Costs and benefits of non‐random seed release for long‐distance dispersal in wind‐dispersed plant species

The dispersal ability of plants is a major factor driving ecological responses to global change. In wind‐dispersed plant species, non‐random seed release in relation to wind speeds has been identified as a major determinant of dispersal distances. However, little information is available about the costs and benefits of non‐random abscission and the consequences of timing for dispersal distances. We asked: 1) to what extent is non‐random abscission able to promote long‐distance dispersal and what is the effect of potentially increased pre‐dispersal risk costs? 2) Which meteorological factors and respective timescales are important for maximizing dispersal? These questions were addressed by combining a mechanistic modelling approach and field data collection for herbaceous wind‐dispersed species. Model optimization with a dynamic dispersal approach using measured hourly wind speed showed that plants can increase long‐distance dispersal by developing a hard wind speed threshold below which no seeds are released. At the same time, increased risk costs limit the possibilities for dispersal distance gain and reduce the optimum level of the wind speed threshold, in our case (under representative Dutch meteorological conditions) to a threshold of 5–6 m s^–1. The frequency and predictability (auto‐correlation in time) of pre‐dispersal seed‐loss had a major impact on optimal non‐random abscission functions and resulting dispersal distances. We observed a similar, but more gradual, bias towards higher wind speeds in six out of seven wind‐dispersed species under natural conditions. This confirmed that non‐random abscission exists in many species and that, under local Dutch meteorological conditions, abscission was biased towards winds exceeding 5–6 m s^–1. We conclude that timing of seed release can vastly enhance dispersal distances in wind‐dispersed species, but increased risk costs may greatly limit the benefits of selecting wind conditions for long‐distance dispersal, leading to moderate seed abscission thresholds, depending on local meteorological conditions and disturbances.     

Factors influencing the nonrandom abscission of Solidago canadensis seeds

 为揭示加拿大一枝黄花(Solidago canadensis)种群扩散机制, 明确种子的脱落及风传扩散在其种群蔓延中的作用, 在人工环境下测定了不同湍流强度、风速和湿度处理下种子脱落的差异, 并对脱落种子与未脱落种子进行形态学特征对比。结果表明: 加拿大一枝黄花的种子脱落受湍流、风速和湿度等因素的共同影响。水平气流下种子的脱落阈值为5.1 m·s^–1, 并随着风速增加, 种子的脱落率增加。与模拟水平气流相比, 模拟垂直气流下种子的脱落阈值显著偏小。相对于层流状态, 湍流的存在显著提高了种子的脱落率, 平均增幅超过300%; 但单纯提高湍流强度对种子脱落率的影响不显著。增加湿度则显著降低种子的脱落率。种子形态学特征对比结果表明, 脱落种子的冠毛数量和冠毛夹角显著高于未脱落种子。该研究结果为研究加拿大一枝黄花种子脱落规律和风传扩散机制提供了科学依据, 也为其他入侵性杂草种子的扩散机制及入侵过程提供了借鉴。     

Predicting dispersal of auto‐gyrating fruit in tropical trees: a case study from the Dipterocarpaceae

Seed dispersal governs the distribution of plant propagules in the landscape and hence forms the template on which density‐dependent processes act. Dispersal is therefore a vital component of many species coexistence and forest dynamics models and is of applied value in understanding forest regeneration. Research on the processes that facilitate forest regeneration and restoration is given further weight in the context of widespread loss and degradation of tropical forests, and provides impetus to improve estimates of seed dispersal for tropical forest trees. South‐East Asian lowland rainforests, which have been subject to severe degradation, are dominated by trees of the Dipterocarpaceae family which constitute over 40% of forest biomass. Dipterocarp dispersal is generally considered to be poor given their large, gyration‐dispersed fruits. However, there is wide variability in fruit size and morphology which we hypothesize mechanistically underpins dispersal potential through the lift provided to seeds mediated by the wings. We explored experimentally how the ratio of fruit wing area to mass (“inverse wing loading,” IWL) explains variation in seed dispersal kernels among 13 dipterocarp species by releasing fruit from a canopy tower. Horizontal seed dispersal distances increased with IWL, especially at high wind speeds. Seed dispersal of all species was predominantly local, with 90% of seed dispersing <10 m, although maximum dispersal distances varied widely among species. We present a generic seed dispersal model for dipterocarps based on attributes of seed morphology and provide modeled seed dispersal kernels for all dipterocarp species with IWLs of 1–50, representing 75% of species in Borneo.     

