Oikos 119: 1841–1847, 2010 doi: 10.1111/j.1600-0706.2010.18547.x © 2010 The Authors. Oikos © 2010 Nordic Society Oikos Subject Editor: Robin Pakeman. Accepted 26 March 2010
Density-dependent pre-dispersal seed predation and fruit set in a tropical tree F. A. Jones and L. S. Comita F. A. Jones ([email protected]
), Smithsonian Tropical Research Inst., Apartado 2072 Balboa, Ancon, Republic of Panama, and: Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, Berks, SL5 7PY, UK. – L. S. Comita, Dept of Ecology, Evolution and Environmental Biology, Columbia Univ., 1200 Amsterdam Avenue, New York, NY 10027, USA.
Negative density-dependent demographic processes operating at post-dispersal seed, seedling, and juvenile stages are the dominant explanation for the coexistence of high numbers of tree species in tropical forests. At adult stages, the eﬀect of pollinators and pre-dispersal fruit predators are often dependent on the density or abundance of ﬂowers and fruit in the canopy, but each have opposite eﬀects on individual realized reproduction. We studied the eﬀect of density on total and mature fruit set and pre-dispersal predation rates within individual tree canopies in a common canopy tree species, Jacaranda copaia in a 50-ha forest census plot in central Panama. We sampled all reproductive sized trees in the plot (n ⫽ 188) across three years and estimated fruit set and predation rates. Population-wide pre-dispersal seed predation averaged between 6–37% across years. Using linear mixed eﬀects models, we found that increased density and fecundity of conspeciﬁc neighbours increased focal tree fruit set, but also the rate of pre-dispersal predation. An interaction between individual and neighbourhood fruit production predicted lower predation rates at high individual and neighbourhood fecundities, which suggests predator satiation at high fruit abundance levels. However, the rate at which fruit set increased with conspeciﬁc neighbour fruit production was greater than the rate at which fruit were lost to predation, resulting in an overall positive eﬀect of neighbour density on mature fruit production in focal trees. Our results run counter to the expectation of a uniformly negative eﬀect of density across all life stages in tropical trees and suggest further exploration of the role of spatial clumping, pollen dispersal limitation, and predation at pre-dispersal adult stages in maintenance of species diversity in plant communities.
Negative density-dependent recruitment is one of the bestsupported explanations for the coexistence of hundreds to thousands of tree species on scales less than 1 km2 in tropical forest communities (Wright 2002). Negative density-dependent processes regulate tropical tree populations by reducing fecundity, survival, growth, or recruitment, which slows the rate of competitive exclusion and therefore maintains species diversity (Janzen 1970, Connell 1971). While negative density-dependent growth and survival of trees at juvenile and adult life stages has been well documented (Harms et al. 2000, Packer and Clay 2000, Hubbell et al. 2001, Hille Ris Lambers et al. 2002, Blundell and Peart 2004, Uriarte et al. 2004, Queenborough et al. 2007, Comita and Hubbell 2009), conspeciﬁc neighbours can have indirect positive eﬀects on individual rates of reproduction. For example, high-density neighbourhoods of ﬂowering adults attract pollinators, increasing both quantity and quality of pollen from neighbouring trees, which can increase fruit and seed set, particularly in self-incompatible species (Ghazoul et al. 1998, Ghazoul 2005, Aizen and Harder 2007). Positive density-dependent reproduction, survival, and growth have important implications for the maintenance of diversity. Positive density-dependent fruit set, if not oﬀset
at some later stage, would be expected to destabilize species coexistence by causing common species to become more common at the expense of rare ones (Blundell and Peart 2004, Zhou and Zhang 2008). On the one hand, the positive eﬀects of conspeciﬁc neighbours on seed and fruit production could be ﬂeeting if high densities of reproductive trees also attract pre-dispersal seed and fruit predators at suﬃciently high numbers to cause a net negative eﬀect of density on mature fruit set. Janzen (1970) hypothesized that such negative density-dependent pre-dispersal seed and fruit predation occurred within adult tree canopies and that species-speciﬁc pre-dispersal seed and fruit predators were common to most tropical forest tree species. This hypothesis further states that density-dependent pre-dispersal seed and fruit predators within the canopy of individuals and among near neighbours slows competitive exclusion by reducing the number of seeds available for regeneration, thereby reducing the number of seeds and seedlings that are able to escape density- and distance-dependent enemies (Carson et al. 2008). On the other hand, very high densities of seeds or fruits within canopies or neighbourhoods can also result in predator satiation, which lowers the probability of seeds being predated at high fruit abundances (Augspurger 1981,
