Ecography 39: 001–012, 2016 doi: 10.1111/ecog.02191 © 2016 The Authors. Ecography © 2016 Nordic Society Oikos Subject Editor: Thorsten Wiegand. Editor-in-Chief: Miguel Araújo. Accepted 2 August 2016
Exploring the interaction of avian frugivory and plant spatial heterogeneity and its effect on seed dispersal kernels using a simulation model Andrew P. McKenzie Pegman, George L. W. Perry and Mick N. Clout A. P. McK. Pegman (
[email protected]), Laingholm, Auckland, New Zealand. – G. L. W. Perry and APMcKP, School of Environment, The Univ. of Auckland, Auckland, New Zealand. – M. N. Clout (
[email protected]), School of Biological Sciences, The Univ. of Auckland, Auckland, New Zealand.
Seed dispersal by avian frugivores is one of the key processes influencing plant spatial patterns, but may fail if there is disruption of plant–frugivore mutualisms, such as decline in abundance of dispersers, fragmentation of habitat, or isolation of individual trees. We used simulation model experiments to examine the interaction between frugivore density and behaviour and the spatial arrangement of fruiting plants and its effect on seed dispersal kernels. We focussed on two New Zealand canopy tree species that produce large fruits and are dispersed predominantly by one avian frugivore (Hemiphaga novaeseelandiae). Although the mean seed dispersal distance decreased when trees became more aggregated, there were more frugivore flights between tree clusters, consequently stretching the tails of the dispersal kernels. Conversely, when trees were less aggregated in the landscape, mean dispersal distances increased because seeds were deposited over larger areas, but the kernels had shorter tails. While there were no statistically meaningful changes in kernel parameters when frugivore density changed, decreases in density did cause a proportional reduction in the total number of dispersed seeds. However, birds were forced to move further when fruit availability and fruit ripening were low. Sensitivity analysis showed that dispersal kernels were primarily influenced by the model parameters relating to disperser behaviour, especially those determining attractiveness based on distance to candidate fruiting trees. Our results suggest that the spatial arrangement of plants plays an important role in seed dispersal processes – although tree aggregation curbed the mean seed dispersal distance, it was accompanied by occasional long distance events, and tree dispersion caused an increase in mean dispersal distance, both potentially increasing the probability of seeds finding suitable habitats for germination and growth. Even though low frugivore densities did not cause dispersal failure, there were negative effects on the quantity of seed dispersal because fewer seeds were dispersed.
Dispersal of seeds, for example by avian frugivores, in large part determines the spatial pattern of seedling recruitment and is essential for colonisation of landscapes via long distance events (Wenny 2000, Santamaria et al. 2007). However, seed dispersal may fail if plant-disperser mutualisms are disrupted, for example, via decline in abundance of keystone seed dispersers or isolation of trees (Cordeiro and Howe 2003, Sekercioglu et al. 2004, Nathan 2005). One way of testing this assertion is by comparing empirical seed distributions, obtained by matching dispersed propagules with their parents, across different plant–frugivore scenarios (Bullock et al. 2006, Cortes and Uriarte 2013). However, such data are difficult to obtain because long distance seed dispersal is challenging to quantify (Robledo-Arnuncio et al. 2014) and deposition patterns emerge from multiple interactions between frugivore behaviour and the distribution of fruit, both of which vary spatially and temporally (Levey et al. 2008, Cortes and Uriarte 2013). As an alternative, virtual in silico (Zurell et al. 2010) experiments can
be conducted using simulation models in order to reconstruct seed dispersal distributions and derive dispersal kernels (including parameter values) directly from information describing the natural history of seed production and behaviour of dispersal agents. The seed dispersal kernel is the probability of a seed being deposited at a particular distance from the parent plant (Nathan and Muller-Landau 2000) and is described in terms of its essential parameters: 1) the mean seed dispersal distance, and 2) the rate at which the tail of the distribution decays with distance. In the Weibull distribution, for example, mean seed dispersal distance and its variance set the spatial ‘scale’ of dispersal and ‘shape’, the inverse function of the kurtosis of the kernel, indicates long distance seed dispersal when it is numerically low (Morales and Carlo 2006). Seed dispersal effectiveness incorporates these parameters and is the product of the total number of dispersed seeds and the probability that a dispersed seed produces a new adult, all of which influence demographic features of plant populations, such as the rate and pattern of Early View (EV): 1-EV
spread and colonisation of new areas (Schupp 1993, Cousens and Rawlinson 2001, Levin et al. 2003, Spiegel and Nathan 2007, Schupp et al. 2010). To quantify the effect of disruption of plant–frugivore mutualisms via decline in frugivore density or changes in tree spatial patterns, we developed a spatially explicit individual-based simulation model (SEIBM, DeAngelis and Mooij 2005) combining disperser foraging and movement rules with data describing frugivore gut passage time of seeds and individual tree distributions. We varied frugivore density across different spatial patterns of trees to evaluate how seed dispersal kernels were affected by changes in frugivore density or by the effects of forest structure on frugivore movements. Based on our results, we discuss what the demographic effects might be for the tree species we consider. We applied our model to Hemiphaga novaeseelandiae (New Zealand pigeon or kereru, Columbidae), which is endemic to New Zealand (NZ) and has a conservation dependent but increasing status (Clout et al. 1991, Miskelly et al. 2008, Kelly et al. 2010). This large frugivore is the only widespread avian disperser capable of dispersing the propagules of large-fruited native trees, such as our exemplars, Vitex lucens (NZ teak or puriri, Verbenaceae) and Prumnopitys ferruginea (brown pine or miro, Podocarpaceae).