How important is long‐distance seed dispersal for the regional survival of plant species?

Long‐distance seed dispersal is generally assumed to be important for the regional survival of plant species. In this study, we quantified the importance of long‐distance seed dispersal for regional survival of plant species using wind dispersal as an example. We did this using a new approach, by first relating plant species’ dispersal traits to seed dispersal kernels and then relating the kernels to regional survival of the species. We used a recently developed and tested mechanistic seed dispersal model to calculate dispersal kernels from dispersal traits. We used data on 190 plant species and calculated their regional survival in two ways, using species distribution data from 36,800 1 km²‐grid cells and 10,754 small plots covering the Netherlands during the largest part of the 20th century. We carried out correlation and stepwise multiple regression analyses to quantify the importance of long‐distance dispersal, expressed as the 99‐percentile dispersal distance of the dispersal kernels, relative to the importance of median‐distance dispersal and other plant traits that are likely to contribute to the explanation of regional survival: plant longevity (annual, biennial, perennial), seed longevity, and plant nutrient requirement. Results show that long‐distance dispersal plays a role in determining regional survival, and is more important than median‐distance dispersal and plant longevity. However, long‐distance dispersal by wind explains only 1–3% of the variation in regional survival between species and is equally important as seed longevity and much less important than nutrient requirement. In changing landscapes such as in the Netherlands, where large‐scale eutrophication and habitat destruction took place in the 20th century, plant traits indicating ability to grow under the changed, increasingly nutrient‐rich conditions turn out to be much more important for regional survival than seed dispersal.     

Which factors have stronger explanatory power for primary wind dispersal distance of winged diaspores: the case of Zygophyllum xanthoxylon (Zygophyllaceae)?

Aims How seed dispersal distance is related to various factors is a major challenge for seed ecologists. However, there are different answers as to which factor is most important in determining wind dispersal distance. This study is to quantitatively describe the relationship between various factors and primary wind dispersal distance of winged diaspores.Methods The dispersal distances of five morphologies of winged diaspores in Zygophyllum xanthoxylum (Zygophyllaceae) were measured under controlled conditions in a wind tunnel. The explanatory power of environmental factor (i.e. wind speed), plant trait (i.e. release height) and diaspore attributes (i.e. wing loading (the ratio of diaspore mass to projected area), settlement-velocity, shape index (the variance of diaspore length, width and thickness)) to the variation in dispersal distance was assessed by releasing diaspores at varying wind speeds and release heights.Important findings Wind speed and seed release height were the strongest explanatory factors to dispersal distance, contributing 41.1% and 24.8% (P < 0.01) to total variation in dispersal distance, respectively. Wind speed accounted more for relatively light disc-shaped seeds than for relatively heavy spherical seeds. Wing loading, shape index and settlement-velocity explained 9.0% (P < 0.01), 1.4% (P < 0.01) and 0.9% (not significant) of the variation in dispersal distance, respectively. From disc-shaped to four-winged diaspores, relative contributions of wing loading and shape index decreased but contribution of settlement-velocity increased. The relative contributions of various factors to wind seed dispersal distance may change with the change in seed morphology.     

Seed release by invasive thistles: the impact of plant and environmental factors

Dispersal is a key process in biological studies of spatial dynamics, but the initiation of dispersal has often been neglected, despite strong indications that differential timing of dispersal can significantly affect dispersal distances. To investigate which plant and environmental factors determine the release of plumed seeds by the invasive thistles Carduus acanthoides and Carduus nutans, we exposed 192 flower heads of each species to increasing wind speeds in a full-factorial wind tunnel experiment with four air flow turbulence, three flower head wetness and two flower head temperature levels. The number of seed releases was highest under dry and turbulent conditions and from heads that had already lost a considerable number of seeds, but was not affected by flower head size, head angle or temperature. Inspection of the trials on video showed that higher wind speeds were needed to meet the seed release threshold in laminar flows and for C. acanthoides heads that had been wet for a longer time. Species differences were minimal, although seed release was more sensitive to lower levels of turbulence in the larger-headed and more open C. nutans heads. Knowledge of seed release biases towards weather conditions favourable for long-distance dispersal improves our understanding of the spread of invaders and allows managers to increase the efficiency of their containment strategies by applying them at crucial times.     

