Neighborhood models of plant population dynamics 3. Models with spatial heterogeneity in the physical environment

Population dynamic models are developed for communities of annual plants in spatially heterogeneous environments. These models are constructed from submodels of the survivorship, fecundity, germination, and dispersal of individual plants. The submodels include the effects of spatially local interactions on plant performance and the spatial variation in performance caused by spatial heterogeneity in the physical environment. It is possible to estimate the submodels from data on experimental communities in either the field or greenhouse and so it is possible to empirically calibrate the population dynamic models developed. Each population dynamic model explicitly includes the spatial distribution of individuals in a plant community.Several two-species models for plants in patchy environments are studied to examine the community-level consequences of spatial heterogeneity in the physical environment. The results fall into two classes. First, community structure is in part determined by a relation between patch size and mean seed dispersal distance. Specifically, coexistence is, in some cases, possible only if patches are sufficiently larger than the mean dispersal distance. Second, community structure is also affected by relations between patch size and the maximum distance over which two plants interact (termed the neighborhood radius). In some cases, coexistence is possible only if patch size is sufficiently larger than the neighborhood radius. In others, the species coexist only if patch size is sufficiently smaller than the neighborhood radius. In still other cases, coexistence is possible only if patch sizes are within critical bounds, where the sizes of the critical bounds are in units of the neighborhood radius. All results involving relations between the neighborhood radius and patch size are direct consequences of the sedentary nature of plants and the fact that individual plants interact primarily with nearby plants.     

Plant-disperser mutualisms in a semi-arid habitat invaded by <Emphasis Type="Italic">Lantana camara</Emphasis> L.

Dispersal is an important ecological process that affects plant population structure and community composition. Invasive plants with fleshy fruits rapidly form associations with native and invasive dispersers, and may affect existing native plant-disperser associations. We asked whether frugivore visitation rate and fruit removal was associated with plant characteristics in a community of fleshy-fruited plants and whether an invasive plant receives more visitation and greater fruit removal than native plants in a semi-arid habitat of Andhra Pradesh, India. Tree-watches were undertaken at individuals of nine native and one invasive shrub species to assess the identity, number and fruit removal by avian frugivores. Network analyses and generalised linear mixed-effects models were used to understand species and community-level patterns. All plants received most number of visits from abundant, generalist avian frugivores. Number of frugivore visits and time spent by frugivores at individual plants was positively associated with fruit crop size, while fruit removal was positively associated with number of frugivore visits and their mean foraging time at individual plants. The invasive shrub, Lantana camara L. (Lantana), had lower average frugivore visit rate than the community of fleshy-fruited plants and received similar average frugivore visits but greater average per-hour fruit removal than two other concurrently fruiting native species. Based on the results of our study, we infer that there is little evidence of competition between native plants and Lantana for the dispersal services of native frugivores and that more data are required to assess the nature of these interactions over the long term. We speculate that plant associations with generalist frugivores may increase the functional redundancy of this frugivory network, buffering it against loss of participating species.     

Spatially explicit neutral models for population genetics and community ecology: Extensions of the Neyman-Scott clustering process

Spatially explicit models relating to plant populations have developed little since Felsenstein (1975) pointed out that if limited seed dispersal causes clustering of individuals, such models cannot reach an equilibrium. This paper aims to resolve this issue by modifying the Neyman-Scott cluster point process. The new point processes are dynamic models with random immigration, and the continuous increase in the clustering of individuals stops at some level. Hence, an equilibrium state is achieved, and new individual-based spatially explicit neutral coalescent models are established. By fitting the spatial structure at equilibrium to individual spatial distribution data, we can indirectly estimate seed dispersal and effective population density. These estimates are improved when genetic data are available, and become even more sophisticated if spatial distribution and genetic data pertaining to the offspring are also available.     

