Estimating seed and pollen movement in a monoecious plant: a hierarchical Bayesian approach integrating genetic and ecological data

The scale of seed and pollen movement in plants has a critical influence on population dynamics and interspecific interactions, as well as on their capacity to respond to environmental change through migration or local adaptation. However, dispersal can be challenging to quantify. Here, we present a Bayesian model that integrates genetic and ecological data to simultaneously estimate effective seed and pollen dispersal parameters and the parentage of sampled seedlings. This model is the first developed for monoecious plants that accounts for genotyping error and treats dispersal from within and beyond a plot in a fully consistent manner. The flexible Bayesian framework allows the incorporation of a variety of ecological variables, including individual variation in seed production, as well as multiple sources of uncertainty. We illustrate the method using data from a mixed population of red oak (Quercus rubra, Q. velutina, Q. falcata) in the NC piedmont. For simulated test data sets, the model successfully recovered the simulated dispersal parameters and pedigrees. Pollen dispersal in the example population was extensive, with an average father-mother distance of 178 m. Estimated seed dispersal distances at the piedmont site were substantially longer than previous estimates based on seed-trap data (average 128 m vs. 9.3 m), suggesting that, under some circumstances, oaks may be less dispersal-limited than is commonly thought, with a greater potential for range shifts in response to climate change.     

A Bayesian hierarchical trend analysis finds strong evidence for large-scale temporal declines in stream ecological condition around Melbourne, Australia

Knowledge of temporal change in ecological condition is important for the understanding and management of ecosystems. However, analyses of trends in biological condition have been rare, as there are usually too few data points at any single site to use many trend analysis techniques. We used a Bayesian hierarchical model to analyse temporal trends in stream ecological condition (as measured by the invertebrate-based index SIGNAL) across Melbourne, Australia. The Bayesian hierarchical approach assumes dependency amongst the sampling sites. Results for each site "borrow strength" from the other data because model parameter values are assumed to be drawn from a larger common distribution. This leads to robust inference despite the few data that exist at each site. Utilising the flexibility of the Bayesian approach, we also modelled change over time as a function of catchment urbanisation, allowed for potential temporal and spatial autocorrelation of the data and trend estimates, and used prior information to improve the estimate of data uncertainty. We found strong evidence of a widespread decline in SIGNAL scores for edge habitats (areas of little or no flow). The rate of decline was positively associated with catchment urbanisation. There was no evidence of such declines for riffle habitats (areas with rapid and turbulent flow). Melbourne has experienced a decline in rainfall, indicative of either drought and/or longer-term climate change. The results are consistent with the expected coupled effects of these rainfall changes and increasing urbanisation, but more research is needed to isolate a causal mechanism. More immediately, however, the Bayesian hierarchical approach has allowed us to identify a pattern in a biological monitoring data set that might otherwise have gone un-noticed, and to demonstrate a large-scale temporal decline in biological condition.     

Habitat overlap of enemies: temporal patterns and the role of spatial complexity

Environmental heterogeneity can promote coexistence of conflicting species by providing spatial or temporal refuges from strong interactions (e.g., intraguild predation, competition). However, in many systems, refuge availability and effectiveness may change through time and space because of variability in habitat use by either species. Here I consider how the intensity of intraguild predation risk varies from day to night for aquatic insects that use both vegetated and open water habitats. Large (1,265 l) and small (42 l) mesocosms were used to test the hypothesis that Buenoa would choose an open-water habitat that minimized predation by the ambush predator Notonecta during the day, but that at night Buenoa would safely use both vegetated and open water. Regardless of container size, Notonecta remained in vegetated water during the day and exploited both habitats at night, despite exhibiting greatest instantaneous predation rates in open water during the day. In contrast, Buenoa maintained an even distribution throughout the mesocosms during day and night, even though habitat-specific predation risks were fivefold lower in open waters than in vegetation during the day and habitat-specific predation risk would have been reduced threefold by fully exploiting open waters. Thus, temporal heterogeneity was both beneficial and detrimental to Buenoa; darkness of night reduced predation, but spatial refuges also disappeared. Together, these patterns suggest that while environmental heterogeneity can dampen intense biotic interactions, enemies do not select habitats solely on the basis of conflict avoidance. Instead, it appears that habitat-specific variation in other biotic (e.g., visual predators) or physical factors (e.g., UV radiation) may also mediate species interactions by influencing habitat selection.     