Seed dispersal by lizards on a continental‐shelf island: predicting interspecific variation in seed rain based on plant distribution and lizard movement patterns

Aim We estimated the patterns of seed deposition provided by the eyed lizard, Timon lepidus, and evaluated whether these patterns can be generalized across plant species with different traits (fruit and seed size) and spatial distributions. Location Monteagudo Island, Atlantic Islands National Park (north‐western Spain). Methods We radio‐tracked seven lizards for 14 days and estimated their home ranges using fixed kernels. We also geo‐referenced all fruit‐bearing individuals of four plant species dispersed by eyed lizards in the study area (Corema album, Osyris alba, Rubus ulmifolius and Tamus communis), measured the passage time of their seeds through the lizard gut, and estimated seed predation in four habitats (bare sand, grassland, shrub and gorse). Seed dispersal kernels were estimated using a combination of these data and were combined with seed predation probability maps to incorporate post‐dispersal seed fate (‘seed survival kernels’). Results Median seed gut‐passage times were around 52–98 h, with maximum values up to 250 h. Lizards achieved maximum displacement in their home ranges within 24–48 h. Seed predation was high (80–100% of seeds in 2 months), particularly under Corema shrub and gorse. Seed dispersal kernels showed a common pattern, with two areas of preferential seed deposition, but the importance of these varied among plant species. Interspecific differences among dispersal kernels were strongly reduced by post‐dispersal seed predation; hence, seed survival kernels of the different plant species showed high auto‐ and pairwise‐correlations at small distances (< 50 m). As a result, survival to post‐dispersal seed predation increased with dispersal distance for O. alba and T. communis, but not for C. album. Main conclusions Seed dispersal by lizards was determined primarily by the interaction between the dispersers’ home ranges and the position of the fruit‐bearing plants. As a result, seed rain shared a common template, but showed considerable variation among species, determined by their specific spatial context. Seed predation increased the spatial coherence of the seed rain of the different species, but also resulted in contrasting relationships between seed survival and dispersal distance, which may be of importance for the demographic and evolutionary processes of the plants.     

Are Plant Species Able to Keep Pace with the Rapidly Changing Climate?

Future climate change is predicted to advance faster than the postglacial warming. Migration may therefore become a key driver for future development of biodiversity and ecosystem functioning. For 140 European plant species we computed past range shifts since the last glacial maximum and future range shifts for a variety of Intergovernmental Panel on Climate Change (IPCC) scenarios and global circulation models (GCMs). Range shift rates were estimated by means of species distribution modelling (SDM). With process-based seed dispersal models we estimated species-specific migration rates for 27 dispersal modes addressing dispersal by wind (anemochory) for different wind conditions, as well as dispersal by mammals (dispersal on animal''s coat – epizoochory and dispersal by animals after feeding and digestion – endozoochory) considering different animal species. Our process-based modelled migration rates generally exceeded the postglacial range shift rates indicating that the process-based models we used are capable of predicting migration rates that are in accordance with realized past migration. For most of the considered species, the modelled migration rates were considerably lower than the expected future climate change induced range shift rates. This implies that most plant species will not entirely be able to follow future climate-change-induced range shifts due to dispersal limitation. Animals with large day- and home-ranges are highly important for achieving high migration rates for many plant species, whereas anemochory is relevant for only few species.     

Environmental variability and the initiation of dispersal: turbulence strongly increases seed release

Dispersal is a critical process in ecology. It is an important biological driver of, for example, invasions, metapopulation dynamics, spatial pattern formation and pathogen movement. Much is known about the effect of environmental variability, including turbulence, on dispersal of diaspores. Here, we document experimentally the strong but under-explored influence of turbulence on the initiation of dispersal. Flower heads of two thistle species (Carduus nutans and Carduus acanthoides) with ripe seeds were exposed to series of laminar and turbulent air flows of increasing velocity in a wind tunnel. Seed release increased with wind speeds for both laminar and turbulent flows for both species. However, far more seeds were released, at significantly lower wind speeds, during turbulent flows. These results strongly suggest a need for more quantitative studies of abscission in the field, as well as dispersal models that incorporate variability in the diaspore release phase.     

