin and Dale 2005) into the function: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L(d) K(d) =p The observed point pattern x is assumed to be a realization of a random point process X (Baddeley and Turner Figure 1. Example of the observed acorn dispersal pattern from a supply point (left) and its corresponding fitted trend (right). Note that the sums of raw residuals on both dimensions (X and Y) are cumulative. 181 2005). The null model is a homogeneous Poisson point process. In our case, because of clear deviations from stationarity of the observed patterns (see Supplementary material Appendix 1 for visual inspection), we used the conditional intensity of an inhomogeneous Poisson process on the spatial pattern W. We assume X has a probability density f(x; U) with respect to the distribution of the Poisson process with intensity 1 on W. The distribution is governed by a p-dimensional parameter U. We then used the Papangelou conditional intensity which is defined (Baddeley and Turner 2005) for a location u W and observed point pattern x as: lU (u; x) f (x@ fug; U f (x =u; U) This has an intensity function l:W 0D, which has a conditional intensity of l (u, x)l(u), where l is the intensity of points. The conditional intensity lU (u) will depend on U to reflect the ‘spatial trend’ (a change in intensity across the region of observation) (Baddeley and Turner 2005). This resulting function will be referred to hereafter as inhomK(d). The Diggle nearest neighbor function, G(w), is the cumulative distribution function of the distance from a point of the pattern X to the nearest other point of X. G(w) summarizes the clustering of near-neighbour pairs of points, and is defined as: G(w) 1exp(l p w 2 ) where w indicates the distance between a point and its nearest neighbour. We then compared the observed distribution at each supply point to an inhomogeneous Poisson process with the same area and number of acorns (H0: complete spatial randomness, CSR) to see if the spatial pattern followed a random, clumped, or homogeneous distribution. Tests of significance were estimated by a Monte Carlo procedure using 200 permutations (Wiegand et al. 2007). Rejection limits were estimated as the envelopes of the simulation. If the observed distribution was above the envelopes the distribution was considered as clumped, within the envelopes as random, and below the envelopes as homogeneous. Finally, when the null hypothesis (CSR) was rejected, we followed the suggestion of Barot et al. (1999) and computed the maximum discrepancy distance (dmax) between the theoretical and observed Ripley’s inhomogeneous K and Diggle’s G functions (dmaxK and dmaxG, respectively) and subsequently used them as dependent variables. These maximum discrepancy distances were computed as: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dmaxK sup j K(d)=p K + (d)=pj d dmaxG sup jG(w)G+ (w)j w where the first part of the equations corresponds to the observed empirical functions for each plot while the second part corresponds to the theoretical functions (H0: complete spatial randomness following an inhomogeneous Poisson distribution). 182 For clumped patterns, dmax can be viewed as a measure of the ‘compactness’ of the clump. For example, in the case of G(w) it measures the average distance between points within a clump (Barot et al. 1999). Thus, the larger the value of dmax the less ‘compact’ the spatial distribution of the acorns and vice versa (Barot et al. 1999). Each point, or dispersed acorn, can be classified by fate as cached or eaten. We included this information on fate (‘marks’ in geostatistical terminology and hereafter) for each point and then calculated inhomK(d) including the information of this mark to compute a maximum discrepancy distance (dmaxKF) as described above. Finally, we divided the acorns into eaten and cached and separately computed the inhomK(d) and G(w) functions to calculate dmaxK and dmaxG for each acorn category (dmaxKEATEN, dmaxKCACHED, dmaxGEATEN, dmaxGCACHED, respectively) in order to investigate whether acorn fate affected patterns of dispersion. We performed all spatial computations using Spatstat 1.86 under R 2.5.0 (Baddeley and Turner 2005, R development Core Team 2007). Statistical analysis We used two-way ANOVAs to compare median and maximum dispersal distances between years, exclosure treatments, and the interaction year exclosure. In these analyses we included the calculated median and the measured maximum distance for each supply point as dependent variables. Medians rather than means were calculated for each supply