Coevolution of mistletoes and frugivorous birds?*

Small frugivorous birds that feed largely on the fruits of stem-parasitic mistletoes have independently evolved in various parts of the world. Local populations of mistletoes may be dispersed almost exclusively by these birds. Four attributes of mistletoe dispersal systems may have enhanced the evolution of reciprocal dependence between mistletoes and specialized dispersers: (1) Safe sites for mistletoe seeds (i.e. the young branches of a compatible host) are precisely defined in space and time. (2) The viscidity of mistletoe seeds induces smaller dispersers to deposit seeds in safe sites. (3) Frugivores differ markedly in the efficiency with which they disperse mistletoe seeds to safe sites. (4) Relatively large viscid fruits and adaptive fruiting displays exclude or deter most members of the potential disperser guild. Some birds have anatomical adaptations as a result of dietary specialization on mistletoe fruit, and some mistletoes have fruiting displays that target specialized birds or a narrow disperser spectrum. Coevolution between guilds of mistletoes and specialized dispersers is therefore probable. The uncoupled selective pressures that might have driven their coevolution are the mistletoes’ provision of fruit crops that are unavailable to more generalized frugivores, in return for seed dispersal to the small stems most suitable for infection. As in other mutualistic seed dispersal systems, phylogenetic, ecological and life history factors constrain the evolution of monophyletic interdependence, resulting in varying degrees and patterns of reciprocal specificity between mistletoes and dispersers.     

Spatiotemporal Variation of Mistletoes: a Dynamic Modeling Approach

Mistletoes are common aerial stem-parasites and their seeds are dispersed by fruit-eating birds. In the mutually beneficial relationships between mistletoes and bird species that disperse mistletoes’ seeds, the preference of birds for infected trees influences the spread of mistletoes and the spatiotemporal pattern formation of mistletoes. We formulate a deterministic model to describe the dynamics of mistletoes in an isolated patch containing an arbitrary number of trees. We establish concrete criterions, expressed in terms of the model parameters, for mistletoes establishing in this area. We conduct numerical simulations based on a field study to reinforce and expand our results.     

Specialized Seed Dispersal in Epiphytic Cacti and Convergence with Mistletoes

Mistletoes represent the best example of specialization in seed dispersal, with a reduced assemblage of dispersal agents. Specific dispersal requirements mediated by the specificity of seed deposition site have apparently led to the evolution of such close relationships between mistletoes and certain frugivores. Here, we provide evidences for another case of specialization involving epiphytic cacti in the genus Rhipsalis, and small Neotropical passerines Euphonia spp., which also act as the main seed dispersers of mistletoes in the family Viscaceae. With field observations, literature search, and observations on captive birds, we demonstrated that Rhipsalis have specific establishment requirements, and euphonias are the most effective dispersers of Rhipsalis seeds in both quantitative and qualitative aspects, potentially depositing seeds onto branches of host plants. We interpret the similar dispersal systems of Rhipsalis and Viscaceae mistletoes, which involve the same dispersal agents, similar fruit morphologies, and fruit chemistry as convergent adaptive strategies that enable seeds of both groups to reach adequate microsites for establishment in host branches.     

Spatial autocorrelation and dispersal in mistletoes: field and simulation results

The infections of two species of mistletoes in Baja California, Mexico were investigated for spatial patterns of abundance, and for an effect of the dispersal patterns of mistletoe seeds on these spatial patterns. Mistletoe distributions were mapped and the dispersal of mistletoe seeds was observed. Most mistletoes seeds were dispersed locally to the parent tree or to nearby trees. While mistletoe distributions were highly clumped at the level of the individual tree, no spatial pattern was found above the scale of the individual tree. Infected trees were no more clumped than the overall host population, and infected trees had no more mistletoes on nearby surrounding trees than did uninfected trees. Trees showed no spatial autocorrelation in the number of mistletoes they supported. Simulations using a spatially explicit simulation model with local dispersal and stochasticity in seed dispersal, host mortality, and mistletoe mortality were used to interpret the field results. Simulation results suggest that dispersal patterns affect the overall level of variance in the number of mistletoes per tree but do not lead to spatial patterns in abundance above the scale of the tree. Thus, both simulation and field systems give the surprising result that local dispersal does not lead to spatial autocorrelation in the numbers of mistletoes per tree.Abbreviations AI = Arroyo Inspiracion - VSR = Valle San Rafael     

