*Correspondence author. Department of Biology, the Pennsylvania State University, University Park, PA 16802. E-mail: email@example.com
1Frugivores disperse the seeds of the majority of woody plant species world-wide. Thus, insights on how frugivores influence the dispersal of plants and the variability of this process are crucial for understanding plant population dynamics in a rapidly changing world.
2We used a spatially explicit, stochastic, individual-based model that simulates fruit-removal and seed dispersal by birds to assess bird density, landscape and neighbourhood effects on the inequalities of within-population fruit-removal rates and seed dispersal. We also compared model predictions with spatially-explicit field data.
3In our simulations, bird density had a strong effect on the distribution of fruit-removal rates creating large inequalities among plants. Also, for equal bird densities, inequalities increased with the landscape level aggregation of plants.
4Fruit removal increased with increasing plant neighbourhood density although there was a tendency to decline at the highest densities. Neighbourhood density also changed average dispersal distances, but with shorter distances at higher densities. Plants with few neighbours not only had longer distance dispersal but also a larger variance in seed rain across distances than plants with ten or more neighbours. These relationships between neighbourhood density and fruit removal and dispersal distance were scale-dependent with a peak in correlations at 150-m radius.
5Similar to model predictions, field data shows an inverse relationship between dispersal distances (inferred from bird movements) and fruiting neighbourhood density. Also, fruit-removal rates observed in the field show large numbers of plants receiving little or zero fruit-removal. Fruit-removal rate distributions were statistically indistinguishable between the simulation and field data. But, distributions were strikingly different from two alternative models that lacked spatial effects.
6Synthesis. Our model and field data show that as fruiting plants become aggregated, inequalities in fruit-removal rates increase and seed dispersal distance decreases. Both of these processes could help create and maintain plant aggregation and affect genetic structuring. The model also predicts that small-scale neighbourhood effects can be controlled by large-scale processes such as overall frugivore abundance and landscape-level plant aggregation. Most importantly, both simulations and field data shows an interaction between plant spatial pattern and bird foraging, which results in neighbourhood-specific dispersal and rates of fruit removal.
Seed dispersal processes are essential for the persistence of plant populations, and are fundamental mechanisms for the organization and maintenance of species richness in plant communities (Nathan & Muller-Landau 2000; Chave et al. 2002; Condit et al. 2002; Herrera 2003; Bascompte & Jordano 2007). In many plant communities, fruit-eating animals (i.e. frugivores) disperse the seeds of most woody species, with proportions of species exceeding 90% in many tropical forests, and up to 30–50% in temperate ones (Aizen et al. 2002; Herrera 2003). But despite the importance of frugivores as agents of seed dispersal, the general mechanisms by which animals potentially shape plant populations and influence community organization are still absent from the theoretical core of community ecology (Carlo et al. 2007).
Simulation models are useful tools to examine the behaviour of complex phenomena and produce testable predictions and hypotheses about system function (DeAngelis & Mooij 2005). Here we use a model that simulates fruit-removal and seed dispersal by birds, and compare some of its predictions to data from a field study. Our model allows manipulation of the spatial configuration of plants, as well as the number and behaviour of birds. Because the model records the final destination of dispersed seeds from each plant, we used it to conduct detailed analyses on factors affecting rates of fruit-removal and the frequency distribution of seed dispersal distances (hereafter dispersal kernels, Clark et al. 1999; Nathan & Muller-Landau 2000). We have previously used this model to examine how landscape aggregation and bird abundance affect kernel characteristics (Morales & Carlo 2006). We found that much variation in the characteristics of kernels is expected within frugivore-dispersed plant populations, and that bird-generated kernels deviate significantly from the expectation of simple diffusion models (Morales & Carlo 2006). Here we examine the causes of kernel variability and fruit-removal rates and we contrast model output to empirical data.
Our first objective is to examine how three interacting factors create inequalities on fruit-removal rates and dispersal kernels in model populations: (i) large-scale aggregation patterns of plants (hereafter landscape patterns), (ii) local-scale aggregation patterns (hereafter neighbourhoods), and (iii) the abundance of frugivorous birds. We define inequalities as large differences among individual plants in the quantity of removed fruits and in dispersal kernels. Fruit-removal rates measure the number of seeds that are dispersed from a plant, while dispersal kernels are independent of such quantities and describe the probability of a seed landing at particular distances from the source (Clark et al. 1999). To our knowledge there have been no attempts to examine the factors that promote variability in fruit-removal rates and/or dispersal kernels within plant populations.