Ghazoul and Satake 2009). This eﬀect would would reinforce positive density-dependent fruit set and require that other negative density-dependent processes operate at postdispersal stages if diversity is to be maintained. The relative strengths of pollinator attraction and success, pre-dispersal seed predation, and predator satiation ultimately determine whether conspeciﬁc neighbourhood density has a net positive or negative eﬀect on the realized fecundity of individual plants. In the present study, we examined how conspeciﬁc neighbour density inﬂuences pre-dispersal seed predation and potential and realized fecundity in a common Neotropical tree species, Jacaranda copaia. We have previously shown that total fruit set in this self-incompatible species increases as an individual is surrounded by more reproductive conspeciﬁcs (controlling for soil nutrients, heterospeciﬁc competition, and genetic relatedness of neighbours) likely due to increased pollinator attraction and pollen availability (Jones and Comita 2008). However, during that study we noted that many fruits were attacked and prematurely lost due to a pre-dispersal galling wasp seed predator. The present study therefore aims to quantify rates of pre-dispersal insect seed predation in J. copaia and to assess the degree to which the previously documented positive density-dependent fruit set is oﬀset, if at all, by negative density-dependent pre-dispersal fruit predation (hereafter predation) within focal tree canopies and local neighbourhoods. To do this, we measured total fruit production and predation rates of all reproductive sized (n ⫽ 188) Jacaranda copaia individuals within a fully mapped forest census plot in central Panama over three years. Using these data, we address two questions: 1) is predation negatively density-dependent within tree canopies and within local tree neighbourhoods? And 2) is the strength of negatively density-dependent predation great enough to oﬀset positively density-dependent fruit set, as measured by the total mature (unpredated) fruit set?
Methods Site and species description We conducted our research in three of four years (2000– 2003) on the Barro Colorado Island (BCI) 50-ha Forest Dynamics Plot (FDP), Panama. The BCI FDP was established in 1980 and consists of a standing number of ∼ 240 000 mapped stems ⱖ1 cm diameter at 1.3 m above ground (DBH) of approximately 300 species and is completely recensused every ﬁve years (Hubbell et al. 1999, Hubbell 2005). We used information from the 2000 census to identify reproductive sized adults of our focal species, Jacaranda copaia. Jacaranda copaia is a canopy tree whose seedlings colonize large tree-fall gaps (Brokaw 1987, Wright et al. 2003). The species ranges from Bolivia to Belize and is a common pioneer in central Panama. It ﬂowers at the peak of the dry season on BCI and produces large abundant ﬂoral displays in a cornucopia strategy typical of many Bignoniaceae (Gentry 1974). Pollination of J. copaia occurs via large assemblage of bees but primarily by medium-sized solitary bees (Degen and Roubik 2004, Maues et al. 2008). The species is an allogamous outcrosser with late acting self-incompatibility and like many tropical tree species fruit set can be strongly 1842
pollen limited (James et al. 1998, Jones and Comita 2008, Maués et al. 2008). The minimum reproductive size of J. copaia is 20 cm DBH (Wright et al. 2005a). Jacaranda copaia seeds are produced in large woody capsules that when mature are approximately 10–15 cm long each with two locules (Fig. 1a). Each fruit contains approximately 250 seeds (S. J. Wright pers. comm.). Seeds have a mean mass of 6.5 mg and a mean area of 4.6 cm2 (Augspurger 1983), are wind-dispersed, and show median dispersal distances ranging from 15 to 26 m, but also have a signiﬁcant fraction travelling distances ⬎ 1 km (Jones et al. 2005, Jones and Muller-Landau 2008, Wright et al. 2008). Seed dispersal occurs in late August and September. After fruits ripen, dehisce, and release their seeds, the dry woody halves fall to the ground beneath the tree and persist in litter up to a year after seed dispersal (Fig. 1a). Capsules that are predated by a chalcid wasp (Chalcidiodea) form a characteristic woody gall in one locule and can be readily diﬀerentiated from mature and immature fallen fruit (Fig. 1b). Within the infected locule, 5–10 wasp larvae consume all seed material and pupate within the galled capsule. Infected galled fruit fall from the canopy and do not release seeds. Therefore, predation of fruit results in the destruction or immature abortion of all seeds within both locules. We know that infection occurs at the pre-dispersal stage and that this insect predator is common in Panama because infected capsules have been observed in the canopy from a canopy crane, and wasp predation and capsule galling is present in other populations across the