Predicting the spread of all invasive forest pests in the United States

We tested whether a general spread model could capture macroecological patterns across all damaging invasive forest pests in the United States. We showed that a common constant dispersal kernel model, simulated from the discovery date, explained 67.94% of the variation in range size across all pests, and had 68.00% locational accuracy between predicted and observed locational distributions. Further, by making dispersal a function of forest area and human population density, variation explained increased to 75.60%, with 74.30% accuracy. These results indicated that a single general dispersal kernel model was sufficient to predict the majority of variation in extent and locational distribution across pest species and that proxies of propagule pressure and habitat invasibility – well‐studied predictors of establishment – should also be applied to the dispersal stage. This model provides a key element to forecast novel invaders and to extend pathway‐level risk analyses to include spread.     

Modeling and analysis of stochastic invasion processes

In this paper we derive spatially explicit equations to describe a stochastic invasion process. Parents are assumed to produce a random number of offspring which then disperse according to a spatial redistribution kernel. Equations for population moments, such as expected density and covariance averaged over an ensemble of identical stochastic processes, take the form of deterministic integro-difference equations. These equations describe the spatial spread of population moments as the invasion progresses. We use the second order moments to analyse two basic properties of the invasion. The first property is permanence of form in the correlation structure of the wave. Analysis of the asymptotic form of the invasion wave shows that either (i) the covariance in the leading edge of the wave of invasion asymptotically achieves a permanence of form with a characteristic structure described by an unchanging spatial correlation function, or (ii) the leading edge of the wave has no asymptotic permanence of form with the length scales of spatial correlations continually increasing over time. Which of these two outcomes pertains is governed by a single statistic, φ which depends upon the shape of the dispersal kernel and the net reproductive number. The second property of the invasion is its patchy structure. Patchiness, defined in terms of spatial correlations on separate short (within patch) and long (between patch) spatial scales, is linked to the dispersal kernel. Analysis shows how a leptokurtic dispersal kernel gives rise to patchiness in spread of a population. Received: 11 August 1997 / Revised version: 22 September 1998 / Published online: 4 October 2000     

Predicting the time to colonization of the parasitoid Diadegma semiclausum: The importance of the shape of spatial dispersal kernels for biological control

The time at which natural enemies colonize crop fields is an important determinant of their ability to suppress pest populations. This timing depends on the distance between source and sink habitats in the landscape. Here we estimate the time to colonization of sink habitats from a distant source habitat, using empirical mark-capture data of Diadegma semiclausum in Broccoli. The data originated from experiments conducted at two locations and dispersal was quantified by suction sampling before and after a major disturbance. Three dispersal kernels were fitted to the dispersal data: a normal, a negative exponential, and a square root negative exponential kernel. These kernels are characterized by a thin, intermediate and a fat tail, respectively. The dispersal kernels were included in an integro-difference equation model for parasitoid population redistribution to generate estimates of time to colonization of D. semiclausum in sink habitats at distances between 100 and 2000 m from a source. We show that the three dispersal kernels receive similar support from the data, but can produce a wide range of outcomes. The estimated arrival time of 1% of the D. semiclausum population at a distance 2000 m from the source ranges from 12 days to a length of time greatly exceeding the life span of the parasitoid. The square root negative exponential function, having the thickest tail among the tested functions, gave the fastest spread and colonization in three of the four data sets, but it gave the slowest redistribution in the fourth. In all four data sets, the rate of accumulation at the target increased with the mean dispersal distance of the fitted kernel model, irrespective of the fatness of the tail. This study underscores the importance of selecting a proper dispersal kernel for modelling spread and colonization time of organisms, and of the collection of pertinent data that enable kernel estimation and that can discriminate between different kernel shapes.     