Biotic interactions boost spatial models of species richness

Biotic interactions are known to affect the composition of species assemblages via several mechanisms, such as competition and facilitation. However, most spatial models of species richness do not explicitly consider inter‐specific interactions. Here, we test whether incorporating biotic interactions into high‐resolution models alters predictions of species richness as hypothesised. We included key biotic variables (cover of three dominant arctic‐alpine plant species) into two methodologically divergent species richness modelling frameworks – stacked species distribution models (SSDM) and macroecological models (MEM) – for three ecologically and evolutionary distinct taxonomic groups (vascular plants, bryophytes and lichens). Predictions from models including biotic interactions were compared to the predictions of models based on climatic and abiotic data only. Including plant–plant interactions consistently and significantly lowered bias in species richness predictions and increased predictive power for independent evaluation data when compared to the conventional climatic and abiotic data based models. Improvements in predictions were constant irrespective of the modelling framework or taxonomic group used. The global biodiversity crisis necessitates accurate predictions of how changes in biotic and abiotic conditions will potentially affect species richness patterns. Here, we demonstrate that models of the spatial distribution of species richness can be improved by incorporating biotic interactions, and thus that these key predictor factors must be accounted for in biodiversity forecasts.     

Properties of some density-dependent integrodifference equation population models.

Integrodifference equations may be used as models of populations with discrete generations inhabiting continuous habitats. In this paper integrodifference equation models are formulated for annual plant populations without a seed bank; these models differ in the stage of the life cycle at which intraspecific competition acts to reduce vital rates. The models exhibit a sequence of period-doubling bifurcations leading to chaotic spatial and temporal behavior. The behavior of the models when modal dispersal distances are at the origin is compared with their behavior when these distances are displaced away from the origin. The models are capable of predicting stable, cyclical, and chaotic asymptotic behavior. They also predict that the variance of dispersal distances is an important indicator of the colonizing ability of a species.     

Habitat distribution models,spatial autocorrelation,functional traits and dispersal capacity of alpine plant species

Abstract. We evaluate the potential influence of disturbance on the predictability of alpine plant species distribution from equilibrium‐based habitat distribution models. Firstly, abundance data of 71 plant species were correlated with a comprehensive set of environmental variables using ordinal regression models. Subsequently, the residual spatial autocorrelation (at distances of 40 to 320 m) in these models was explored. The additional amount of variance explained by spatial structuring was compared with a set of functional traits assumed to confer advantages in disturbed or undisturbed habitats. We found significant residual spatial autocorrelation in the habitat models of most of the species that were analysed. The amount of this autocorrelation was positively correlated with the dispersal capacity of the species, levelling off with increasing spatial scale. Both trends indicate that dispersal and colonization processes, whose frequency is enhanced by disturbance, influence the distribution of many alpine plant species. Since habitat distribution models commonly ignore such spatial processes they miss an important driver of local‐ to landscape‐scale plant distribution.     

Comparing classical community models: theoretical consequences for patterns of diversity

Abstract: Mechanisms proposed to explain the maintenance of species diversity within ecological communities of sessile organisms include niche differentiation mediated by competitive trade-offs, frequency dependence resulting from species-specific pests, recruitment limitation due to local dispersal, and a speciation-extinction dynamic equilibrium mediated by stochasticity (drift). While each of these processes, and more, have been shown to act in particular communities, much remains to be learned about their relative importance in shaping community-level patterns. We used a spatially-explicit, individual-based model to assess the effects of each of these processes on species richness, relative abundance, and spatial patterns such as the species-area curve. Our model communities had an order-of-magnitude more individuals than any previous such study, and we also developed a finite-size scaling analysis to infer the large-scale properties of these systems in order to establish the generality of our conclusions across system sizes. As expected, each mechanism can promote diversity. We found some qualitative differences in community patterns across communities in which different combinations of these mechanisms operate. Species-area curves follow a power law with short-range dispersal and a logarithmic law with global dispersal. Relative-abundance distributions are more even for systems with competitive differences and trade-offs than for those in which all species are competitively equivalent, and they are most even when frequency dependence (even if weak) is present. Overall, however, communities in which different processes operated showed surprisingly similar patterns, which suggests that the form of community-level patterns cannot in general be used to distinguish among mechanisms maintaining diversity there. Nevertheless, parameterization of models such as these from field data on the strengths of the different mechanisms could yield insight into their relative roles in diversity maintenance in any given community.     