Our second objective is to compare model predictions to empirical data from a spatially-explicit field study. We do this by comparing field rates of fruit-removal, bird movements and conspecific neighbourhood effects with outputs from three different models (see Methods Section). The first is the full simulation model as described by Morales & Carlo (2006). This stochastic model combines parameters of bird gut-passage times for seeds, bird perching time on plants and bird visitation probabilities to plants defined by ‘attraction’ parameters that are based on crop sizes and displacement distances. Thus, this model allows for the emergence of fruit removal and seed dispersal patterns from interactions between bird behaviour and plant distribution. The second model is a modified version of Morales & Carlo (2006) where bird visitation probabilities to fruiting plants were not influenced by displacement distances between plants. We did this modification to examine how frugivory and seed dispersal are affected by space while keeping in the model the stochastic influence of bird behaviour and landscape patterns. Finally, and in contrast with the previous two, our third model lacks spatial/behavioural effects and assumes that if a fixed number of fruits are removed from a plant population, fruit-removal rates should follow a binomial distribution. Contrasting the output of these three models with empirical data is critical to begin to understand the influences of space and bird foraging decisions in mediating frugivore–plant interactions, which remain poorly explored despite the fact that frugivory and seed dispersal are intrinsically spatial processes (Carlo et al. 2007).
We used a spatially explicit stochastic simulation of fruiting plant aggregation, fruit production, fruit-removal and seed dispersal. The simulation keeps track of the number of seeds removed from each individual plant and the spatial coordinates of each dispersed seed. We used these model outputs to construct and evaluate fruit-removal rates and dispersal kernels. To compare and examine fruit-removal rate distributions we used four types of data obtained from: (i) the full simulation model (hereafter model 1), (ii) an alternative, modified simulation model (hereafter model 2), (iii) an alternative model based on the Binomial distribution (hereafter model 3); and (iv) field data. Model 2 was a modified version of our simulation model where birds ignored how far they have to travel when making foraging decisions but retained attraction due to fruit abundance (see Bird foraging and seed dispersal below). Model 3 assumed that fruits were removed at random and without behavioural constraints. In this case, the number of fruits removed per plant followed a Binomial distribution.
First we present a summary of models 1 and 2 (a full description can be found in Morales & Carlo (2006)). Our choice of functional forms and parameter values was mostly guided by published and unpublished behavioural observations and data, but some functions and parameters were chosen for simplicity and flexibility. We have previously tested the importance of most assumptions with a sensitivity analysis (Morales & Carlo 2006).
fruiting plant landscapes and fruit production in models 1 and 2
The simulation algorithm generated landscapes by first placing 200 plants randomly on a 5000 × 5000-m landscape. More plants were added to the landscape one at a time by randomly choosing one of the first 200 ‘parent’ plants, and then adding the new plant at a random direction from it. Distances were randomly sampled from a Weibull distribution with shape equal to 2. The process was repeated until a total of 1000 plants were placed on each landscape, which simulates a Neyman-Scott process (Zollner & Lima 1999). We used three different scale parameters for the Weibull distribution to determine the degree of plant aggregation (see bottom of Fig. 1): low (Weibull scale = 0.00001, average nearest neighbour distance = 75.9 ± 44.2(SD)), medium (Weibull scale = 0.0001, average nearest neighbour distance = 19.0 ± 15.4(SD)) and high (Weibull scale = 0.01, average nearest neighbour distance = 6.6 ± 12.1(SD)). Each of the 1000 plants started with 100 fruits, which was the maximum crop possible. Each fruit had one seed; hence, fruit-removal is equivalent to the number of dispersed seeds. At the end of every simulated day plants could produce up to 20 fruits according to a regrowth model.