Families of discrete kernels for modeling dispersal

Integer lattices are important theoretical landscapes for studying the consequences of dispersal and spatial population structure, but convenient dispersal kernels able to represent important features of dispersal in nature have been lacking for lattices. Because leptokurtic (centrally peaked and long-tailed) kernels are common in nature and have important effects in models, of particular interest are families of dispersal kernels in which the degree of leptokurtosis can be varied parametrically. Here we develop families of kernels on integer lattices with several important properties. The degree of leptokurtosis can be varied parametrically from near 0 (the Gaussian value) to infinity. These kernels are all asymptotically radially symmetric. (Exact radial symmetry is impossible on lattices except in one dimension.) They have separate parameters for shape and scale, and their lower order moments and Fourier transforms are given by simple formulae. In most cases, the kernel families that we develop are closed under convolution so that multiple steps of a kernel remain within the same family. Included in these families are kernels with asymptotic power function tails, which have provided good fits to some observations from nature. These kernel families are constructed by randomizing convolutions of stepping-stone kernels and have interpretations in terms of population heterogeneity and heterogeneous physical processes.     

Effectiveness of Mistletoe Seed Dispersal by Tyrant Flycatchers in a Mixed Andean Landscape

The dependence of mistletoes on few dispersers and the directed dispersal they provide is well known, yet no recent work has quantified either the effectiveness of these ‘legitimate’ dispersers, or the extent of redundancy among them. Here, I use the seed dispersal effectiveness (SDE) framework to analyze how birds (Mionectes striaticollis and Zimmerius bolivianus) contribute to mistletoe (Struthanthus acuminatus and Phthirusa retroflexa) infection in traditional mixed plantations within a humid montane forest in Bolivia. I calculated SDE for each bird–mistletoe pair and for the disperser assemblage, by estimating both the quantity and the quality of dispersal. The quantity of dispersal was measured as: (1) disperser abundance; (2) frequency of visits; and (3) number of seeds dispersed per visit, and the quality of dispersal was measured as: (1) germination percentage and speed of germination of seeds regurgitated by birds; and (2) the concordance of deposited seeds and seedling distribution patterns with adult mistletoe distribution at three scales (habitat, host, and microhabitat). Dispersers were not redundant: the more generalist species M. striaticollis dispersed more seeds, but provided lower quality seed dispersal, whereas the mistletoe specialist Z. bolivianus provided low‐quantity and high‐quality seed dispersal. Whereas S. acuminatus benefited more from the SDE of Z. bolivianus, P. retroflexa benefited from the complementary seed dispersal provided by both birds. These results demonstrate how sympatric mistletoes that share the same disperser assemblage may develop different relationships with specific vectors, and describe how the services provided by two different dispersers (one that provides high‐quality and one that provides high‐quantity dispersal) interact to shape spatial patterns of plants.     

Dynamical effects of nonlocal interactions in discrete-time growth-dispersal models with logistic-type nonlinearities

The paper is devoted to the study of discrete time and continuous space models with nonlocal resource competition and periodic boundary conditions. We consider generalizations of logistic and Ricker's equations as intraspecific resource competition models with symmetric nonlocal dispersal and interaction terms. Both interaction and dispersal are modeled using convolution integrals, each of which has a parameter describing the range of nonlocality. It is shown that the spatially homogeneous equilibrium of these models becomes unstable for some kernel functions and parameter values by performing a linear stability analysis. To be able to further analyze the behavior of solutions to the models near the stability boundary, weakly nonlinear analysis, a well-known method for continuous time systems, is employed. We obtain Stuart–Landau type equations and give their parameters in terms of Fourier transforms of the kernels. This analysis allows us to study the change in amplitudes of the solutions with respect to ranges of nonlocalities of two symmetric kernel functions. Our calculations indicate that supercritical bifurcations occur near stability boundary for uniform kernel functions. We also verify these results numerically for both models.     