In response to the continuum model for fauna research: a hierarchical, patch-based model of spatial landscape patterns

Models of nature are implicitly influenced by the scale of observation of the processes on which they are founded. The continuum model and the hierarchical patch-based model are two alternate approaches for the spatial modelling of fauna distribution. The continuum model aggregates continuous approximations to individual landscape characteristics, whereas the hierarchical patch-based model constructs a hierarchy in which classifications of landscape characteristics describe an interconnected series of patches. We propose the hierarchical patch-based theory for models of population distributions and landscapes in which the spatial patterns can be effectively represented by mosaics at the variety of levels within the set of individual process models. Given that observations are typically made as points or pixels, and that discrete boundaries exist in both natural and human-modified landscapes, we suggest that the hierarchical patch-based method has many applications in conservation and management.     

Hierarchical spatial organization and prioritization of wetlands: a conceptual model for wetland rehabilitation in South Africa

Wetland rehabilitation planning needs to take into account many different aspects of the wetland and its context. In South Africa, much emphasis is placed on the delivery of ecosystem services, poverty relief and skills development for those involved in labour-intensive rehabilitation measures. A framework is presented that facilitates decision-making with regards to wetland rehabilitation planning. This starts with prioritizing which wetlands need attention within a catchment. This is followed by decisions regarding which rehabilitation measures would be effective in improving certain ecosystem services based upon the aims of rehabilitation and the social context of the surrounding catchment. The functional unit that is most suitable to work with for rehabilitation is the Hydrogeomorphic (HGM) Unit, defined as a section of a wetland with more or less uniform hydrological and geomorphological characteristics. An individual wetland may comprise several HGM units, and a HGM Unit itself can be sub-divided into several smaller habitat or vegetation units. Different rehabilitation measures have been identified which are appropriate for the different scales in this spatial framework. Two case studies are presented as examples of how this spatial framework impacts upon the decisions made by the rehabilitation practitioner.     

A full Bayesian hierarchical mixture model for the variance of gene differential expression

Background  

In many laboratory-based high throughput microarray experiments, there are very few replicates of gene expression levels. Thus, estimates of gene variances are inaccurate. Visual inspection of graphical summaries of these data usually reveals that heteroscedasticity is present, and the standard approach to address this is to take a log₂ transformation. In such circumstances, it is then common to assume that gene variability is constant when an analysis of these data is undertaken. However, this is perhaps too stringent an assumption. More careful inspection reveals that the simple log₂ transformation does not remove the problem of heteroscedasticity. An alternative strategy is to assume independent gene-specific variances; although again this is problematic as variance estimates based on few replications are highly unstable. More meaningful and reliable comparisons of gene expression might be achieved, for different conditions or different tissue samples, where the test statistics are based on accurate estimates of gene variability; a crucial step in the identification of differentially expressed genes.     

Genetic evidence for long-term population decline in a savannah-dwelling primate: inferences from a hierarchical bayesian model

The purpose of this study was to test for evidence that savannah baboons (Papio cynocephalus) underwent a population expansion in concert with a hypothesized expansion of African human and chimpanzee populations during the late Pleistocene. The rationale is that any type of environmental event sufficient to cause simultaneous population expansions in African humans and chimpanzees would also be expected to affect other codistributed mammals. To test for genetic evidence of population expansion or contraction, we performed a coalescent analysis of multilocus microsatellite data using a hierarchical Bayesian model. Markov chain Monte Carlo (MCMC) simulations were used to estimate the posterior probability density of demographic and genealogical parameters. The model was designed to allow interlocus variation in mutational and demographic parameters, which made it possible to detect aberrant patterns of variation at individual loci that could result from heterogeneity in mutational dynamics or from the effects of selection at linked sites. Results of the MCMC simulations were consistent with zero variance in demographic parameters among loci, but there was evidence for a 10- to 20-fold difference in mutation rate between the most slowly and most rapidly evolving loci. Results of the model provided strong evidence that savannah baboons have undergone a long-term historical decline in population size. The mode of the highest posterior density for the joint distribution of current and ancestral population size indicated a roughly eightfold contraction over the past 1,000 to 250,000 years. These results indicate that savannah baboons apparently did not share a common demographic history with other codistributed primate species.     