bird foraging and seed dispersal in models 1 and 2
Bird foraging behaviour was simulated by combining parameters that determined the perching time on a plant, the number of fruits ingested, and the next plant to visit. Perching time was determined by drawing from a γ-distribution, with shape parameter set at 4, and scale parameter set at 1.25. This function produces perching times similar to those reported by field studies (Wheelwright 1991; Carlo & Aukema 2005). Fruit ingestion at plants followed a hyperbolic functional response but was limited by available volume in the birds’ guts. Bird guts had a capacity of 15 fruits/seeds. The maximum number of fruits eaten per visit was 10, which was based on observations by Carlo (2005) in which birds (i.e. Tyrannus dominicensis and Mimus polyglottus, see Field Study section below) tend to eat the same number of fruits per visit as long as crop size is larger than gut capacity. After ingestion, gut passage time was sampled from a γ-distribution with scale and shape parameters chosen to match seed gut-passage rates reported from several frugivorous bird species (e.g. Murray 1988; Wahaj et al. 1998). Seed defecation by birds was dictated by gut passage time, irrespective of whether the animals were perching or flying. The program recorded the spatial coordinates of each dispersed seed, as well as the identity of the mother plant. Birds moved from plant to plant in straight lines and at constant speed of 6 m s−1. When choosing where to go next, frugivores sampled from a ‘plant attraction’ distribution that was compiled by weighting fruit abundance and distance from a bird's current location (attraction increased with plant crop size but decreased with distance, see Morales & Carlo 2006). For model 2 we eliminated the function that made plant attractivity decrease with distance in order to eliminate spatial effects on bird foraging. Simulated birds kept moving, eating and dispersing seeds until they accumulated 6 h of daily activity.
simulation experiment – model 1
We performed a simulation experiment following a 3 × 3 factorial design in which the two variables of interest were the landscape aggregation of plants (low, medium, high) and the abundance of frugivores (1, 10, 100). Response variables were the number of dispersed seeds per plant (i.e. fruit-removal rate) and the distances of seed dispersal. For each factor combination we ran 30 replicate runs (each replicate lasted 180 simulated hours, or 30 ‘days’ of 6-h foraging activity) with a new simulated landscape generated for each replicate run. At the start of a replicate run, birds started at randomly chosen plants on the landscape.
binomial distribution of fruit-removal rates – model 3
In this case, the number of fruits removed per plant followed a Binomial distribution
( eqn 1)
where k is the number of fruits removed per plant given that the total number of fruit removed in the population is N and the probability of choosing a particular plant for any one of the N fruit-removal events is P = 1/number of plants.
model output summary and analyses
First, we examined how landscape aggregation and frugivore abundance affected fruit-removal rate distributions. For this, we grouped plants by fruit-removal rate categories (i.e. 0, 1–10, 11–20, 21–30, etc.) within each replicate simulation run (models 1 and 2 only) and then calculated the average of each category across the 30 replicate runs of each factor combination. We compared distributions of fruit-removal rates using Contingency Tables since counts on the fruit-removal categories are not independent of one another. Model 3 (Eqn 1) gives fruit-removal rate distributions analytically.
Next, we examined the effects of the density of fruiting neighbours on (i) fruit-removal rates, and (ii) the average seed dispersal distances and kernels. Again, averages were calculated across the 30 replicate runs of each factor combination in the simulation experiment. For neighbourhood analyses we only use data from model 1. Since the number of neighbours for each plant depends on the scale at which neighbourhoods are defined, we first examined how the correlation between number of neighbours and fruit removal changed with scale. The scale of maximum correlation was 150 m, and thus we use this as the effective radius to calculate neighbourhood density.
To compare and evaluate fruit-removal rates and neighbourhood effects from models we conducted a field study during January–April of 2003 in a cattle ranch in the valley of Rio Blanco, municipality of Naguabo, south-east Puerto Rico (18°13′17 N, 065°46′48 W). In an 18-ha plot we mapped the most abundant plant, Cestrum diurnum (Solanaceae, n = 696), using portable GPS units (Magellan Sportrak Pro). The plot was divided by fences into 10 grazing fields of similar area and shape. Plants were found mostly near fences but many also occurred in the open pastures. The fruits of these plants were consumed by M. polyglottus (hereafter Mimus) and T. dominicensis (hereafter Tyrannus). Both Mimus and Tyrannus are generalist omnivores found at open habitats elsewhere. The counted number of territorial and resident birds in the plot was 25 (6 Mimus, 19 Tyrannus).