A discrete space model for continuous space dispersal processes

The simulation of dispersal processes in landscapes over large spatial extents is challenging because of the large difference in geographical scale between overwhelmingly dominant localised dispersal events, and rare long-distance dispersal events which typically drive overall rates of spread. While localised dispersal may point to high resolution individual level models, long-distance dispersal events are likely to involve much coarser grid-based models. In this paper we propose a discrete space (i.e., grid-based) model for dispersal processes in continuous space. We start by illustrating the behaviour of continuous space walks when their movement is discretised to a grid. The importance of short time period cell-to-cell moves which return a walk to its previous grid cell location is identified. A conceptual model which uses a Markov chain buffer phase between cells to replicate the observed behaviour of discretised continuous space walks is proposed. Analysis of the Markov chain shows that it can be parameterised using just two parameters in addition to the dispersal kernel. An algorithm for implementation of the proposed model is presented. Empirical results demonstrate that the proposed mechanism produces good matches to continuous space dispersal processes with both exponential and heavy-tailed dispersal kernels.     

Consequences of Dispersal Heterogeneity for Population Spread and Persistence

Dispersal heterogeneity is increasingly being observed in ecological populations and has long been suspected as an explanation for observations of non-Gaussian dispersal. Recent empirical and theoretical studies have begun to confirm this. Using an integro-difference model, we allow an individual’s diffusivity to be drawn from a trait distribution and derive a general relationship between the dispersal kernel’s moments and those of the underlying heterogeneous trait distribution. We show that dispersal heterogeneity causes dispersal kernels to appear leptokurtic, increases the population’s spread rate, and lowers the critical reproductive rate required for persistence in the face of advection. Wavespeed has been shown previously to be determined largely by the form of the dispersal kernel tail. We qualify this by showing that when reproduction is low, the precise shape of the tail is less important than the first few dispersal moments such as variance and kurtosis. If the reproductive rate is large, a dispersal kernel’s asymptotic tail has a greater influence over wavespeed, implying that estimating the prevalence of traits which correlate with long-range dispersal is critical. The presence of multiple dispersal behaviors has previously been characterized in terms of long-range versus short-range dispersal, and it has been found that rare long-range dispersal essentially determines wavespeed. We discuss this finding and place it within a general context of dispersal heterogeneity showing that the dispersal behavior with the highest average dispersal distance does not always determine wavespeed.     

Density-dependent dispersal in host-parasitoid assemblages

Most spatial population models assume constant rates of dispersal. However, in a given community, dispersal may not only depend on the density of conspecifics, i.e. density‐dependent dispersal, but also on the density of other species, a phenomenon we term ‘community‐dependent dispersal’. We co‐vary the densities of both the beetle host Callosobruchus chinensis and its parasitoid wasp, Anisopteromalus calandrae, in a laboratory study and record the proportions of each species that disperse within a two‐hour period. The parasitoid in these systems exhibits community‐dependent dispersal – dispersing more frequently when parasitoid density is high and larval host density is low. This supported our prediction that individuals should disperse according to competition for available resources. However, in this study the host's dispersal was independent of density. We suggest that this may be due to less intense selection acting on host dispersal strategies than on the parasitoid. We consider some possible consequences of community‐dependent dispersal for a number of spatial population processes. A well‐known host‐parasitoid metapopulation model is expanded so that it includes a greater range of dispersal functions. When the model is parameterised with the parasitoid community‐dependent dispersal function observed in the empirical study, similar population dynamics are obtained as when fixed‐rate dispersal functions are applied. The importance of dispersal functions for invasions of both competitive and host‐parasitoid systems is also considered. The model results demonstrate that understanding how individuals disperse in response to different species’ population densities is important in determining the rate of spread of an invasion. We suggest that more empirical studies are needed to establish what determines dispersal rate and distance in a range of species, combined with theoretical studies investigating the role of the dispersal function in determining spatial population processes.     