point because the distributions of distances were highly skewed. Only dispersed seeds (i.e. moved ]50 cm) were used in these analyses. The effects of exclosure and year on the spatial patterns of dispersed acorns as measured by dmax were explored using general linear mixed models (GLMM): dmaxK Yearr Exclosure dmaxG Yearr Exclosure We then fit the same GLMMs described above, but also including acorn fate, in order to see the effect of exclosure and year on the spatial patterns of acorns after controlling for their fate. dmaxKF Yearr Exclosure Subsequently, we divided the data into cached and eaten acorns to separately compute the following GLMMs for cached dmaxK CACHED Yearr Exclosure dmaxGCACHED Yearr Exclosure and eaten acorns dmaxK EATEN Yearr Exclosure dmaxGEATEN Yearr Exclosure Finally, we analyzed whether the spatial pattern of the acorns differed as a function of fate by comparing the dmaxK and dmaxG between cached and eaten acorns. For this, we fit the general linear models (GLM) dmaxK Fate dmaxG Fate In all models, the supply point was the experimental unit. Response variables were previously transformed to improve normality using log or arcsin(square root) transformations. Year was considered a random factor and exclosure a fixed factor. Significance of the random factor was calculated by comparing models with and without the random factor (Pinheiro and Bates 2000, Pinheiro et al. 2006). All analyses were performed using R (R Development Core Team 2007). Results Although mean dmax values appeared to be greater outside than inside the exclosure, results were only marginally significant for dmaxK and not close to significant for dmaxG (Table 1, Fig. 3). Thus, dispersed acorns were marginally more sparsely distributed outside the exclosure in the presence of ungulates than inside the exclosure in the absence of ungulates. The percentage of the total variance of the whole model (Table 1) explained by the random factor (year) for dmaxK and dmaxG was 20.5% and 29.7%, respectively. Acorn fate effect Dispersal distances The median dispersal distances did not differ significantly between years or exclosure treatments (Fig. 2). However, maximum dispersal distances were significantly less in the higher acorn year 2003 (370.94 cm9350.20, mean9SE of maximum dispersal distance) than in the lower acorn year 2004 (1591.86 cm9210.06). The interaction was not significant in either analysis. Spatial pattern of acorn dispersal For all supply points in both years all observed distributions and distance classes were above the envelopes of the simulations, whether considering the inhomK(d) or the G(w) function. Thus, the observed point patterns of dispersed acorns were all significantly clumped at a B 0.05, (see Supplementary material Appendix 1 for visual inspection of the patterns). Year and exclosure effects The inhomK(d) and G(w) functions showed analogous results. Both dmaxK and dmaxG were significantly greater in 2004 than in 2003 (Table 1, Fig. 3). Thus, in 2004, the year with lower acorn production, the spatial pattern of dispersed acorns appears to be less compact, or less clumped, than in 2003, a year with more acorns. There was no significant effect of either year or exclosure on dmaxKF (Table 1). Despite the lack of significance of year on dmaxKF, the AIC in all cases demonstrates that the best models were those containing the random factor (year). The percentage of the variance of the whole model explained by the random factor (year) was 14.6% for dmaxKF. Thus, there is still strong evidence that spatial patterns were more compact in 2003 than in 2004, even when acorn fate was controlled for. Finally, there were significant differences in dmaxG between acorns that were eaten immediately following dispersal and those that were cached (Table 2, Fig. 4); the distances between neighbouring cached acorns were greater than the distances between neighbouring eaten acorns. Though not significant, there were also noticeable differences for dmaxK between eaten and cached acorns, with a tendency for cached acorns to be dispersed in a less clumped distribution (Table 2, Fig. 4). When splitting the acorns into eaten versus cached, the year factor was highly significant in all cases (Table 3). Thus, as in the overall combined analysis, acorns were more clumped in 2003 than in 2004 for both cached and eaten acorns (Fig. 4). Exclosure significantly affected the spatial pattern of eaten acorns but not the clumping of cached acorns (Table 3). Eaten acorns were less clumped outside the ungulate exclosure (824.069150.98; mean9 SE dmaxKEATEN) than inside the exclosure (388.649 150.98). The opposite pattern was found with distances among nearest neighbour acorns, which were greater Figure 2. Results of the two-way Anovas for year and exclosure effects on median and maximum dispersal distances. DFmodel 67, DFfactors 1, DF. *p B0.01. 