Potential differences in seed dispersals of low‐height vegetation between single element and windbreak‐like clumps

Wind speed is one of the most important factors for seed wind dispersal. A wind speed reduction region, which could be influenced by vegetation arrangement, will form in the lee of vegetation and therefore affects the seed dispersal. Here, by taking shrub as an example, quantitative differences in seed dispersals of low vegetation between single element and windbreak‐like clumps are numerically investigated. The local variation of stream‐wise wind speed is focused. Empirically parameterized functions of leeward wind distributions are employed. It reveals that the accumulative probability of dispersed seeds from a point source with considering leeward wind reduction could be well fitted by a logistic function. For a fixed release height or vegetation porosity, accumulative probabilities for single element and those for windbreak‐like clumps would intersect at a leeward location. This intersection location decreases linearly with release height but exponentially with porosity. The fitting parameter r₀ (the center of logistic function) for single element increases as the same manner for windbreak‐like clumps, with regard to the increase of release height, porosity, and height. But, the increasing rates for single element are higher than those for windbreak‐like clumps. The fitting parameter p (the power index of logistic function) for single element is generally larger than that for windbreak‐like clumps. With the increase of release height, p decreases at first but increases then for single element, while it shows opposite trend for windbreak‐like clumps. p decreases with porosity for both single element and windbreak‐like clumps. But, the decreasing rate for single element is lower than that for windbreak‐like clumps. p increases exponentially with height for windbreak‐like clumps, while it almost keeps constant for single element. These results suggest the potential importance of vegetation arrangement on seed dispersal and therefore possibly provide additional reason for the disagreement among observed dispersal kernels.     

Drivers of plant species’ potential to spread: the importance of demography versus seed dispersal

Understanding the ability of plants to spread is important for assessing conservation strategies, landscape dynamics, invasiveness and ability to cope with climate change. While long‐distance seed dispersal is often viewed as a key process in population spread, the importance of inter‐specific variation in demography is less explored. Indeed, the relative importance of demography vs seed dispersal in determining population spread is still little understood. We modelled species’ potential for population spread in terms of annual migration rates for a set of species inhabiting dry grasslands of central Europe. Simultaneously, we estimated the importance of demographic (population growth rate) versus long‐distance dispersal (99th percentile dispersal distance) characteristics for among‐species differences in modelled population spread. In addition, we assessed how well simple proxy measures related to demography (the number and survival of seedlings, the survival of flowering individuals) and dispersal (plant height, terminal velocity and wind speed during dispersal) predicted modelled spread rates. We found that species’ demographic rates were the more powerful predictors of species’ modelled potential to spread than dispersal. Furthermore, our simple proxies were correlated with modelled species spread rates and together their predictive power was high. Our findings highlight that for understanding variation among species in their potential for population spread, detailed information on local demography and dispersal might not always be necessary. Simple proxies or assumptions that are based primarily on species demography could be sufficient.     

Recruitment trade-offs and the evolution of dispersal mechanisms in plants

In this study we place seed size vs. seed number trade-offs in the context of plant dispersal ability. The objective was to suggest explanations for the evolution of different seed dispersal mechanisms, in particular fleshy fruits, wind dispersal and the maintenance of unassisted dispersal. We suggest that selection for improved dispersal may act either by increasing the intercept of a dispersal curve (log seed number vs. distance) or by flattening the slope of the curve. 'Improved dispersal' is defined as a marginal increase in the number of recruits sited at some (arbitrary) distance away from the parent plant. Increasing the intercept of the dispersal curve, i.e. producing more seeds, is associated with a reduction in seed size, which in turn affects the recruitment ability, provided that this ability is related to seed size. If recruitment is related to seed size there will be a recruitment cost of evolving increased seed production. On the other hand, a flattening of the slope by evolving dispersal attributes is likely to be associated with a fecundity cost. An exception is wind dispersal where smaller (and hence more numerous) seeds may lead to more efficient dispersal. We derive two main predictions: If recruitment is strongly related to seed size, selection for improved dispersal acts on the slope of the dispersal curve, i.e. by favouring evolution of dispersal attributes on seeds or fruits. If, on the other hand, recruitment is only weakly related to seed size (or not related, or negatively related), selection for improved dispersal favours increased seed production. Despite its simplicity, the model suggests explanations for (i) why so many plant species lack special seed dispersal attributes, (ii) differences in dispersal spectra among plant communities, and (iii) adaptive radiation in seed size and dispersal attributes during angiosperm evolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Seed fate and decision‐making processes in scatter‐hoarding rodents