Isthmus of Panama (Jones unpubl.). Fecundity and predation estimation We established transects in each cardinal direction (N, S, E, W) beneath the canopy of each of the 188 reproductive-size adult J. copaia individuals in the BCI FDP in November – December 2000, 2002 and 2003 (Fig. 1c). Fruit production in 2001 was almost non-existent; therefore we did not collect fecundity or predation information in that year. For each tree, the transect extended to the edge of the tree’s canopy. Jacaranda copaia individual canopies do not overlap with conspeciﬁc or heterospeciﬁc canopies due to shade avoidance (Wright et al. 2005a). At 1 m intervals along each transect, the total number of mature dehisced capsules, immature non-dehisced capsules and galled capsules infected with wasp seed predators were counted within a ½ m2 square PVC frame laid on the ground. We refer to the combined total of each of these as the total fruit set below. Current year capsule production was diﬀerentiated from previous year by the state of decay of the capsule. Canopy area of each tree was estimated from the length of each transect beneath each tree and used to determine the area of an ellipse along the two main axes. We estimated the total fruit set for each individual in each year by determining the mean fruit set per m2 canopy area and multiplied it by the total canopy area of the individual (Jones and Comita 2008). Fecundity and predation modelling To determine whether the density of fruit within a tree’s canopy and within its local neighbourhood inﬂuenced rates of pre-dispersal seed predation, we used generalized linear
Figure 1. (a) Mature capsule of Jacaranda copaia. (b) Predated capsule of J. copaia. (c) Map of reproductive J. copaia in the 50-ha Forest Dynamics Plot on Barro Colorado Island. Circle size corresponds to the total capsule production of each tree in 2000 (small: ⱕ50, medium: 51–200, large: ⬎200 capsules). Shading corresponds to the proportion of capsules attacked by pre-dispersal wasp seed predators (light grey: ⬍25%, dark grey: 25–50%, black: ⬎50% predation). Grey lines are 5 m contour intervals.
mixed-eﬀects models with binomial error. The number of successes was equal to the number of capsules predated and the number of trials was equal to the total number of capsules counted in the transects beneath the tree. Individual tree fecundity was calculated by multiplying the number of capsules per m2 by the canopy area of the individual, as described above. Neighbourhood fecundity was calculated by summing up the total capsules produced by all J. copaia individuals within 30 m of the mapped coordinates of each focal tree, not including those produced by the focal individual. A radius of 30 m was selected based on preliminary analyses in which we compared AIC values for models with neighbourhood radii ranging from 25 to 50 m (Appendix 1). When individuals were less than 30 m from the edge of plot, we assumed that the portion of the circle located outside of the plot had the same average neighbourhood fecundity as the portion within the plot. Predation rate was modelled as a function of year, log-transformed individual fecundity, log-transformed neighbourhood fecundity, and the interaction between individual and neighbourhood fecundity. Because we had repeated measures for individual trees across three years, we included
individual as a random eﬀect in the model. Predation rates of individuals spaced less than 25 m apart tended to be correlated (Appendix 2a). We therefore divided the plot into 800 25 ⫻ 25 m quadrats and included the quadrats as a random eﬀect to account for any spatial autocorrelation that was not due to neighbourhood fecundity. Examination of model residuals revealed that the model adequately accounted for spatial autocorrelation (Appendix 2b). We also studied the eﬀect of neighbourhood fecundity on the total number of capsules produced per tree (mature, immature, and depredated) using a linear mixed eﬀects model to allow for direct comparison with the analysis of seed predation. The model included year, log-transformed values of DBH, and log-transformed neighbourhood fecundity as ﬁxed eﬀects, and both quadrat and individual as random eﬀects as above. We then tested whether pre-dispersal predation negated the positive eﬀect of neighbours on fruit set by using an identical model to analyze eﬀect of neighbours on the realized fecundity for each individual, i.e. the number of mature, non-predated capsules produced. If negative density-dependent predation was suﬃciently strong 1843
Proportion of capsules predated
1.0 0.8 0.6 0.4 0.2 0.0 h Neig log (
Figure 2. The interaction between individual fruit production, neighbourhood fruit production, and proportion of predated capsules within individual trees of Jacaranda copaia on Barro Colorado Island for the year 2000. Stars represent the observed values for focal trees (n⫽ 188) and the grey mesh represents the surface generated from the predicted values of the predation model for that year.