183 Table 1. Effects of year and exclosure on spatial patterns of seed dispersal. GLMM considering the factor Year as random and Exclosure as fixed. In all cases the best model in terms of Akaike information criterion (AIC) was the model containing the random factor (pB0.05 contrasting models with and without the random factor). R2 correspond to the total variance explained by the whole model. dmax variables consist of the maximum discrepancy distance between the observed and theoretical spatial pattern (dmax) for Ripley’s K and Diggle’s G. dmaxKF, corresponds to dmax considering the mark of the fate of the acorns (eaten vs cached). DF dmaxK F Year Exclosure R2 1 1 66 3.793 0.146 dmaxG p B0.05 0.056 inside the exclosure (0.4190.07; mean9SE dmaxGEATEN) than outside (0.3690.07). Discussion The spatial pattern of holm oak acorn dispersal by rodents differed between the two years, whether we considered all dispersed acorns together or considered eaten and cached acorns separately. During 2003, the year with a larger crop, seed dispersal was more clumped than in 2004. Interestingly, these changes in spatial patterns occurred without a change in median dispersal distances, although the maximum dispersal distances were greater in 2004. More acorns were put out per supply point in 2004 (30) than in 2003 (25), and with more acorns tracked one would expect to find greater maximum dispersal distances by chance. However, a 20% increase in the number of acorns should not result in a four-fold increase in observed maximum dispersal distances. Additionally, acorn dispersal in this system is highly biased to particular microhabitats (e.g. oaks and shrubs), but this behaviour is unlikely to affect our results since there was no difference between 2003 and 2004 in the distribution of dispersed acorns among microhabitats (Gómez et al. 2008). A number of studies have shown that differences in seed crop size can result in differences in some aspect of seed dispersal patterns, such as the proportion of seeds dispersed (Jordano and Schupp 2000, Jansen et al. 2004), F 1.207 0.155 dmaxKF p B0.05 0.276 F 2.586 0.118 p ns 0.113 the speed of seed dispersal (Vander Wall 2002), or the proportion of dispersed seeds placed in primary (Jansen et al. 2004) or secondary (Vander Wall 2002) caches. Furthermore, a number of studies also have shown that crop size affects distances seeds are dispersed (Vander Wall 2002, Jansen et al. 2004, Li and Zhang 2007, Moore et al. 2007). Our results contradict somewhat the conventional theoretical optimization models that predict that with increasing seed abundance rodents will cache further from the seed source (parent) in order to maintain a low density and high spacing of cached seeds and reduce pilfering (Stapanian and Smith 1978, Moore et al. 2007). However, our results are compatible with other studies that have documented shorter dispersal differences with increased seed abundance (Jansen et al. 2004, Moore et al. 2007). Though they are to some extent contrary to the model prediction, these results are not necessarily surprising. As noted by Moore et al. (2007), the original prediction failed to consider that food abundance can directly affect the behaviour and impact of potential cache pilferers. In smaller crop years it should be even more important to have widely-spaced caches that are more isolated from parents because with fewer seed resources available, pilfering pressure will be much greater than in larger crop years. In years with smaller crops, rodents are expected to be more dependent on stored supplies which should favor more effective hoarding (Broding et al. 2001) and increased cache spacing. Other important factors not considered in this study, such as among-year variation in rodent populations, may Figure 3. Box-plots showing the median (points), 2575% quantiles (boxes), and 1090% (whiskers) values between years (2003 had higher acorn production than 2004) and exclosure treatments. Values consist of the maximum discrepancy distance between the observed and theoretical spatial pattern (dmax) for Ripley’s K (left) and Diggle’s G (right). Larger dmax values mean a greater distance between neighboring seeds (dmaxG) and a less clumped distribution of dispersed seeds (dmaxK). 