What causes conspecific plant aggregation? Disentangling the role of dispersal,habitat heterogeneity and plant–plant interactions

Spatial patterns of plant species are determined by an array of ecologica factors including biotic and abiotic environmental constraints and intrinsic species traits. Thus, an observed aggregated pattern may be the result of short‐distance dispersal, the presence of habitat heterogeneity, plant–plant interactions or a combination of the above. Here, we studied the spatial pattern of Mediterranean alpine plant Silene ciliata (Caryophyllaceae) in five populations and assessed the contribution of dispersal, habitat heterogeneity and conspecific plant interactions to observed patterns. For this purpose, we used spatial point pattern analysis combined with specific a priori hypotheses linked to spatial pattern creation. The spatial pattern of S. ciliata recruits was not homogeneous and showed small‐scale aggregation. This is consistent with the species’ short‐distance seed dispersal and the heterogeneous distribution of suitable sites for germination and establishment. Furthermore, the spatial pattern of recruits was independent of the spatial pattern of adults. This suggests a low relevance of adult‐recruits interactions in the spatial pattern creation. The difference in aggregation between recruits and adults suggests that once established, recruits are subjected to self‐thinning. However, seedling mortality did not erase the spatial pattern generated by seed dispersal, as S. ciliata adults were still aggregated. Thus, the spatial aggregation of adults is probably due to seed dispersal limitation and the heterogeneous distribution of suitable sites at seedling establishment rather than the presence of positive plant–plant interactions at the adult stage. In fact, a negative density‐dependent effect of the conspecific neighbourhood was found on adult reproductive performance. Overall, results provide empirical evidence of the lack of a simple and direct relationship between the spatial structure of plant populations and the sign of plant–plant interactions and outline the importance of considering dispersal and habitat heterogeneity when performing spatial analysis assessments.     

On detecting and measuring competition in spatially structured plant communities

Recent models have shown that the development of spatial structure in plant mixtures may make strong competitive interactions between species hard to detect owing to spatial segregation of the competing species. Here we address the issue of measuring interspecific competition using a simulation based on a neighbourhood population model which assumes that both dispersal and competitive interactions are localized. Using known parameter combinations we use the model to test the power and efficiency of two approaches for detecting and measuring competition. The first approach is based on measuring the response of communities to the removal of neighbours. Measures of interspecific competition based on this approach are extremely biased by spatial segregation of species, although this bias may be partially overcome by altering the spatial scale at which the effects of removals are recorded. The second approach is based on multiple regression of per capita population growth rates on local densities of the interacting species. When dispersal is restricted, the regression approach provides accurate estimates of interspecific competition coefficients when the scale of the sampling unit (i.e. the quadrats within which plants are counted) is large compared to the scale at which interactions and dispersal occur. When seeds disperse globally the removal method performs best; the regression method fails because sampling units do not form closed dynamic systems. Our results highlight the importance of tailoring methods for detecting competition to the characteristics of the species in question. They also indicate that rapid nonmanipulative estimates of competition coefficients may be the best approach in communities where dispersal is restricted and competitive interactions localized, which is likely to be the case for the majority of plants.     

Nonrandom spatial structuring of orchids in a hybrid zone of three Orchis species

? Nonrandom species-species associations may arise from a range of factors, including localized dispersal, intra- and interspecific interactions and heterogeneous environmental conditions. Because seed germination and establishment in orchids are critically dependent upon the availability of suitable mycorrhizal fungi, species-species associations in orchids may reflect associations with mycorrhizal fungi. ? To test this hypothesis, we examined spatial association patterns, mycorrhizal associations and germination success in a hybrid zone containing three species of the genus Orchis (Orchis anthropophora, Orchis militaris and Orchis purpurea). ? Hybridization occurred predominantly between O. purpurea and O. militaris. The spatial distribution patterns of most pure species and hybrids were independent from each other, except that of O. purpurea and its hybrids. The fungal community composition of established individuals differed significantly between pure species, but not between hybrids and O. purpurea. Seed germination experiments using pure seeds showed that the highest number of protocorms were found in regions where adult individuals were most abundant. In the case of hybrid seeds, germination was restricted to areas where the mother plant was most abundant. ? Overall, these results suggest that the observed nonrandom spatial distribution of both pure and hybrid plants is dependent on the contingencies of the spatial distribution of suitable mycorrhizal fungi.     