in 2000 (86.7%), and was lower in 2002 (68.6%) than in 2003 (72.8%). Predation rates were the highest in 2000, with an average of 38% per tree, followed by 2002 (7%) and 2003 (6%). High fruit abortion and predation rates in 2000 substantially reduced realized fecundity, such that the mean number of mature fruits per tree was lower in 2000 than in the other years, despite high total fruit set (Table 1). Predation rates varied with year, individual fecundity, and neighbourhood fecundity (Table 2). The proportion of capsules predated increased as the total fruit set of the focal individual increased and as the fruit set of neighbouring J. copaia trees increased, indicating negative densitydependent pre-dispersal predation. However, the individual by neighbourhood interaction term had a signiﬁcant, negative eﬀect on predation rates, resulting in decreased predation rates when both individual and neighbourhood fecundity values were high (Fig. 2). As expected, both tree size (DBH) and neighbourhood fecundity had a signiﬁcant positive eﬀect on total fruit production (Table 3). The number of mature, non-predated fruit produced (i.e. realized fecundity) remained positively inﬂuenced by both tree size and neighbourhood fecundity, indicating that increased seed predation on individuals with high fruit production and in high-density areas did not cancel out the positive eﬀect of conspeciﬁc neighbours on total fruit production. Thus, overall, increased adult density had the eﬀect of increasing net realized fruit production.
Discussion to oﬀset positive density-dependent fruit set, we expect the neighbourhood fecundity eﬀect to no longer be signiﬁcantly positive when analyzing only mature, non-predated capsules. All analyses were done in the R 2.7.1 operating environment (R Development Core Team 2008), using the ‘lme4’ (Bates and Maechler 2009) and ‘nlme’ packages (Pinheiro et al. 2009) for mixed eﬀects models.
Results Jacaranda copaia showed wide variability in reproduction, individual fruit set and predation rates across years (Table 1). The mean number of capsules produced by neighbours within 30 m of the focal individuals ranged from 340 (SD ⫽ 598) to 606 (SD ⫽ 1535). Population-wide reproduction (percentage of trees with total capsule count ⬎ 0) was the greatest
We found evidence for both positive density-dependent fruit set and negative density-dependent pre-dispersal predation in the common Neotropical rainforest tree J. copaia. However, the relative strengths of each eﬀect diﬀered. Negative density-dependent predation was not strong enough to oﬀset positive density-dependent fruit set, resulting in a net positive eﬀect of neighbourhood tree density on reproductive output of focal trees over the three years of this study. Positive density-dependent fruit set, if it translates into greater propagule availability for regeneration and is not oﬀset by negative density-dependent processes at later stages, has important implications for the maintenance of forest diversity in both natural and disturbed landscapes. Below, we discuss our results in terms of what is known about positive and negative density-dependence in tropical forest trees and suggest future avenues of research on this topic.
Table 1. Summary statistics for fruit set and pre-dispersal seed predation in the Neotropical tree, Jacaranda copaia (n ⫽ 188), from the Forest Dynamics Plot on Barro Colorado Island, Panama. Year
Population-wide total fruit production Mean (SD) capsule production (tree–1) Mean (SD) proportion of fruit predated (tree–1) Mean (SD) mature capsules (tree–1)* Mean (SD) number of fruit within 30 m Proportion of reproductive trees *capsules not aborted or predated.