such as open husks and teeth marks; however, this is again infrequent and Pegman (2012) showed that only 2.2 1.3% of dispersed P. ferruginea seeds (n 434 seeds across 6 trees) had open husks, and mammal damage to dispersed V. lucens seeds was not observed. We utilised these two tree species because 1) they are the two large-fruited NZ species for which there are data to parameterize our model, 2) they differ in their environmental requirements, therefore not growing together, 3) they have different reproductive strategies, and 4) they have differing spatial distributions. Mean annual fruit production for P. ferruginea (ca 5000) is around twice that of V. lucens, and the proportion of annual fruit production that is actively dispersed by H. novaeseelandiae is ca 46% for both tree species (Pegman 2012). Field measurements showed that the distance between P. ferruginea trees (30.2 6.1 m, n 3 sites) is around twice the respective value for V. lucens (Pegman 2012). The two tree species also have different shaped seeds (V. lucens is irregular, whereas P. ferruginea is smooth), affecting frugivore gut passage time (Table 1, Supplementary material Appendix 1, Traveset 1998). All of these factors may result in different outcomes for each tree species in our simulations.
Methods
Our model is concerned with how patterns in seed deposition emerge from interactions between frugivore behaviour and the environment, represented by different tree spatial patterns. The model is semi-mechanistic, spatially explicit, individual-based, stochastic, and event driven; it encompasses fruit production and avian frugivore foraging in simulated forests and was ‘built from the ground up’, having fundamental elements in common with other models of seed dispersal such as those described by Morales and Carlo (2006) and Will and Tackenberg (2008). We implemented our model in NetLogo 5.3 (Wilensky 1999). A complete description of our model following the ODD (overview, design concepts, details) protocol of Grimm et al. (2010) and the code are provided in the Supplementary material Appendix 1 and 2 (see Supplementary material Appendix 1, Fig. A1 for schematic overview). In brief, our model represents the movement of variable numbers of individual birds (in our case, H. novaeseelandiae) through landscapes of fixed abundance of fruiting plants (in our case, V. lucens or P. ferruginea) whose spatial arrangement can be varied. Individual birds select the tree they move to based on the multiplicative interaction of its available fruit and the distance from the bird’s current location. The rationale for this interaction is that there is a positive correlation of frugivory with fruit abundance (Saracco et al. 2005) and that frugivores prefer local, rather than more distantly located, resources. For example, plants in denser neighborhoods have greater fruit removal rates than more isolated plants, even when the latter have desirable fruit (Levey et al. 1984, Morales et al. 2012). However, this rationale provides no indication about the mathematical function that most closely describes such relationships. In our model, there is one feeding bout at
Study system and species Hemiphaga novaeseelandiae are large (ca 650 g adult) frugivorous pigeons. They live in lowland forests throughout NZ and are highly mobile, inferred from inter-annual changes in the numbers in northern forests and radio-telemetry data, but individuals can also be sedentary (Clout et al. 1991, Wotton 2007). Vitex lucens are large angiosperm trees up to 20 m tall, with trunks up to 1.5 m wide, occurring mainly in temperate coastal areas of NZ (Salmon 1980). Hermaphroditic flowers are produced all year, with bright red fruits being present mainly between December and June. Prumnopitys ferruginea are tall dioecious gymnosperm trees up to 25 m tall, with trunks up to 1 m wide, occurring in shady environments throughout NZ, from lowland forest to ca 1000 m elevation (Salmon 1980). Male trees have cones and female trees produce large red diaspores, mainly between December and June, consisting of a single seed surrounded by fleshy ovuliferous cone scales (McEwen 1988) – for convenience, these structures will henceforth also be referred to as ‘fruit’. The fruit of both tree species are long (V. lucens: 15.4 0.2 mm, n 286 fruit; P. ferruginea: 16.1 0.1 mm, n 702 fruit; Pegman 2012) and have single seeds that are hard and ‘woody’ surrounded by nutritious, edible, and ‘fleshy’ pulp, indicating that they are consumed by fruiteating animals (Coates-Estrada and Estrada 1988, Tiffney 2004). Because fruits and birds vary in size within species, mid-sized birds such as tui Prosthemadera novaezelandiae or blackbird Turdus merula can consume smaller individual fruits of both tree species, but this occurs infrequently (Kelly et al. 2010). Mammals may also act as dispersers since seeds of our study species occasionally showed signs of predation 2-EV