Effects of zoochory on the spatial genetic structure of plant populations

Spatial genetic structure (SGS) of plants results from the nonrandom distribution of related individuals. SGS provides information on gene flow and spatial patterns of genetic diversity within populations. Seed dispersal creates the spatial template for plant distribution. Thus, in zoochorous plants, dispersal mode and disperser behaviour might have a strong impact on SGS. However, many studies only report the taxonomic group of seed dispersers, without further details. The recent increase in studies on SGS provides the opportunity to review findings and test for the influence of dispersal mode, taxonomic affiliation of dispersers and their behaviour. We compared the proportions of studies with SGS among groups and tested for differences in strength of SGS using Sp statistics. The presence of SGS differed among taxonomic groups, with reduced presence in plants dispersed by birds. Strength of SGS was instead significantly influenced by the behaviour of seed dispersal vectors, with higher SGS in plant species dispersed by animals with behavioural traits that result in short seed dispersal distances. We observed high variance in the strength of SGS in plants dispersed by animals that actively or passively accumulate seeds. Additionally, we found SGS was also affected by pollination and marker type used. Our study highlights the importance of vector behaviour on SGS even in the presence of variance created by other factors. Thus, more detailed information on the behaviour of seed dispersers would contribute to better understand which factors shape the spatial scale of gene flow in animal‐dispersed plant species.     

Point process models,the dimensions of biodiversity and the importance of small-scale biotic interactions

Aims Recent mechanistic explanations for community assembly focus on the debates surrounding niche-based deterministic and dispersal-based stochastic models. This body of work has emphasized the importance of both habitat filtering and dispersal limitation, and many of these works have utilized the assumption of species spatial independence to simplify the complexity of the spatial modeling in natural communities when given dispersal limitation and/or habitat filtering. One potential drawback of this simplification is that it does not consider species interactions and how they may influence the spatial distribution of species, phylogenetic and functional diversity. Here, we assess the validity of the assumption of species spatial independence using data from a subtropical forest plot in southeastern China.Methods We use the four most commonly employed spatial statistical models—the homogeneous Poisson process representing pure random effect, the heterogeneous Poisson process for the effect of habitat heterogeneity, the homogenous Thomas process for sole dispersal limitation and the heterogeneous Thomas process for joint effect of habitat heterogeneity and dispersal limitation—to investigate the contribution of different mechanisms in shaping the species, phylogenetic and functional structures of communities.Important findings Our evidence from species, phylogenetic and functional diversity demonstrates that the habitat filtering and/or dispersal-based models perform well and the assumption of species spatial independence is relatively valid at larger scales (50×50 m). Conversely, at local scales (10×10 and 20×20 m), the models often fail to predict the species, phylogenetic and functional diversity, suggesting that the assumption of species spatial independence is invalid and that biotic interactions are increasingly important at these spatial scales.     

A field test of simple dispersal models as predictors of movement in a cohort of lake-dwelling brook charr

1. Dispersal can be a major determinant of the distribution and abundance of animals, as well as a key mechanism linking behaviour to population dynamics, but progress in understanding dispersal has been hampered by the lack of a general framework for modelling dispersal. 2. This study tested the capacity of simple models to summarize and predict the lake-wide dispersal of an emerging cohort of young-of-the-year brook charr Salvelinus fontinalis, over 12 surveys conducted during a 2-month period. 3. The models are based on two types of dispersal kernel, the normal distribution from a simple diffusion process, and a Laplace distribution depicting exponential decay of the frequency of dispersers away from the point of origin. In all, four models were assessed: one-group diffusion (D1S) and exponential (E1S) models assuming homogeneous dispersal behaviour within the cohort, and two-group diffusion (D2S) and exponential (E2S) models accounting for intrapopulation differences in dispersal between sedentary and mobile individuals. 4. A rigorous cross-validation, based on calibrating the models to the distributions from the first two surveys only and then validating them on the remaining 10 distributions, was used to compare model predictions with observed values for five properties of the dispersal distributions: counts in individual shoreline sections; mean lateral displacement, variance and kurtosis of displacements; and the percentage of long-distance dispersers. 5. Substantial intrapopulation heterogeneity in dispersal behaviour was apparent: 83% of all individuals were estimated to be sedentary and the remainder mobile. Remarkably, the two-group exponential model E2S - calibrated to data from only two surveys conducted 3.5 and 8.5 days after the beginning of emergence - predicted reasonably well all properties of the spatial distribution of the cohort until the end of the study, 7 weeks later. 6. Standardized measures of mobility derived from simple models may lead to better understanding of population dynamics and improved management. Specifically, the ability to accurately predict long-distance dispersal may be critical to assessing population persistence and cohort strength whenever key habitats, such as refugia or productive areas supporting a large proportion of the cohort, are sparsely distributed or distant from the point of origin.     