48 694 298.7 (890.0) 0.38 (0.26) 47.4 (159.4) 606.4 (1535.4) 0.867
50 168 388.9 (641.7) 0.07 (0.08) 265.6 (461.2) 589.0 (1119.0) 0.686
25 890 188.9 (510.7) 0.06 (0.15) 112.0 (305.1) 340.0 (598.9) 0.728
Table 2. Results of the generalized linear mixed effects model of fruit predation in Jacaranda copaia across three years on Barro Colorado Island, Panama. Estimates of the intercept for years 2002 and 2003 are calculated as the difference relative to 2000. Parameters
Intercept year 2000 year 2002 year 2003 log(individual fruit production) log (neighbourhood fruit production) individual fruit production ⫻ neighbourhood fruit production
–1.792 –2.232 –2.990 0.269
0.299 –6.0 0.055 –40.0 0.087 –34.3 0.052 5.2
p ⬍ 0.001 ⬍ 0.001 ⬍ 0.001 ⬍ 0.001 0.0002 ⬍ 0.001
Negative density-dependent pre-dispersal seed predation Negative density-dependent survival and growth has been well documented in plant neighbourhoods at both the population and community levels (Harms et al. 2000, Uriarte et al. 2004, Comita and Hubbell 2009, Comita et al. 2009). Due to the diﬃculty of accessing tree canopies, much less information is available about eﬀects of neighbourhood density on fruit production and pre-dispersal seed predation, despite their potentially strong eﬀect on population dynamics at later stages. Given that the highest densities of fruit will necessarily occur within the canopy before dispersal, strong negative density-dependent pre-dispersal predation can have extreme eﬀects on the number of seeds available for dispersal and regeneration (Janzen 1970). Pre-dispersal predation can be very high in the J. copaia population studied here, with individual losses of fruits averaging 38% in one year of our study. Our results reveal negative density-dependent predation is a function of both the fecundity of individual trees and the fecundity of neighbouring trees up to scales of 30 m. Trees with larger fruit crops also experienced greater predation rates, as did focal trees situated in neighbourhoods with high aggregations of fruiting adults. Enemies may be attracted to and persist in areas of high Table 3. Results of the generalized linear mixed effects models of (a) total and (b) mature (nonpredated and nonaborted) fruit production in Jacaranda copaia across three years on Barro Colorado Island, Panama. Estimates of the intercept for years 2002 and 2003 are calculated as the difference relative to 2000.
(a) Total fruit model Intercept year 2000 year 2002 year 2003 log (DBH) log (neighbourhood fruit production) (b) Mature fruit model Intercept year 2000 year 2002 year 2003 log (DBH) log (neighbourhood fruit production)
–11.36 0.544 –0.515 2.452 0.109
1.850 0.146 0.145 0.292 0.034
–6.16 3.73 –3.54 8.41 3.20
⬍0.0001 0.0002 0.0005 ⬍0.0001 0.0015
–10.47 2.19 0.886 2.002 0.102
1.722 0.159 0.158 0.272 0.032
–6.08 13.73 5.60 7.37 3.16
⬍0.0001 ⬍0.0001 ⬍0.0001 ⬍0.0001 0.0018
resources (Root 1973). In the case of our wasp seed predator, it may be attracted to trees and neighbourhoods with high fruit densities and remain in the focal tree or neighbourhood area depositing multiple broods in fruits. Moreover, if pupa remain in galled fruit or soil near focal parent plant and emerge in the following years to reproduce and lay eggs, this would create persistent predator loads in the local area in subsequent years, leading to consistent patterns of heavy predation across years within high density neighbourhoods. We did not have a long enough time series in our data to test for this eﬀect in our data. However, the cyclical nature of reproduction in J. copaia, which generally alternates between high and low reproductive years, may reduce the local build-up of pre-dispersal seed predators in this species if insect populations dynamics are coupled to annual tree fecundity. The signiﬁcant negative interaction term between focal tree and neighbourhood fecundity (Table 2) indicates that predation rates decrease at high levels of individual and neighbourhood fecundity, a result that is consistent with predator satiation. Indeed, our ﬁnding of pre-dispersal predator satiation in this system is consistent with many studies of insect pre-dispersal predation that have demonstrated lowered rates of predation within large fruit crops relative to small crops (reviewed by Wright et al. 2005b). Predator satiation in areas of high abundance serves to reinforce the positive densitydependent fruit set observed at the earlier stage. Positive density-dependence in total fruit production In a previous study, we found strong positive density-dependent fruit set in this J. copaia population, even when controlling for genetic relatedness, soil nutrients, liana infestation, and heterospeciﬁc competition (Jones and Comita 2008). In the present study, by analyzing both total and mature fruit set, we showed that negative density-dependent predation was weaker than positive density-dependent fruit set (Table 3). One potential explanation is that J. copaia is likely pollinated by a variety of generalist pollinators (Maues et al. 2008) whose abundances may be greater than and vary less among years than the abundance of the wasp seed predator, which we suspect to be a specialist on J. copaia fruit. Since J. copaia is self-incompatible, the attraction of these