tracking bird movements as a surrogate of seed dispersal distances
For 10 days within a 2-week period we recorded movements and fruit-removal of Tyrannus and Mimus birds in the study site using two observers. The whole site was observed each day from 06:30 to 11:30 hours, with each observer covering half of the site systematically. Observers spent 1 h within each fenced field, changing fields in a fixed rotation order (five fields covered every day by one observer, for a total of 10 fields per day). Each day we started observation in a different field, rotating the start point each day systematically. After 10 days, the two observers sampled the entire plot so that each field was sampled at every observation period equally by the two observers.
At each field, we recorded the start and end point of bird flights with portable GPS units. Observers stayed in the centre of fields to avoid disturbing birds while keeping track on paper of the flight locations. After the fifth consecutive flight or after a bird left the field (whichever occurred first), the observer approached the locations of movement and took the coordinates. When birds left the field and went into another, observers noted the endpoint of the flight to later record coordinates. Observers noted the number of fruits that birds ate at each plant.
plant phenology and fruit-removal
For each plant in the study site we recorded the number of ripe fruits using abundance categories: 0 (no ripe fruits), 1 (1–10 fruits), 2 (11–50 fruits), 3 (51–100 fruits), 4 (101–500 fruits) and 5 (501–1000 fruits). Using the same scale, observers recorded the number of fruits removed from each Cestrum diurnum by counting empty bracts on infrutescences. Bracts persist on the plant after birds remove fruit, while non-removed fruits dry on the infrutescence and fall to the ground still attached. All plants at the study site were surveyed once during the 10-day bird observation period. We also gathered phenology and removal data for the months of February and March, but due to space constraints we use data from April because it was the month for which we measured bird movements.
data analyses of field data and comparisons with model data
We calculated correlations between bird flight distances and the number of fruiting plants at fixed radii, for 100 different radii ranging from 1 to 100 m. We determined the significance of correlation coefficients using a Bonferroni adjustment (Pi/100). We did the same to compare the correlation of fruit-removal rate indexes of plants with fruit density at different radii. We then used the radius at the peak of maximum correlation to examine the relationship between fruit density in the radius and flight distances. This way we could determine the ‘effective’ neighbourhood radius to then, like we did with simulations, examine the neighbourhood's effects on fruit-removal rates and seed dispersal. To compare fruit-removal rates from the field and the three models we ran an additional set of simulations for models 1 and 2 using the number and actual coordinates of the 696 Cestrum plants in the field site (i.e. field plant map), and with 25 birds (the observed number of birds in the field site). For model 3 we also calculated the Binomial expectation of fruit-removal rates for 25 birds and 696 plants. We used contingency tables Bonferroni-corrected elsewhere to statistically compare frequency distributions of fruit-removal services.
inequalities in fruit-removal rates
In our simulations, bird density had a strong effect on the distribution of fruit-removal rates creating large inequalities among plants (Fig. 1). At low bird densities, between 95% and 98% of the plants at any landscape obtained zero fruit-removal, while less than 0.2% had over 60 fruits removed (Fig. 1, top panels). Conversely, fruit-removal rates at high bird densities were fairly symmetric around a distinctive mean (Fig. 1, bottom panel), although with heavy distribution tails. Landscape aggregation also affected fruit-removal rates. For example, inequalities in fruit-removal rates increased with increasing landscape level aggregation of plants. Regardless of bird density, highly aggregated landscapes showed higher numbers of plants with zero fruit-removal as well as higher numbers of plants experiencing high fruit-removal rates than landscapes with medium and low aggregation (all panels Fig. 1). At low bird density and low landscape aggregation, fewer plants had more than 50 fruits removed than in medium and high aggregation landscapes (Fig. 1, top panels). Landscape aggregation strongly affected fruit-removal rates at medium bird density (i.e. 10 frugivores, Fig. 1) where the percentage of plants experiencing absolute fruit-removal limitation (i.e. zero removal) averaged 55.9% (± 0.011, SE) in highly aggregated landscapes but just 17.17% (± 0.008, SE) in low aggregation landscapes.