Pollen dispersal in spatially aggregated populations

We perform a theoretical study of effective pollen dispersal within plant populations exhibiting intraspecific spatial aggregation. We simulate nonuniform distributions of individuals by means of a Poisson cluster process and use an individual-based spatially explicit model of pollen dispersal to assess the effects of different aggregation patterns on the effective pollen pool size (N(ep)) and the axial variance of pollen dispersal (sigma (p)). Results show clear interactions between clumping and both N(ep) and sigma (p), whose precise form and intensity depend on the relative spatial scale of aggregation to pollen dispersal range. If clump size is small relative to dispersal range, clumping results in lower N(ep) and sigma (p) than in randomly distributed populations. Interestingly, by contrast, aggregation may actually enlarge N(ep) and has minimum impact on sigma (p) if clump size is near or above the scale of dispersal. High intraclump to global density ratios enhance the sensitivity of both N(ep) and sigma (p) to clumping, while leptokurtic pollen dispersal generates sharper reductions of both N(ep) and sigma (p) for small clump sizes and stronger increments of N(ep) for larger clump sizes. Overall, our results indicate that isolation-by-distance models in plants should not ignore the effects of intraspecific spatial aggregation on effective dispersal.     

Rethinking plant community theory

Plant communities have traditionally been viewed as either a random collection of individuals or as organismal entities. For most ecologists however, neither perspective provides a modern comprehensive view of plant communities, but we have yet to formalize the view that we currently hold. Here, we assert that an explicit re-consideration of formal community theory must incorporate interactions that have recently been prominent in plant ecology, namely facilitation and indirect effects among competitors. These interactions do not suppport the traditional individualistic perspective. We believe that rejecting strict individualistic theory will allow ecologists to better explain variation occurring at different spatial scales, synthesize more general predictive theories of community dynamics, and develop models for community-level responses to global change. Here, we introduce the concept of the integrated community (IC) which proposes that natural plant communities range from highly individualistic to highly interdependent depending on synergism among: (i) stochastic processes, (ii) the abiotic tolerances of species, (iii) positive and negative interactions among plants, and (iv) indirect interactions within and between trophic levels. All of these processes are well accepted by plant ecologists, but no single theory has sought to integrate these different processes into our concept of communities.     

Long distance seed dispersal by wind: measuring and modelling the tail of the curve

The size and shape of the tail of the seed dispersal curve is important in determining the spatial dynamics of plants, but is difficult to quantify. We devised an experimental protocol to measure long-distance dispersal which involved measuring dispersal by wind from isolated individuals at a range of distances from the source, but maintaining a large and constant sampling intensity at each distance. Seeds were trapped up to 80 m from the plants, the furthest a dispersal curve for an individual plant has been measured for a non-tree species. Standard empirical negative exponential and inverse power models were fitted using likelihood methods. The latter always had a better fit than the former, but in most cases neither described the data well, and strongly under-estimated the tail of the dispersal curve. An alternative model formulation with two kernel components had a much better fit in most cases and described the tail data more accurately. Mechanistic models provide an alternative to direct measurement of dispersal. However, while a previous mechanistic model accurately predicted the modal dispersal distance, it always under-predicted the measured tail. Long-distance dispersal may be caused by rare extremes in horizontal wind speed or turbulence. Therefore, under-estimation of the tail by standard empirical models and mechanistic models may indicate a lack of flexibility to take account of such extremes. Future studies should examine carefully whether the widely used exponential and power models are, in fact, valid, and investigate alternative models. Received: 7 March 1999 / Accepted: 2 April 2000     