Model design
Table 1. Baseline simulation model parameters and sources. Parameter nK v e c d aPT bPT aGPTP bGPTP aGPTV bGPTV aF bF aD bD pLONG rtA maxFP maxFV rF nT k sP sV mF
Description
Value
Number of kereru Mean kereru flying speed Maximum gut capacity of kereru Max. consumption rate in hyperbolic functional response Half saturation in hyperbolic functional response Scale of gamma distribution of kereru PT Shape of gamma distribution of kereru PT Scale of gamma distribution of miro GPT Shape of gamma distribution of miro GPT Scale of gamma distribution of puriri GPT Shape of gamma distribution of puriri GPT Factor in tree attractiveness based on number of fruits Exponent in tree attractiveness based on number of fruits Factor in tree attractiveness based on distance Exponent in tree attractiveness based on distance Probability (p) of kereru moving to a random new tree Roost tree attractiveness at p 0.3 Maximum number of miro fruits per tree Maximum number of puriri fruits per tree Fruit ripening rate per day Number of fruiting trees Number of tree clusters per landscape Degree of miro tree aggregation Degree of puriri tree aggregation Background fruit loss per day
ha–1
800 or 2 7 m s–1 30 fruits 10 fruits visit–1 2 fruits 0.67 min 0.02 13.89 min 0.15 4.06 min 0.04 0.001 2 5 10–5 2 0.01 0.6 5000 2500 50 1200 or 3 ha–1 120 100 m 20 m 0.5%
Source 2, 4 4 4 3, 4 3, 4 5 5 1 1 6 6 3 3 3 3 4 4 4 4 3, 4 4 4 4 4 4
Notes: a scale mean mean/variance, b shape mean/variance, a factor, b exponent, PT daily perching time, GPT frugivore gut passage time of seeds, kereru H. novaeseelandiae, miro P. ferruginea, puriri V. lucens. Sources: 1Clout and Tilley (1992), 2Greene (2003), 3Morales and Carlo (2006), 4Pegman (2012), 5Wotton (2007), 6Wotton et al. (2008).
a random point during the time spent at each tree during a mean of 120 minutes per day of perching time (Wotton 2007). A gut passage time for each feeding event is drawn from an appropriate probability distribution (Supplementary material Appendix 1), seeds are deposited after that time elapses, and in due course the seed dispersal distribution emerges from this activity (Fig. 3b). There are no interactions among birds in the model with respect to their seed dispersal service (they do not flock due to current low densities, although they likely did so in the past) and so the final seed deposition pattern emerges from independent superposition of individual dispersal events across all birds. The parameters of the seed dispersal kernel are then fitted to the simulated seed deposition pattern (see below). Other elements in our model reflect the biology of the systems we considered and include: 1) ‘roost’ trees i.e. trees that are attractive to birds but do not provide a food source (Beveridge 1964 and Johnson 2001 describe the use of Weinmannia racemosa in this way) and 2) the occasional longer distance random movement by individual dispersers within the landscape, rather than on the basis of the attractiveness of trees. We also included background fruit loss from trees due to wind, abscission, predation, mishandling by birds, etc. Model parameterisation, sensitivity and structural analyses, and in silico experiments The model parameterization was informed by data describing the foraging behavior of H. novaeseelandiae and the
physiognomy of V. lucens and P. ferruginea, obtained through experiments, field observations, and from the relevant literature (Table 1). We conducted a univariate sensitivity analysis, following the methods described by Hamby (1994), by imposing a 25% change on each specified baseline model input parameter and then calculating absolute ratios (Sy, x) of change in kernel parameters to assess how these seed dispersal characteristics changed with model parameterization (Table 2 and Supplementary material Appendix 4). The model parameters we tested were chosen because they were a priori deemed to be the most relevant to the questions we were focussing on or were the most uncertain. Because the sensitivity analysis suggested that it was a crucial driver of the model’s dynamics, we also conducted a structural analysis on the mathematical function governing frugivores’ choice of tree based on the distance from its current location (Supplementary material Appendix 1, Eq. A2). Since we were assessing whether the degree of tree aggregation (sigma, s) was a major driver of seed distributions, we used the entire biologically reasonable range (i.e. s 2 to 100 m) in the assessment of its sensitivity. We then conducted a series of in silico plant–frugivore experiments to explore the extent to which seed dispersal kernels are influenced by interactions between tree spatial patterns and frugivore density. A factorial design was employed in which the density of H. novaeseelandiae (nK) varied between 0.1 and 10 ha–1, representing the range of plausible values (Pegman 2012). In support of this, Greene (2003) calculated H. novaeseelandiae densities of 0.1 to 2.6 ha–1 in Pureora Forest Park, NZ, reflecting seasonal movements linked to food availability. The degree of aggregation 3-EV