These inequalities are mostly due to spatial effects since fruit-removal rates in model 1 were broader than model 3 (Fig. 1, solid lines). Bird foraging behaviour explains most of these differences since model 2 produced fruit-removal rates very similar to model 3 (dashed lines Fig. 1). The only difference between model 2 (simulations with birds ignoring travelling costs) and model 3 (the binomial model) was that simulations had lower fruit-removal averages (dashed lines Fig. 1). This discrepancy is explained by birds spending more time travelling, and thus having slightly less time to eat fruit.
neighbourhood effects on fruit-removal rates and seed dispersal
Fruit-removal rates experienced by plants were highly contingent on a plant's neighbourhood density, and to a lesser degree, to an interaction with bird abundance and landscape level aggregation of plants. For most scenarios, fruit-removal rates increased with the number of neighbours up to a saturation point at about 10 plants within a 150 m radius (Fig. 2a–c), and the optimal neighbourhood size (i.e. the size at which plants obtained higher fruit-removal rates) increased when there were more birds, as expected. At low bird density, and medium and high landscape aggregation, fruit-removal rates decreased at the highest neighbourhood densities suggesting competition (Fig. 2, black triangles in panel a). The effects of neighbourhood density on fruit-removal rates were always greater (i.e. had steeper slopes) in low – rather than high – aggregation landscapes (Fig. 2a–c).
Neighbourhood density also changed dispersal distances, but the relationship was inverse (Fig. 2d–f). In aggregated landscapes, dispersal distance dropped faster than in low aggregation landscapes at all bird densities. When looking at dispersal kernels, plants with few neighbours not only had longer distance dispersal but also a larger variance in seed rain across distances than plants with ten or more neighbours (Fig. 3).
We recorded 870 bird observations for six bird species, 755 for the most common Tyrannus and 155 for Mimus. Cestrum diurnum was the most common fruiting plant in the site and we recorded its use 90 times by Tyrannus (n = 119 total fruit-removal records) and 13 by Mimus (n = 19 total fruit-removal records). We mapped 464 flights, 391 for Tyrannus and 73 for Mimus from starting point to endpoint. Correlations were always negative for fruit-removal rate indices and fruit abundance in neighbourhoods, with a significant peak at a 45 m radius (Fig. 4, panel a). The fruit density in the neighbourhoods at the starting point of bird flights was negatively correlated with the distance birds flew, with a sharp peak at 10 m (Fig. 4, panel b). Bird movements were shorter when there were more fruiting plants at flight start points (Fig. 4, panel c) and hence, seed dispersal distances should be expected to be reduced by short movement distances in a high density neighbourhood (Murray 1988; Westcott & Graham 2000).
Neighbourhood density of fruiting plants was negatively correlated with fruit-removal rates of Cestrum (Fig. 4, panel a), suggesting that competition among individuals was stronger in dense neighbourhoods than in sparse ones. When examining the distribution of fruit-removal rates of C. diurnum in the plot, we found that 27.7% of the population showed no removal, 31.7% had few (1–10), and only 4.2% had over 50 fruits removed (Fig. 4d). This distribution of fruit-removal rates in the field was statistically indistinguishable from model 1, but significantly different between models 2 and 3 (Fig. 4d: Contingency Table of Field Data vs. Simulation (25 birds on actual field plant map d.f. = 4, χ2 = 6.5, P = 0.163); Contingency Table of Field Data vs. Model 3 d.f. = 4, χ2 = 43.5, P < 0.0001; Contingency Table of Field Data vs. Model 2 d.f. = 4, χ2 = 206, P < 0.0001). Models 2 and 3 produced fruit-removal rate values only in two categories (1–10 and 11–50 fruits removed, Fig. 4d) and produced no plants with zero or high values, contrary to the large inequalities observed in the field data and model 1.