Spatial models of pollen dispersal in the forage grass meadow fescue

Several bivariate probability distributions, generated by different underlying dispersal mechanisms, are fitted to the observed frequencies of an isozyme marker gene using a maximum likelihood approach. The pollen dispersal data were generated using two experimental populations of meadow fescue (Festuca pratensis Huds.), homozygous for different allozymes at the (Pgi-2) locus, arranged in a circular donor–acceptor field design. The contribution of a plant depends on plant position, fecundity and flowering time, factors which are taken into account when fitting the different models. Several approximate likelihood-ratio tests are done between alternative nested models, and a wind threshold model with bimodality in the wind direction is selected. The evolutionarily important variances and expectations of gene displacement under the selected model are calculated. It is also shown that the underlying probability distribution is significantly more than exponentially leptokurtic. By fitting a distribution of deposition in all three dimensions to the data, taking into account differences in plant height, separate estimates of additional physical parameters are obtained, showing that gravity and vertical random movements are more important than intervening vegetation in limiting pollen dispersal in meadow fescue. According to the model, plants with a high seed yield contribute pollen over-proportionally to neighbouring plants. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于不同零模型的点格局分析

在种群空间格局研究中,定量分析格局及其形成过程已成为生态学家的主要目标。在量化分析的众多方法中,点格局分析是最常用的方法,而在选择零模型时,完全空间随机模型以外的复杂零模型很少使用,实际上,这些零模型可能有助于认识格局的内在特征。为此,我们在研究实例中,选择完全空间随机模型(complete spatial randomness)、泊松聚块模型(Poisson cluster process)和嵌套双聚块模型(nested double-cluster process)对典型草原处于不同恢复演替阶段的羊草(Leymus chinensis)种群空间格局进行了分析。结果发现:完全空间随机模型仅能检测种群在不同尺度下的格局类型;而通过泊松聚块模型和嵌套双聚块模型检验表明,在恢复演替的初期阶段,羊草种群在小尺度范围内偏离泊松聚块模型,而在整个取样范围内完全符合嵌套双聚块模型;随着恢复演替时间的推移,在恢复演替的后期,在整个取样尺度上,羊草种群与泊松聚块模型相吻合。这是很有意义的生态学现象。这一实例表明在应用点格局分析种群空间格局时,仅通过完全空间随机模型的检验来分析格局特征,或许很难论证复杂的生态过程,而选择一些完全空间随机模型以外的较复杂的零模型,可能发现一些有价值的生态学现象,对揭示格局掩盖下的内在机制有所裨益。     

Patch configuration affects alpine plant distribution

The relative importance of niche requirements and dispersal limitation in controlling the landscape‐scale distribution of plants is still contentious. Local occurrence and abundance of alpine plants are commonly thought to be driven by abiotic site conditions due to pronounced environmental gradients over short distances. However, explicit tests of the additional role of dispersal‐related processes for alpine plant distribution patterns are lacking. Here, we combine niche‐based species distribution models with variables describing patch size and connectivity to evaluate if, besides abiotic limitations, spatial habitat configuration affects the occurrence and abundance of six plant species inhabiting patchy snowbed mosaics of the northeastern Calcareous Alps in Austria. Moreover, we assess if eventual effects of spatial patch configuration are more clearly detectable when calculating connectivity based on parameterized mechanistic dispersal kernels for both wind and animal vectors instead of using nearest neighbour metrics. We show that patch size and connectivity are significantly correlated to the occurrence of all and to the abundance of four out of six study species, although the relative importance of these variables, as compared to niche constraints, varies among species. In addition, connectivity measures derived from parameterized dispersal kernels were more closely related to occupancy, and in particular to abundance patterns than a simple nearest neighbour metric. The fitted kernels also suggest that dispersal by alpine chamois plays an important role for inter‐patch seed exchange. We conclude that, despite evident abiotic limitations, recurrent local extinctions and delayed re‐colonizations indeed play a role for the distribution of our study species, and that alpine plants may hence be less in equilibrium with their abiotic environment than commonly thought. Moreover, the relatively high long‐distance dispersal probabilities of animal kernels indicate that the ability of alpine plants to adapt their ranges to a rapidly warming climate may, among other factors, depend on the availability of dispersal services by large mammals.