Long distance dispersal and landscape occupancy in a metapopulation of the cranberry fritillary butterfly

Movements between habitat patches in a patchy population of the butterfly Boloria aquilonaris were monitored using capture-mark-recapture methods during three successive generations. For each data set, the inverse cumulative proportion of individuals moving 100 m distance classes was fitted to the negative exponential function and the inverse power function. In each case, the negative exponential function provided a better fit than the inverse power function. Two dispersal kernels were generated using both negative exponential and inverse power functions. These dispersal kernels were used to predict movements between 14 suitable sites in a landscape of 220 km². The negative exponential function generated a dispersal kernel predicting extremely low probabilities for movements exceeding 1 km. The inverse power function generated probabilities predicting that between site movements were possible, according to metapopulation size. CMR studies in the landscape revealed that long distance movements occurred at each generation, corresponding to predictions of the inverse power function dispersal kernel. A total of 26 movements between sites (up to 13 km) were detected, together with recolonisation of empty sites. The spatial scale of the metapopulation dynamics is larger than ever reported on butterflies and long distance movements clearly matter to the persistence of this species in a highly fragmented landscape.     

The evolution of dispersal

A non-local model for dispersal with continuous time and space is carefully justified and discussed. The necessary mathematical background is developed and we point out some interesting and challenging problems. While the basic model is not new, a spread parameter (effectively the width of the dispersal kernel) has been introduced along with a conventional rate paramter, and we compare their competitive advantages and disadvantages in a spatially heterogeneous environment. We show that, as in the case of reaction-diffusion models, for fixed spread slower rates of diffusion are always optimal. However, fixing the dispersal rate and varying the spread while assuming a constant cost of dispersal leads to more complicated results. For example, in a fairly general setting given two phenotypes with different, but small spread, the smaller spread is selected while in the case of large spread the larger spread is selected. S. Martinez was partially supported by Fondecyt 1020126 and Fondecyt Lineas Complementarias 8000010. K. Mischaikow was supported in part by NSF Grant DMS 0107396. Key words or phases:Non-local dispersal – Integral kernel – Evolution of dispersal     

Allometric scaling of seed retention time in seed dispersers and its application to estimation of seed dispersal potentials of theropod dinosaurs

Seed retention time (SRT), the time interval between seed ingestion and defaecation, is a critical parameter that determines the spatial pattern of seed dispersal created by an animal, and is therefore, an essential component of trait‐based modelling of seed dispersal functions. However, no simple predictive model of SRT for any given animal exists. We explored the linkage between animal traits and SRT. We collected previously published data on mean SRT for 112 species of birds, mammals, reptiles and fishes and investigated the general allometric scaling of mean SRT with body mass for each taxon. Moreover, we analysed the effects of food habit and digestive strategy on mean SRT for birds and mammals. In general, mean SRT increased with body mass in all four taxa, whereas the pattern of allometric scaling varied greatly among the taxa. Birds had a smaller intercept and larger slope than those of mammals, whereas reptiles had a much larger intercept and smaller slope than those of either birds or mammals. For birds, food habit was also detected as an important factor affecting SRT. We applied the allometric scaling that was obtained for birds to estimate mean SRT of extinct Mesozoic dinosaurs (Theropoda) – few of which are assumed to have acted as seed dispersers. SRT for large carnivorous theropods was estimated to be 4–5 days, when considering only body mass. The present study provides allometric scaling parameters of mean SRT for a variety of seed‐dispersing animals, and highlights large variations in scaling among taxa. The allometric scaling obtained could be a critical component of further trait‐based modelling of seed dispersal functions. Further, the potential and limitations of the scaling of animal SRT with body mass and a future pathway to the development of trait‐based modelling are discussed.     