Using simple rules to simulate bird foraging behaviour, we found that fruit-removal rates and seed dispersal kernels are largely affected by bird abundance and plant neighbourhood density, and to a lesser extent, by the landscape-scale aggregation pattern of plants. Neighbourhood density had a strong positive influence on fruit-removal rates that was prevalent in most factor combinations of our simulation experiments. Higher neighbourhood density in clumped landscapes increased the inequalities in the distribution of fruit-removal rates and shortened dispersal distances. Thus, there was an interaction between the spatial distribution of plants and the movements of frugivores that resulted in neighbourhood-specific dispersal patterns and fruit-removal rates. The data from our field study support several of the predictions arising from model 1 – there were large inequalities in fruit-removal rates and neighbourhood density that reduced flight distances, and hence, seed dispersal distances. We discuss two general predictions that stem from model 1, as well as their potential biological relevance.
large-scale aggregation creates and intensifies inequalities in fruit-removal rates
The simulation experiments show that inequalities in the distribution of fruit-removal rates increased with landscape aggregation of plants (Fig. 1). This is because dense neighbourhoods attracted birds and kept them away from isolated plants and/or low density neighbourhoods (Fig. 2a–c) thus increasing inequalities. Inequalities in fruit-removal rates are emergent properties of our simulated system that depend on how birds move and forage on a large spatial scale, and on what parts of the landscape they use more frequently. Plants with zero fruit-removal were common at low bird densities and were present even at high bird densities (100 birds), although only in highly aggregated landscapes (Fig. 1 bottom panel). This model 1 prediction was supported by the fruit-removal rates observed for Cestrum in the field, a distribution that was not statistically different from model 1 run over the Naguabo map (Fig. 4d). We want to underscore that in the field, 27.7% of plants showed zero fruit-removal in April (and 61.2% in March, T. Carlo, unpubl. data) despite a fair abundance of bird frugivores in the site. Both in field and model 1 data, these inequalities are remarkable, and due to the effects of bird movement behaviour that perceives and accounts for the relative position and distances between fruiting plants.
neighbourhood density determines fruit-removal rates and dispersal distances
Our simulations showed a prevalence of positive effects of neighbourhood density on fruit-removal rates (Fig. 3). These effects were stronger in low aggregation landscapes, where increasing number of neighbours facilitated fruit-removal rates at all bird densities (Fig. 3a–c, open circles). There were few instances where plants showed signs of competition, and only in neighbourhoods that had over 15 plants, and only in landscapes of high or medium landscape aggregation (Fig. 3). Yet, competition for fruit-removal was not as marked when many birds were available (Fig. 3, panel c). In our field study we found only negative correlations between neighbourhood density and fruit-removal rates (Fig. 4, panel c). In model 1, differences in fruit quantity between locations strongly guided foraging decisions, while in the field, birds engaged in other activities unrelated to fruit-removal (i.e. feeding on invertebrates in places not necessarily related to fruiting plants). Thus, the model 1 parameterization we used may be more accurate for specialized plant-frugivore systems in which fruit quantity plays the leading role in guiding foraging movements (Kinnaird et al. 1996; Kwit et al. 2004; Saracco et al. 2004).
Neighbourhoods not only largely determined fruit-removal rates of plants, but they also controlled seed dispersal distances. Average seed dispersal distances decreased as landscape aggregation increased, and as the neighbourhood density increased (Fig. 3 panels d–f). This was caused by shorter frugivore movements in denser neighbourhoods and by increases in distances between neighbourhoods/patches at the landscape scale (Morales & Carlo 2006). Conversely, low aggregation landscapes facilitated movement and decreased differences in fruit-removal rates by increasing bird movements among plants (see Morales & Carlo 2006 for analyses of frugivore displacement over time). Within any landscape aggregation pattern and/or bird density, shapes of dispersal kernels were different for plants in different neighbourhoods (Fig. 3). Seed-dispersal kernels had proportionally more long-distance dispersal when plants had few neighbours (Fig. 3). These findings match results from Levey et al. (2008, this volume), which show shorter seed dispersal distances by birds in heterogeneous landscapes compared to homogeneous ones in South Carolina.