A mechanistic understanding of seed movement and survival is important both for the development of theoretical models of plant population dynamics, spatial spread, and community assembly, and for the conservation and management of plant communities under global change. While models of wind‐borne seed dispersal have advanced rapidly over the past two decades, models for animal‐mediated dispersal have failed to make similar progress due to their dependence on interspecific interactions and complex, context‐dependent behaviours. In this review, we synthesize the literature on seed dispersal and consumption by scatter‐hoarding, granivorous rodents and outline a strategy for development of a general mechanistic seed‐fate model in these systems. Our review decomposes seed dispersal and survival into six distinct sub‐processes (exposure, harvest, allocation, preparation, placement, and recovery), and identifies nine intermediate (latent) variables that link physical state variables (e.g. seed and animal traits, habitat structure) to decisions regarding seed allocation to hoarding or consumption, cache placement and management, and deployment of radicle‐pruning or embryo excision behaviours. We also highlight specific areas where research on these intermediate relationships is needed to improve our mechanistic understanding of scatter‐hoarder behaviour. Finally, we outline a strategy to combine detailed studies on individual functional relationships with seed‐tracking experiments in an iterative, hierarchical Bayesian framework to construct, refine, and test mechanistic models for context‐dependent, scatter‐hoarder‐mediated seed fate.     

Realized gene flow within mixed stands of Quercus robur L. and Q. petraea (Matt.) L. revealed at the stage of naturally established seedling

The estimates of contemporary gene flow assessed based on naturally established seedlings provide information much needed for understanding the abilities of forest tree populations to persist under global changes through migration and/or adaptation facilitated by gene exchange among populations. Here, we investigated pollen‐ and seed‐mediated gene flow in two mixed‐oak forest stands (consisting of Quercus robur L. and Q. petraea [Matt.] Liebl.). The gene flow parameters were estimated based on microsatellite multilocus genotypes of seedlings and adults and their spatial locations within the sample plots using models that attempt to reconstruct the genealogy of the seedling cohorts. Pollen and seed dispersal were modelled using the standard seedling neighbourhood model and a modification—the 2‐component seedling neighbourhood model, with the later allowing separation of the dispersal process into local and long‐distance components. The 2‐component model fitted the data substantially better than the standard model and provided estimates of mean seed and pollen dispersal distances accounting for long‐distance propagule dispersal. The mean distance of effective pollen dispersal was found to be 298 and 463 m, depending on the stand, while the mean distance of effective seed dispersal was only 8.8 and 15.6 m, which is consistent with wind pollination and primarily seed dispersal by gravity in Quercus. Some differences observed between the two stands could be attributed to the differences in the stand structure of the adult populations and the existing understory vegetation. Such a mixture of relatively limited seed dispersal with occasional long distance gene flow seems to be an efficient strategy for colonizing new habitats with subsequent local adaptation, while maintaining genetic diversity within populations.     

Seed dispersal characteristics of Brassavola nodosa (Orchidaceae)

We used mathematical models for wind-dispersed seeds and wind-tunnel experiments to predict modal seed dispersal distance of the Neotropical orchid Brassavola nodosa under conditions approximating those found in its natural habitat: mangrove islands in Belize, Central America. Key variables in a simple ballistic model for predicting modal dispersal distance (xm) of an individual seed include: height of release (h); free-stream velocity (Uc); and terminal velocity of the seed (Ut): xm = h Uc/Ut. Modal dispersal distance of dust-like orchid seeds were predicted adequately by this ballistic model at low wind velocities and low release heights, but it underestimated the increasing importance of turbulence at higher wind velocities and greater release heights. We estimated the magnitude and relative importance of one measure of turbulence, vertical mixing velocity (W*), on xm in wind tunnel experiments. Our estimates of W* were within the same order of magnitude as those found for other small dust-like seeds and pollen. In high turbulence conditions, incorporation of vertical mixing velocity effects into the ballistic model of seed dispersal overestimated modal seed dispersal distances.     