Table 2. Univariate sensitivity analysis (exemplified here by V. lucens; see Supplementary material Appendix 4 for P. ferruginea) according to the methods of Hamby (1994). All model runs comprised 30 replicates, each of 14 d. Rank denotes rank of S ratio (the ratio of the relative change in the state variable y for a given relative change in the value of parameter x) based on mean of the ratios. Cases where Sy, x 1 are in bold. See Table 1 for description of baseline model parameter abbreviations. Scale parameter Baseline model parameter bD 2 aD 5 10–5 aPT 0.67 min. bGPT 0.04 bPT 0.02 aGPT 4.06 min pLONG 0.01 bF 2 PT 120 min maxF 2500 rtA 0.60 rF 50 aF 0.001 e 30 fruit No. of roost trees 100 s 20 m
Sy, x (–25%) 6.473 0.634 0.400 0.414 0.313 0.305 0.105 0.017 0.052 0.024 0.008 0.021 0.015 0.016 0.033 0.002
Sy, x ( 25%)
Sy, x (–25%)
Sy, x ( 25%)
Rank
2.521 0.426 0.291 0.243 0.314 0.280 0.134 0.050 0.014 0.022 0.035 0.022 0.028 0.025 0.001 0.004
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1.856 0.260 0.027 0.021 0.017 0.021 0.168 0.024 0.007 0.031 0.014 0.021 0.021 0.010 0.003 0.030
1.298 0.195 0.082 0.014 0.034 0.014 0.086 0.021 0.010 0.010 0.003 0.003 0.000 0.000 0.003 0.026
1 2 4 9 5 10 3 6 13 8 12 11 14 15 16 7
of trees (sigma, s) was varied by tightening or relaxing clusters in the Thomas point process, used to simulate patterns of individual trees from aggregated (low s) to diffuse (high s), with ca 86% of all trees of a given cluster located within 2s of the cluster centre (Illian et al. 2008, Supplementary material Appendix 1, Fig. A2). We varied s from 10 to 200 m (representing nearest fruiting tree neighbors at ca 11 to 28 m) and held abundance constant at 1200 fruiting trees in 120 clusters per simulated landscape of 400 ha (i.e. 3 trees ha–1), based on field estimates of the density of both tree species (Pegman 2012). We also conducted experiments to assess the combined effects of low fruit availability and low fruit ripening on the seed dispersal kernels. There were 30 simulations for each combination of factors, with each replicate comprising 120 min of daily frugivore perching time (time from arrival until departure from a tree, including foraging, Wotton 2007) across 14 d, adjusting frugivore gut passage time of seeds and fruit production according to the tree species examined (Table 1). Our analyses used seed dispersal events that occurred during the last three days of the model runs; this minimised the risk of ‘burn in’ effects, but still had ample sample size for robust parameter estimation. Each individual bird started the simulation at a randomly chosen tree, and the number of fruit removed from each tree and the dispersal distance of every seed were recorded. Seed dispersal distributions were summed across individual birds to characterize the population level pattern for each tree species. A Weibull probability density function (Weibull 1951, Eq. 1) was fitted to the distributions by maximum likelihood estimation using the ‘fitdistr’ command in the MASS library in R–3.1.1 (R Development Core Team). We used the Weibull distribution because it is flexible, approximating a number of other probability distribution functions that have been used to summarize seed dispersal kernels, and it quantifies the properties of dispersal kernels that we are interested in i.e. scale (mean seed dispersal distance) and 4-EV
Shape parameter Rank
shape (i.e. kurtosis–1; low shape values equate to high kurtosis and ‘fat’ long tails and vice versa). β x β−1 (1) f ( x | α, β ) = e − ( x / α )β α α where x distance from tree, a scale parameter, and b shape parameter, all 0. For each analysis, we estimated the scale and shape parameters of the seed dispersal kernels; for these data, we were most interested in the scenario analyses that used empirically derived ‘field’, or ‘observed pattern’, estimates of tree aggregations while varying disperser densities, and vice versa. We also quantified the total number of dispersed seeds, seed rain map plots, frugivore foraging ranges (via convex hulls, computed in the R Spatstat library, Baddeley and Turner 2005) and the flight distances that resulted in them, and performed a spatial analysis of seed rain using a bivariate pair correlation function (Illian et al. 2008) based on spatial association between trees and deposition events. Data available from the Dryad Digital Repository: (Pegman et al. 2016).