Because neighbourhood density increased fruit-removal rates but also reduced dispersal distances, trade-offs could take place between dispersal distance and fruit-removal rates. Trade-offs between quantity and distance of seed dispersal can lead to positive feedback on the local seed rain in areas of high fruit density. Experiments (Aukema & Martínez del Río 2002) and field studies (Martínez del Río et al. 1995) have shown such positive feedbacks. In our field study, although we did not measure seed dispersal directly, we believe that the reductions in flight distances of Tyrannus and Mimus associated with areas of high neighbourhood density (Fig. 4, panels a and c) could lead to reductions in dispersal distances (see Westcott & Graham 2000 and Westcott et al. 2005; Levey et al. 2008 this volume).
Despite the complexity of plant–frugivore interactions, model 1 suggests that some aspects of the dispersal patterns and neighbourhood effects could be general when accounting for the patchiness of a population and the relative abundance of frugivores. Model 1 shows that fruit-removal rates and seed dispersal kernels vary greatly within a plant population, and that neighbourhood and landscape characteristics are important predictors of this variability. These findings are at odds with the common assumption that dispersal functions are a species’ property where all individuals in the population have the same chances of dispersal for each of their seeds (Levin 1974; Levin & Kerster 1975; Bolker & Pacala 1999; Chesson 2000).
Our study also shows the strong potential of plant–frugivore interactions to influence the genetic structuring of plant populations. In a seminal model, Levin & Kerster (1975) show that the spread and time to fixation of alleles is influenced by the types of functions describing pollen and seed dispersal, as well as by the neighbourhoods in which genes were initially found. Levin and Kerster assumed that all plants obey the same dispersal function regardless of neighbourhood. In contrast model 1 suggests that the potential for allele fixation could be greatly increased or decreased depending on the initial spatial position of the alleles of interest due to the extreme inequalities caused by neighbourhoods and large-scale aggregation interacting with frugivore foraging. For example, some studies that have traced the dispersal (or pollination) of tropical trees in the field have found a strong reproductive dominance of a few individuals that can be attributable to interactions with frugivores and/or pollinators (Chase et al. 1996; Aldrich & Hamrick 1998; Sezen et al. 2005). This type of dispersal dominance is predicted by model 1 and is especially obvious when frugivores are rare and plants clumped (Fig. 1). Our findings are potentially relevant for models including ‘source’ effects on dispersal parameters like the one presented by Schurr et al. (2008, this volume), because neighbourhood density and landscape patterns affect dispersal by influencing biotic interactions with frugivores.
In conclusion, under the conditions of our simulations, we found that the abundance of frugivores and the large-scale aggregation of a plant population can create inequalities in the distribution of fruit-removal rates and differences in the scale and shape of seed dispersal kernels that are dependent on local neighbourhoods. For frugivore-dispersed plants these results contrast with the traditional notion that individuals of a plant population have the same chances of seed dispersal and emphasize the role of non-random biotic interactions in dispersal processes. Model 1 also shows how the larger context provided by the spatial pattern of a plant population can determine neighbourhood-scale interactions such as competition or facilitation. This implies that particular neighbourhood effects on fruit-removal rates may be observable at certain spatial scales and not others, underscoring the need to avoid arbitrary definitions of neighbourhoods by field studies. Thus, fruiting neighbourhood effects on fruit-removal rates are indirectly defined by frugivore behaviour. In model 1, fruiting neighbourhoods had the strongest effect on fruit-removal rates at a radius of 150 m, while in the field study effects were peaked at 45 m. Some predictions of model 1 found support in our field study. For example, birds moved shorter distances in high-density neighbourhoods, and a significant portion the plant population did not receive seed dispersal services while a few had copious dispersal. Our findings show how plant spatial pattern interacts with frugivore foraging decisions to produce within-population inequalities in dispersal services.
We will like to thank for the help of J. E. Aukema, J. Tewksbury, C. Martínez del Río, B. Bolker, R. Dunn, N. Haddad, K. C. Burns, R. Nathan, D. P. Vázquez, A. Cruz, Y Linhart, A. Martin, M. Martínez-Sánchez, J. A. Collazo, E. Santiago-Valentín, and two anonymous referees. This work was supported in part by NSF grants DEB-0407826 and DBI-0511927 to T.A.C., the University of Colorado, and the Botanical Garden of the University of Puerto Rico. J.M.M. was supported by grants FONCyT and PICT 34126.