184 Table 2. Effect of initial fate of acorns (eaten versus cached) on spatial patterns of seed dispersal. dmax variables consist of the maximum discrepancy distance between the observed and theoretical spatial pattern (dmax) for Ripley’s K and Diggle’s G. R2 correspond to the total variance explained by the whole model. DF Fate R2 1 dmaxK dmaxG F p F p 1.18 0.001 0.28 76.19 0.22 B0.0001 also contribute to the differential dispersal patterns we found. Since the low crop year 2004 was preceded by high crop years, the population of rodents might have increased at the same time that there was a reduction in the availability of resource. The resulting increase in intraspecific competition would further accentuate the need to better protect cached resources in the low crop year, further contributing to a greater spacing of acorns and a greater maximum dispersal distance. Additionally, because heavier acorns tend to be dispersed greater distances than lighter acorns (Gómez et al. 2008), our results might be due at least partly to having heavier acorns in the low crop year of 2004. However, acorns used in our experiments were actually significantly heavier in 2003 (4.7390.05, mean9SE), the year with shorter maximum dispersal distances and more clumped distributions, than in 2004 (3.4690.04; R2 0.12, F 358.56, pB0.0001). Thus, the differences in acorn weight cannot explain our results. While it has generally been assumed that greater dispersal distances result in less clumped patterns, actual patterns of dispersal have not been previously quantified. Our results are at least partially compatible with the assumption, but not entirely. Although maximum dispersal distances were greater in the year with less clumped dispersion, the median dispersal distances did not differ at all. This might suggest that rodents responded in multiple ways, altering distances dispersed to some extent, but perhaps also altering dispersion of caches independent of distance. Although our study cannot directly quantify the effect of dispersal patterns on cache survival due to the very low survival of caches, more hyperdispersed distributions of caches have been experimentally demonstrated to reduce cache pilfering by birds (Male and Smulders 2007, 2008). Although it is often assumed that greater dispersal distances result in greater cache survival, we could not detect a significant effect of distance on survival in this system, probably because of the extremely low survival of caches (Gómez et al. 2008). Thus, there might be a variety of ways that rodent caching behaviour can respond in order to reduce pilfering and increase survival of caches. In a related result, we found strong effects of acorn fate on dispersal pattern. That is, rodents dispersed the acorns in different patterns depending on whether they were to consume or cache them. As expected, acorns cached for future consumption were spaced further apart than were acorns that were eaten immediately after dispersal. Because there was no significant effect of fate on the densityindependent dmaxK, our result might be due to a large extent to the much lower numbers of cached than of consumed seeds (Gómez et al. 2008). Nonetheless, it is still an important result in that acorns were not being aggregated in distinct caching locations to any greater degree than expected based on acorn dispersal in general. Further, the increased spacing of cached acorns, no matter the cause, is expected to decrease pilfering. Although not significant, our results suggest that rodents might disperse acorns slightly more sparsely in the presence of ungulates. Such behaviour is expected to reduce loss to these interspecific competitors. In a similar study in central Spain, the presence of ungulates did not affect the distance A. sylvaticus dispersed acorns of Q. ilex, but did alter the microhabitat destination of caches (Muñoz and Bonal 2007). In this study we also found no difference in median or maximum dispersal distances inside and outside exclosures. A possible explanation of the overall results is that rodents only subtly alter their caching Figure 4. Box-plots showing the median (points), 2575% quantiles (boxes), and the 1090% (whiskers) values between years (2003 had higher acorn production than 2004) and fate of the acorns. Values consist of the maximum discrepancy distance between the observed and theoretical spatial pattern (dmax) for Ripley’s K (left) and Diggle’s G (right). Larger dmax values mean a greater distance between neighboring seeds (dmaxG) and a less clumped distribution of dispersed seeds (dmaxK). 