Results Sensitivity and structural analyses The scale and shape parameters of the seed dispersal kernels were both strongly influenced by the model parameters relating to frugivore movement and also by gut passage time. In particular, seed dispersal kernels were highly sensitive to the coefficient determining attractiveness based on distance to candidate fruiting tree (bD, Table 2). Otherwise, all other model parameters were robust (absolute sensitivity values 1) and outcomes were symmetric (i.e. increases and decreases had similar relative effects). As expected, sigma was robust when held constant while testing the effect of differ-
ent frugivore densities (Table 2), but we found that there was an increase (although less than proportional) of both shape and scale parameters in both tree species when s increased across all of its plausible values (Supplementary material Appendix 3, Table A7). We assumed that there was a strong decline in attractiveness with distance by frugivores for fruiting trees, hence we used a hyperbolic function to determine the effect of distance on tree selection; this function has been used in other similar models that have produced plausible biological outcomes, e. g. Morales and Carlo (2006). There is no empirical data on bird movements at a sufficient resolution to derive empirical fits for this chosen function, or to parameterize it. However, our use of a hyperbolic function was justified by the fact that our frugivore foraging ranges, and movements which resulted in them, were similar to those derived from empirical observation; we focused on movement data and foraging ranges, rather than mean seed dispersal distance, because there is ample empirical data for the first two factors (see below), against which we could validate our model, but little for the latter. Nevertheless, because of the importance of this functional relationship for model results and because it utilised bD (Supplementary material Appendix 1, Eq. A2), which was both a sensitive and uncertain model parameter (Table 2), we conducted a structural analysis to assess the robustness of the model outcomes to this decision. In the structural analysis we assessed three other distance-attractiveness functions: 1) a linear decline, 2) a negative exponential decline (to zero attractiveness at 250 m), and 3) a null model (where all trees were equally attractive irrespective of distance). The linear and negative exponential relationships produced similar foraging range sizes to the hyperbolic (linear hyperbolic ∼ negative exponential), but those from a null model were much larger (Supplementary material Appendix 3, Table A1, exemplified by V. lucens). Morales and Carlo (2006) also rejected a null diffusion model because they found that mean seed dispersal distances were not linearly related to the degree of plant aggregation. The fact that the outcome from the negative exponential is similar to the hyperbolic also suggests that our results do not depend on an arbitrary decision to use a specific function for distance attractiveness. Seed dispersal kernels Across both tree species, our simulated seed dispersal distributions ranged between being exponential to gamma in appearance (Fig. 6), both of which can be described by the Weibull distribution. The shape parameters (b), obtained by fitting the Weibull, corresponded to mainly fat tailed curves at high tree aggregation (b 1), exponential at b 1, and ‘hump’ shaped at low tree aggregation (b 1.1 to 1.4), but none corresponded to simple diffusion i.e. b 2. Variation of the distribution of trees in the landscape translated into clear differences in the scale and shape parameters of the seed dispersal kernels. Because the movement rules are fixed, these differences were the outcome of emergent interactions between seed dispersers and the landscape structure. Increased tree aggregation resulted in shorter mean seed dispersal distances and kernels with long and ‘fat’ tails, as evidenced by low shape parameters. Conversely, tree populations
that were less aggregated resulted in longer mean seed dispersal distances, which were associated with high value shape parameters and kernels with short tails (Fig. 1a, b, 2a, b show results at ‘observed pattern’ bird densities; Supplementary material Appendix 3, Table A3 to A6 show seed dispersal kernel parameter values obtained in different landscape scenarios in the factorial experiments). However, the total number of dispersed seeds was not significantly affected by the spatial distribution of either tree species. Variation of disperser density did not significantly influence mean seed dispersal kernel parameters when fruit availability was high, except in V. lucens forests at the highest simulated frugivore density (i.e. 10 ha–1), but these comprised a difference of only a few metres and so are unlikely to be ecologically important (Fig. 1c, d, 2c, d show results in ‘observed pattern’ forests; Supplementary material Appendix 3, Table A3 to A6 show dispersal kernel parameter values obtained in different frugivore density scenarios in the factorial experiments). The total number of dispersed seeds changed directly in proportion to H. novaeseelandiae density. However, inter-realisation variance of individual kernel shape and scale parameters increased with decreasing disperser density (Fig. 1d and 2d), suggesting that in these scenarios, long distance seed dispersal events will become increasingly stochastic, reducing the predictability of estimates relying on it e.g. plant connectivity, spatial distributions, and dynamics (Nathan 2005). When we concurrently lowered fruit availability and fruit ripening, we found that seed dispersal distances increased when frugivore densities increased because birds had to fly further to locate fruit (Supplementary material Appendix 3, Table A2, exemplified by V. lucens). Frugivore foraging ranges Under ‘observed pattern’, or baseline, conditions, our simulated frugivore foraging ranges (mean one SEM 27.3 2.3 ha, statistical range 1.2 to 134.2 ha, n 100) are consistent, both in area and time frame, with those determined in other studies (Fig. 3a, b, Pierce and Graham 1995, Bell 1996, Hill 2003, Schotborgh 2005, Campbell 2006, Powlesland et al. 2011). For example, Hill (2003) reported values from ca 14 to 704 ha, Bell (1996) reported ca 20 to 30 ha, and Schotborgh (2005) reported ca 2 to 22 ha, all similar to our values. Powlesland et al. (2011) reported much higher values (ca 619 to 31 732 ha) because their data captured infrequent, possibly seasonal, long-distance movements between distinct habitats (from mainland NZ to an offshore island). Hemiphaga novaeseelandiae had larger foraging ranges in simulated P. ferruginea landscapes than in V. lucens landscapes since the former were less aggregated and therefore the birds had to fly further to forage. Our model produced mean flight distances between 60 and 100 m, consistent with a mean one SEM of 77.0 7.0 m in Wotton and Kelly (2012) and ca 11 to 102 m in Powlesland et al. (2011). The short flight distances and rapid flying speed of frugivores (ca 7 ms–1, Pegman 2012) meant that most seeds were deposited at trees rather than during flight in the model, consistent with the observed behaviour of H. novaeseelandiae (McEwen 1978). 5-EV
Figure 1. Seed dispersal kernels and corresponding scale and shape parameters for V. lucens using the Weibull distribution, n 30 model runs 14 d; (a) and (b) are across sigma (s, degree of tree aggregation) of 10 m (highly aggregated trees, dark blue) to 200 m (least aggregated, red) at a disperser density of two H. novaeseelandiae (kereru) ha–1, and (c) and (d) are across kereru densities of 0.1 ha–1 (dark blue) to 10 ha–1 (red) at s 20 m.
Seed rain map plots and spatial analysis In highly aggregated populations of either tree species, maps of the seed rain show that deposition mainly occurred around tree clusters, but was anisotropic and spatially non-uniform across the landscape; the numbers of seeds deposited differed markedly between adjacent areas, with some receiving none, and deposition occurred only occasionally near roost trees (Fig. 4 and 5). Empirical measurements of seed deposition at the sites of individual fruiting trees of our study species showed that it is also anisotropic (Pegman 2012), reflecting biotic factors such as canopy shape, perching behaviour of birds, and overlapping seed shadows, plus abiotic effects such as micro-topography (Bullock et al. 2006). When fruiting trees were less aggregated, seed rain was more uniform across the landscape, reflecting different patterns of disperser movement; anisotropy was still evident, but seed rain occurred more frequently near roost trees. In both scenarios, seed distribution patterns were independent of bird densities, but the total number of dispersed seeds changed directly in proportion to disperser numbers. These outcomes are in agreement with the seed dispersal kernel results presented above, where it was shown that tree patterns, but not bird densities, significantly influenced the main parameters of seed dispersal kernels when resources were not scarce. A spatial association between trees and seed deposition events using the bivariate pair correlation function (Illian et al. 6-EV
2008) based on all seed dispersal events, showed that the distances over which seed deposition occurred with respect to fruiting trees increased when trees became less aggregated (Fig. 6).
Discussion We aimed to investigate how seed dispersal is influenced by the interaction between frugivore behaviour and plant spatial patterns, using in silico experiments. We varied frugivore density across different spatial arrangements of large-fruited tree species prevalent in NZ temperate forests and examined the resulting changes in the main characteristics of seed dispersal kernels, and how these might influence the dynamics of plant populations. Tree spatial distribution influenced bird movement patterns, resulting in clear differences in the main statistical characteristics of the seed dispersal kernels. As forests became more aggregated, the mean seed dispersal distance (or scale of the dispersal kernel) decreased because birds were restricted mainly to clusters of high tree density. One outcome of this limited dispersal distance was reduced seed deposition near roost trees. Previous simulation studies have also suggested that clumped plant spatial patterns influence disperser or pollinator behaviour by confining them to monospecific patches (Morales and Carlo 2006, Hanoteaux
Figure 2. Seed dispersal kernels and corresponding scale and shape parameters for P. ferruginea using the Weibull distribution, n 30 model runs 14 d; (a) and (b) are across sigma (s, degree of tree aggregation) of 10 m (highly aggregated trees, dark blue) to 200 m (least aggregated, red) at two H. novaeseelandiae (kereru) ha–1, and (c) and (d) are across kereru densities of 0.1 ha–1 (dark blue) to 10 ha–1 (red) at s 100 m.
et al. 2013). Over the long-term, shortened seed dispersal distances may amplify any existing local tree aggregation and increase neighborhood competition and negative densitydependent effects (Augspurger and Kelly 1984). In support of this expectation, some spatially explicit models have
shown that localized seed dispersal drives the emergence of aggregated plant spatial distributions (Holmes and Wilson 1998, Fedriani et al. 2010, Rodriguez-Perez et al. 2012). In our case, there were also occasional traverses between tree clusters in aggregated forest settings, resulting in long
Figure 3. (a) Example of distribution of foraging ranges (ha) of 100 H. novaeseelandiae after 14 d in V. lucens and P. ferruginea forests, and (b) example of emergence of a foraging range of a single H. novaeseelandiae after 14 d; colored points depict foraging at trees, with colours representing visitation (blue to red, with unvisited in grey) – in this case the area visited was 22.5 ha.