Wind dispersal in freshwater wetlands: Knowledge for conservation and restoration

Questions: For wetland plants, dispersal by wind is often overlooked because dispersal by water is generally assumed to be the key dispersal process. This literature review addresses the role of seed dispersal by wind in wetlands. Why is wind dispersal relevant in wetlands? Which seeds are dispersed by wind and how far? And how can our understanding of wind dispersal be applied to wetland conservation and restoration? Methods: Literature review. Results and conclusions: Wind is a widely available seed dispersal vector in wetlands and can transport many seeds over long distances. Unlike water, wind can transport seeds in all directions and is therefore important for dispersal to upstream wetlands and to wetlands not connected by surface water flows. Wind dispersal transports seeds to a wider range of sites than water, and therefore reaches more sites but with lower seed densities. Many wetland plant species have adaptations to facilitate wind dispersal. Dispersal distances increase with decreasing falling velocity of seeds, increasing seed release height and selective release mechanisms. Depending on the adaptations, seeds may be dispersed by wind over many km or only a few m. The frequency of long‐distance wind dispersal events depends on these adaptations, the number of produced seeds, the structure of the surrounding vegetation, and the frequency of occurrence of suitable weather conditions. Humans reduce the frequency of successful long‐distance wind dispersal events in wetlands through wetland loss and fragmentation (which reduce the number and quality of seeds) and eutrophication (which changes the structure of the vegetation so that seed release into the wind flow becomes more difficult). This is yet another reason to focus on wetland conservation and restoration measures at increased population sizes, prevention of eutrophication, and the restoration of sites at short distances from seed sources.     

Mechanistic analytical models for long-distance seed dispersal by wind

We introduce an analytical model, the Wald analytical long-distance dispersal (WALD) model, for estimating dispersal kernels of wind-dispersed seeds and their escape probability from the canopy. The model is based on simplifications to well-established three-dimensional Lagrangian stochastic approaches for turbulent scalar transport resulting in a two-parameter Wald (or inverse Gaussian) distribution. Unlike commonly used phenomenological models, WALD's parameters can be estimated from the key factors affecting wind dispersal--wind statistics, seed release height, and seed terminal velocity--determined independently of dispersal data. WALD's asymptotic power-law tail has an exponent of -3/2, a limiting value verified by a meta-analysis for a wide variety of measured dispersal kernels and larger than the exponent of the bivariate Student t-test (2Dt). We tested WALD using three dispersal data sets on forest trees, heathland shrubs, and grassland forbs and compared WALD's performance with that of other analytical mechanistic models (revised versions of the tilted Gaussian Plume model and the advection-diffusion equation), revealing fairest agreement between WALD predictions and measurements. Analytical mechanistic models, such as WALD, combine the advantages of simplicity and mechanistic understanding and are valuable tools for modeling large-scale, long-term plant population dynamics.     

Long-distance seed dispersal in plant populations

Long-distance seed dispersal influences many key aspects of the biology of plants, including spread of invasive species, metapopulation dynamics, and diversity and dynamics in plant communities. However, because long-distance seed dispersal is inherently hard to measure, there are few data sets that characterize the tails of seed dispersal curves. This paper is structured around two lines of argument. First, we argue that long-distance seed dispersal is of critical importance and, hence, that we must collect better data from the tails of seed dispersal curves. To make the case for the importance of long-distance seed dispersal, we review existing data and models of long-distance seed dispersal, focusing on situations in which seeds that travel long distances have a critical impact (colonization of islands, Holocene migrations, response to global change, metapopulation biology). Second, we argue that genetic methods provide a broadly applicable way to monitor long-distance seed dispersal; to place this argument in context, we review genetic estimates of plant migration rates. At present, several promising genetic approaches for estimating long-distance seed dispersal are under active development, including assignment methods, likelihood methods, genealogical methods, and genealogical/demographic methods. We close the paper by discussing important but as yet largely unexplored areas for future research.     

Modelling the establishment and spread of autotetraploid plants in a spatially heterogeneous environment

The establishment and spread of autotetraploids from an original diploid population in a heterogeneous environment were studied using a stochastic simulation model. Specifically, we investigated the effects of heterogeneous habitats and nonrandom pollen/seed dispersal on the critical value (micro) of unreduced 2n gamete production necessary for the establishment of autotetraploids as predicted by deterministic models. Introduction of a heterogeneous environment with random pollen/seed dispersal had little effect on the micro value. In contrast, incorporating nonrandom pollen/seed dispersal into a homogeneous environment considerably reduced the micro value. Incorporating both heterogeneous habitats and nonrandom pollen/seed dispersal may lead either to an increase or to a decrease in the micro value compared to that with random dispersal, indicating that the two factors interact in a complex way.