Colonization patterns of the invasive Brazilian peppertree, Schinus terebinthifolius, in Florida

Invasive species are believed to spread through a process of stratified dispersal consisting of short-distance diffusive spread around established foci and human mediated long-distance jumps. Brazilian peppertree (Schinus terebinthifolius), native to South America, was introduced twice as an ornamental plant into Florida, USA, just over 100 years ago. A previous study indicated that these two introductions were from genetically differentiated source populations in the native range. In this study, we took advantage of these contrasting genetic signatures to study the spatial spread of Brazilian peppertree across its entire range in Florida. A combination of spatial genetic and geostatistical analyses using chloroplast and nuclear microsatellite markers revealed evidence for both diffusive dispersal and long-distance jumps. Chloroplast DNA haplotype distributions and extensive bands of intra-specific hybridization revealed extensive dispersal by both introduced populations across the state. The strong genetic signature around the original introduction points, the presence of a general southeast to northwest genetic cline, and evidence for short-distance genetic spatial autocorrelation provided evidence of diffusive dispersal from an advancing front, probably by birds and small mammals. In the northernmost part of the range, there were patches having a high degree of ancestry from each introduction, suggesting long-distance jump dispersal, probably by the movement of humans. The evidence for extensive movement throughout the state suggests that Brazilian peppertree will be capable of rapidly recolonizing areas from which it has been eradicated. Concerted eradication efforts over large areas or the successful establishment of effective biocontrol agents over a wide area will be needed to suppress this species.     

Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity

Abstract In the presence of permanent spatial heterogeneity, local dispersal, especially short‐range dispersal, can facilitate coexistence by concentrating low‐density species in the areas where their rates of increase are higher. We present a framework for predicting the effects of local dispersal on coexistence for arbitrary forms of dispersal and arbitrary spatial patterns of environmental variation. Using the lottery model as an example, we find that local dispersal contributes to coexistence by enhancing the effects of environmental variation on scales longer than typical dispersal distances, which can be characterized solely by the variance of the dispersal kernel. Higher moments of the dispersal kernel are not important.     

Statistical mechanics of animal movement: Animals's decision-making can result in superdiffusive spread

Peculiarities of individual animal movement and dispersal have been a major focus of recent research as they are thought to hold the key to the understanding of many phenomena in spatial ecology. Superdiffusive spread and long-distance dispersal have been observed in different species but the underlying biological mechanisms often remain obscure. In particular, the effect of relevant animal behavior has been largely unaddressed. In this paper, we show that a superdiffusive spread can arise naturally as a result of animal behavioral response to small-scale environmental stochasticity. Surprisingly, the emerging fast spread does not require the standard assumption about the fat tail of the dispersal kernel.     

Distribution and dispersal of desert mistletoe is scale-dependent, hierarchically nested

Spatial patterns are important to many ecological processes, and scale is a critical component of both patterns and processes. I examined the pattern and scale of the spatial distribution of infection of host plants by the desert mistletoe, Phoradendron californicum, in a landscape that spans several square kilometers. I also studied the relationship between mistletoe infection and seed dispersal. I found elevated seed rain in areas with a high prevalence of mistletoes and I found that a greater proportion of trees receive seeds than are infected, suggesting that mistletoes will be aggregated in space. Using nested analysis of variance and variograms, I found that mistletoe infections were distributed in hierarchical patches. Mistletoes were aggregated within trees and mistletoe prevalence was correlated at scales of <1500 m, and at scales >4000 m. Patterns at the largest scales were correlated with elevation: sites at higher elevations showed reduced mistletoe infection compared to those at lower elevations. I propose that at small scales, mistletoe distributions are primarily the result of aggregation of seed-dispersing birds, and that the elevational effect could reflect the recent colonization of higher elevations by the mistletoes' mesquite hosts or the limits of the mistletoes' physiological tolerance to freezing-induced cavitation.