7-EV
Figure 4. Seed deposition by H. novaeseelandiae across landscapes of 400 ha (2000 2000 m, showing ‘patches’, each 100 m2) with 1200 V. lucens trees (black points) and 100 roost trees (white points) after one fruiting season, at varying disperser density (D, H. novaeseelandiae ha–1) and tree aggregation i.e. s (m), low values indicate high tree aggregation and vice versa. Legends indicate the total number of seeds deposited ha–1 (note they vary across sub plots).
distance seed dispersal events, consequently stretching the tail of the dispersal kernel; such events, even if rare, enhance seed dispersal efficiency and allow plant population spread (Howe and Miriti 2004). Conversely, when the distribution of trees was less aggregated, mean dispersal distances increased because birds had larger foraging ranges and therefore had the opportunity to disperse seeds at longer distances and in a more uniform pattern, including under roost trees. Variation in frugivore density did not significantly influence seed dispersal kernels in our factorial experiments. Increased disperser densities had no direct effect on seed dispersal kernels because they arose from independent superposition of individual seed shadows of all birds, and resources did not become scarce, so birds did not have to venture out of fruiting patches to obtain more fruit. Both of the tree species we considered have high annual fruit production, with up to 83% of V. lucens fruit and 70% of P. ferruginea fruit falling uneaten beneath their respective canopies, due in part to low disperser numbers in modern ecosystems (Clout and Hay 1989, Wotton and Kelly 2011, 8-EV
Pegman 2012). However, fruit depletion in some ecosystems can be very high (Forget 1992) and in such cases, frugivore movement patterns are different. For example, the plant taxon represented in the model by Morales and Carlo (2006) was frequently depleted of fruit, resulting in longer frugivore foraging movements and an increase in mean seed dispersal distance and kurtosis of the dispersal kernels. Decreased disperser abundance in our simulations did, however, result in a proportional reduction in the total number of dispersed seeds, with the commensurate effect of decreasing the probability of long distance seed dispersal, thus reducing seed dispersal efficiency and potentially diminishing population spread (Spiegel and Nathan 2007, Nathan et al. 2008). In support of this finding, Wotton and Kelly (2011) showed that lack of seed dispersal has resulted in low recruitment rates in large-fruited NZ tree species. Conversely, increased disperser abundance resulted in a proportional increase in the total number of dispersed seeds in our simulations. We also tested a mechanism of frugivore density that indirectly had the potential to change the shape of the seed rain, by
Figure 5. Seed deposition by H. novaeseelandiae across landscapes of 400 ha (2000 2000 m, showing ‘patches’, each 100 m2) with 1200 P. ferruginea trees (black points) and 100 roost trees (white points) after one fruiting season, at varying disperser density (D, H. novaeseelandiae ha–1) and tree aggregation i.e. s (m), low values indicate high tree aggregation and vice versa. Legends indicate the total number of seeds deposited ha–1 (note they vary across sub plots).
concurrently reducing the availability and ripening of fruits on trees in the model. As a result, at high frugivore densities, birds were forced to move further afield to forage, as evidenced by significantly longer mean seed dispersal distances. Other simulations that investigated how plant–frugivore mutualisms affect seed dispersal kernels have produced different outcomes, possibly due to the different ways in which they represented disperser activity or landscape structure. For example, despite clear changes in bird movement in response to landscape configuration, Uriarte et al. (2011) stated that there was negligible effect of landscape structure on seed dispersal distances. However, their model used fragmented forest patches that did not take into account aggregation of individual trees. Will and Tackenberg (2008) found that seed dispersal kernels, based on epizoochorous and endozoochorous dispersal by mammals, are influenced more by changes in the animal disperser than on the variation of vegetation, but this was determined using random rather than directional disperser movement. Wotton and
Kelly (2012) reported that seed dispersal distances were established primarily by frugivore movements, but did not comment on the role of landscape structure in this process. Our sensitivity analyses revealed that the model parameters having the largest influence on the results were those relating to bird behaviour, while the effect of landscape characteristics (sigma) was much smaller (Table 2 and Supplementary material Appendix 4). Mean seed dispersal distances increased disproportionately when the parameter (i.e. bD) that was used to calculate the hyperbolic decline in tree attractiveness with distance varied (shape also increased, but to a lesser degree, Table 2). The sensitivity of this model parameter suggests that frugivore movement plays an important role in the emergence of the seed dispersal kernel; this finding is consistent with other studies, which have shown that spatial patterns of recruitment are influenced by movement patterns of animal dispersers (Wenny 2000, Santamaria et al. 2007). Although we found little empirical information with which to estimate bD for our study taxa, our hyperbolic functional response (which utilised bD, see above) produced 9-EV
Figure 6. The left hand column shows seed dispersal kernels generated by 30 randomly selected H. novaeseelandiae from the total pool (grey shaded), with the red curved line showing the kernel density estimated across all frugivores, with s, the degree of tree aggregation, increasing from top to bottom (highly aggregated to diffuse trees). The right hand column shows the spatial association between trees and seed deposition events using the bivariate pair correlation function (PCF, Illian et al. 2008) for each of 30 replicates (grey lines) for each value of s. The red straight line is the theoretical expection (g[r] ≡ 1) under a null homogeneous Poisson model, and the distance (x-axis) at which the grey lines approach this value gives an estimate of the distances over which seed deposition occurred with respect to fruiting trees.