185 Table 3. Effects of year and exclosure on the spatial pattern of seed dispersal for cached and eaten acorns. DF Cached acorns Eaten acorns dmaxK 2 Year Exclosure R2 Variance (%) 1 1 61 dmaxG x p 17.64 1.91 0.27 42.94 B0.0001 0.17 dmaxK 2 p x 8.39 0.63 0.004 0.428 0.12 10.30 7.40 0.42 48.61 x 23.61 2 dmaxG 2 p x p 0.001 0.006 16.19 4.14 0.46 63.02 B0.0001 0.042 GLMM considering the factor Year as random and Exclosure as fixed. dmax variables consist of the maximum discrepancy distance between the observed and theoretical spatial pattern (dmax) for Ripley’s K and Diggle’s G. R2 correspond to the total variance explained by the whole model. behaviour in response to interspecific competitors. Alternatively, rodents may not have responded to competitors at all, but rather to other factors that obscured the response to competitors. For example, the ungulate exclosures likely increased the amount of acorns available inside the exclosures relative to outside, which, based on our results on annual variation in patterns of dispersal, might have directly resulted in the slightly greater dispersion of caches outside relative to inside exclosures. Either way, our results overall tentatively suggest that rodents consider other acorn consumers with similar predation and foraging behaviors, such as conspecifics and perhaps even jays, as more of a pilfering threat than ungulates. Although our study cannot document that the plastic caching behaviour found here leads to greater plant recruitment, results suggest that it is likely to affect the qualitative component of dispersal effectiveness. First, as previously described in Gómez et al. (2008) and noted above, 2003 and 2004 did not differ in frequencies of acorns dispersed to different microhabitats. Thus, greater dispersal distances and greater clumping did not result in more acorns being dispersed to lower quality microsites. On the positive side, although greater acorn mortality is expected in the low crop year of 2004 due to large numbers of rodents feeding on the few acorns (Jansen et al. 2004), the shift in the spatial pattern of caching is expected to increase acorn survival over what would occur if the rodents did not cache more sparsely in low acorn years. That is, the decreased clumping and increased spacing of seeds in 2004 is expected to have positive consequences for further establishment (Russo and Augspurger 2004) that can help alleviate to some extent the expected greater loss due to the lower acorn crop. First, the decreased clumping is expected to result in a reduction in cache pilfering, which in turn should lead to an increased chance of surviving to germination. In addition, many post-dispersal processes are to some extent dependent on density or spacing among individuals. For example, intraspecific seedling competition, pathogen attack, and predation sensu lato of seeds or seedlings likely depend on the density and distances among dispersed propagules (Augspurger and Kelly 1984, Harms et al. 2000, Nathan and Muller-Landau 2000, Schupp et al. 2002, Gómez and Hódar 2008). Thus, from the perspective of spatial patterns of dispersed seeds, the plastic caching behaviour of rodents appears to some extent to have increased the quality of dispersal in low crop years over what would be expected if caching behaviour was constant. That is, although few acorns survived in 186 the low crop year, without changes in rodent caching behaviour it is likely that even fewer would have survived. To a minor extent, the same appears to have been true in the presence of acorn competitors. In conclusion, we have demonstrated the importance of considering the actual spatial pattern of seed dispersal, not simply the distance-based dispersal kernel. We show that in a smaller crop year acorns were dispersed to greater maximum distances and in a less tightly clumped seed dispersal pattern without altering the median dispersal distance. Although with only two years of data we cannot unequivocally demonstrate that the change in crop size caused the shifts in dispersal patterns, the results are compatible with our present understanding of how caching strategies should change in order to reduce pilfering in years where stored items are more valuable. This plastic caching behaviour likely has important consequences for seed dispersal effectiveness by affecting post-dispersal density-dependent processes including cache pilfering. Acknowledgements We deeply appreciate the guidance of Marcelino de la Cruz through the statistical analysis of spatial point patterns. 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