pollinators via large ﬂoral displays is likely to have a strong eﬀect on fruit production. Further, the movement capacity of pollinators and predators determines whether or not their eﬀect is dependent on the density of resources. Even small insect pollinators can regularly move very large distances (⬎ 10 km) between individual tropical trees and populations (Nason et al. 1998, Dick et al. 2008) but less is known about dispersal abilities of enemies within these same systems. Ultimately, predator dispersal capacity and host detection ability plays a large role in determining whether a seed predator operates in a density-dependent or independent manner (Platt 1974). The interaction between attracting mutualists and avoiding antagonists ultimately determines how density-dependent factors regulate populations (Antonovics and Levin 1980, Strauss and Irwin 2004), the evolution of reproductive synchrony (Brody 1997, Elzinga et al. 2007), and future patterns of spatial clumping (Platt et al. 1974, Silander 1978, Nathan and Casagrandi 2004). Although most studies of density-dependence have focused on enemies and the 1845
negative consequences for plants growing at high densities, our results suggest that mutualists play a critical role in determining spatial patterns of fruit and seed production, which have an eﬀect on later stages by determining the number of viable seeds dispersed. Another topic that remains to be investigated as to the demographic importance of pollinators is whether large ﬂoral displays found in high density areas also increase outcrossing rates which in turn lead to increased seed set and seedling survival (Wright et al. 2005b). Other studies of neighbourhood eﬀects have largely focused on the negative impacts of neighbour density on ﬁtness measured as growth and survival with the ultimate goal of explaining why tropical forests are capable of maintaining so many species. Positive density dependence, when deﬁned as higher individual reproductive success at high individual densities, even when weak, is predicted to lead to competitive exclusion and thus a decrease in the number of coexisting species (Zhou and Zhang 2008). Although negative density-dependent predation may not compensate for positive density-dependent fruit production in J. copaia at the pre-dispersal stage and predator satiation may enhance initial positive density-dependent fruit set, a variety of other factors may be operating in Jacaranda that serve to regulate the population and account for its’ relatively low abundances within the BCI forest. These include negative densitydependent growth and survival at seed and seedling stages (Harms et al. 2000, Wright et al. 2005b), a tradeoﬀ between the number of seeds per fruit or seed viability and total fruit set, strong dispersal limitation (Jones et al. 2005, Jones and Muller-Landau 2008), and narrow habitat requirements (i.e. strong light-gap dependence). Assuming that increases in fruit number are correlated with an increase in seed number, our ﬁnding that fruit gains due to positive density-dependent fruit set are not oﬀset by negative density-dependent pre-dispersal seed predators in J. copaia suggests that positive density-dependent reproduction and predator satiation at the reproductive stage along with spatial or temporal variation in negative density dependence at later stages may enhance spatial aggregation in tropical trees. For example, despite the pervasiveness of negative density-dependence at seedling and juvenile stages in Jacaranda and all other species examined on the BCI plot, there still exists a positive non-linear correlation between the number of seeds deposited in an area and the number of seeding recruits (Wright et al. 2005b). Therefore, the positive density-dependence in reproduction shown here if it increases seed set would be expected to increase or at least maintain patterns of spatial aggregation. A full analysis of the implications of positive and negative density-dependence integrated across all life stages in Jacaranda copaia and other species would aid in our understanding of the role of spatial and temporal variation in pollination success, pre-dispersal predation, and realized fecundity and how it eﬀects population demography and community coexistence. Acknowledgements – P. Jansen, N. Beckman, P. Rymer, C. Devaux, T. Paine and A. Pappadopolous provided thoughtful comments that improved the manuscript. FAJ acknowledges the support of a Tupper Postdoctoral Fellowship in Tropical Biology from STRI. We thank R. Condit, S. Hubbell and R. Foster for
access to FDP data and permission to work within the plot. This work was supported by the National Science Foundation (DEB 0129874, 608512, 043665).
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Appendix 1. AIC values of generalized linear mixed models of predispersal seed predation with differing neighbour radii. The best ﬁt model (indicated by the lowest AIC value) is in bold. Neighbourhood radius (m) 25 30 35 40 50
AIC 1270.4 1248.7 1254.6 1272.2 1268.9
Appendix 2. Variograms illustrating the spatial autocorrelation in (A) observed pre-dispersal seed predation rates of trees of Jacaranda copaia in the BCI 50-ha plot and (B) residuals of the generalized linear mixed model of predation.