frugivore foraging ranges, and movements that resulted in them, that were closest to empirical values, providing support for our representation of this process. Frugivore gut passage time of seeds (GPT) and daily frugivore perching time (PT) also influenced the scale (but not the shape) of the dispersal kernels. As expected, an increase in GPT caused dispersal distances to increase because seeds passed through the frugivore gut more slowly and therefore had the opportunity to travel further. When the shape parameter of the probability distribution describing GPT increased, there was a reduction in mean seed dispersal distances because the shortened tail of the GPT curve did not allow longer passage times, and so seeds typically were expelled at shorter distances. An increase in PT caused a decrease in the mean seed dispersal distances because the longer frugivores remained at a given perch, the more likely they were to disperse seeds under the parent tree or in the immediate vicinity of it. When the shape parameter of the distribution of PT increased, there was a concurrent increase in mean seed dispersal distance, consistent with the shorter perching time resulting from shorter tail of the PT curve. Morales and Carlo (2006) showed in their scenarios that mean seed dispersal distance was primarily influenced by the parameters of the distributions of GPT and PT, but found that plant attractiveness based on distance was less 10-EV
important, on the basis of their sensitivity analysis of aD, the factor in tree attractiveness based on distance (Table 1 and Supplementary material Appendix 1, Eq. A2). However, Wotton and Kelly (2012) showed in their simulations that seed dispersal distances were not determined by GPT since birds never flew for longer than seed retention times, as they did in our scenarios. Simulation models that link plant spatial patterns and the behaviour of organisms are uncommon (Morales and Carlo 2006, Will and Tackenberg 2008), and ours is one of few that include frugivore roosting behaviour. The only previous in silico model of seed dispersal by H. novaeseelandiae is a phenomenological model that combined gut passage time of seeds with radio-telemetry data (Wotton and Kelly 2012). Incorporating other indigenous large-fruited co-fruiting tree species could enhance our model by introducing seasonal variation. The simultaneous representation of multiple tree species would create dynamics that are more realistic because there are usually multiple fruit sources in forests, and the dietary preferences of frugivores may affect where seeds are deposited (Morales and Carlo 2006, Morales et al. 2013). For example, Pegman (2012) showed that seeds of three other large-fruited NZ indigenous tree species (Beilschmiedia tarairi, B. tawa, and Corynocarpus laevigatus) were frequently deposited under P. ferruginea and
V. lucens. The mean seed dispersal distances produced by our simulations may therefore need further refinement because the presence of other local attractive tree species in the landscape may act to reduce seed dispersal distances, assuming all trees are equally attractive. Conversely, if tree species that have low abundance in the landscape are highly favoured, this may act to extend dispersal distances. Based on data from study sites that had multiple fruiting species, Wotton and Kelly (2012) calculated, via simulation, a shorter mean seed dispersal distance for V. lucens than ours, using identical gut passage times of seeds and perching times for H. novaeseelandiae (their value was ca 98 m versus ours of ca 151 m, Supplementary material Appendix 3, Table A3, using nK 2, s 20; nevertheless, up to 20% of V. lucens seeds in their simulations were dispersed 100 m). Conclusion It is challenging to evaluate the link between plant demography and behavior of organisms because they interact reciprocally. Our experiments show the potential of simulation-based approaches for exploring plant–organism interactions and identified that plant spatial heterogeneity is a key determinant of bird behaviour and the seed dispersal kernels that arise from it. Although this outcome is specific to the scenarios we examined, we believe our results apply to other similar mutualisms. Perhaps the most critical result from our simulations is that the loss of dispersers resulted in fewer seeds being transported, decreasing the probability of rare long distance seed dispersal events, reducing seed dispersal effectiveness and therefore ultimately diminishing population spread, genetic connectivity, and survival of tree species (Nathan 2005). Such understanding is essential in view of declining animal dispersers and habitats worldwide. Acknowledgements – This study was funded by a Univ. of Auckland Doctoral Scholarship (awarded to APMcKP), the School of Environment Graduate Research Fund, and the Auckland Regional Council. We thank the editor and reviewers for useful comments on the manuscript and the birds for dispersing seeds.
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