The seed bank in a subtropical freshwater marsh: implications for wetland restoration

Seed bank samples were collected from Huli Marsh, a subtropical shallow water mountainous marsh in Hunan Province, South China. Core samples were divided into upper and lower layers (each 5 cm in depth) and allowed to germinate in three water levels (0, 5 and 10 cm) over a 4-month period. A total of 51 species germinated and the mean density was 9211 ± 7188 seedlings m⁻². In the top 5 cm 41 species and 5747 ± 5111 seedlings m⁻² germinated, whereas 40 species and 3464 ± 3363 seedlings m⁻² did so from 5–10 cm. Germinated seedling density was significantly higher in the upper layer, largely due to differences in eight species. With increasing experimental water depth, less seedlings germinated: respectively, 9788 ± 7157 m⁻², 2050 ± 2412 m⁻² and 1978 ± 2616 m⁻², of 44, 21 and 19 species, submerged under 0, 5 or 10 cm. Seven species could emerge only in 0 water level. Vallisneria natans occurred only in 5 cm water, whereas Ottelia alismoides occurred in 10 cm water. In the vegetation survey of the marsh, 25 species were recorded, which was less than half of the species recorded in the seed bank. The top 10 dominants in the standing vegetation, accounting for 89% of vegetation abundance, represented only 10% in the seed bank. Twenty germinated species that also occurred in the standing vegetation accounted for 56% of the total seed bank. Our observed number of species germinating from a Chinese wetland seed bank is within the range observed elsewhere in the northern hemisphere (15–113 species).     

Composition, diversity, and spatial relationships of anurans following wetland restoration in a managed tropical forest

We investigated the composition, diversity, and patterns of spatial use of an anuran community following a wetland restoration project in a managed tropical monsoon forest in southern Taiwan. Anurans comprising eight species in seven genera and four families reached a mean density of 0.025+/-0.004 anurans m(-2) within a year. The three most important species in terms of frequency of occurrence and relative abundance all had an early appearance; only the most abundant Fejervarya limnocharis (62.2% of total accounts), however, remained present throughout the entire year. The distribution of anurans observed among habitat zones was non-random, with most records occurring in densely planted (42.8%) and running-water (23.9%) zones, and the fewest in a buffer zone adjacent to a paved road. Mean numbers of anurans were correlated with the mean percent vegetation cover among individually divided small pools. Microhyla ornate, M. heymonsi, Polypedates megacephalus, and F. limnocharis appeared to be more heterogeneous in their use of space than Buergeria japonicus. Species differed in their most frequently used habitat zones within the wetland site, with the pairs F. limnocharis and P. megacephalus, and M. ornate and Bufo melanostictus, exhibiting similar respective distributions among zones. Our study demonstrates the value of even a small, isolated wetland in contributing to and maintaining regional amphibian diversity. Patterns of spatial relationships of this anuran community have important implications for the conservation of local populations across species.     

Estimating tsetse population parameters: application of a mathematical model with density-dependence

A density-dependent model is used to describe the dynamics of an open population of tsetse flies (Diptera: Glossinidae). Immigration (or emigration) takes place when the total population is below (or above) a biologically determined threshold value. The population is also subjected to birth and death rates, as well as to the risk of being trapped (continuously or intermittently). During trapping the population decreases toward a 'low' equilibrium population and when trapping ceases the population starts recovering and increases toward a 'high' equilibrium. The model is fitted using data collected on trapped flies in four experiments. The first one was conducted with 'intermittent trapping' (i.e. several trapping-recovery cycles) on Glossina fuscipes fuscipes Newstead in the Central African Republic (Bangui area). In the other experiments, trapping data on Glossina palpalis palpalis (Robineau-Desvoidy) was collected in 'aggregate' form over several days at a time. Two of these were in Congo-Brazzaville (Bouenza area) and one in the Ivory Coast (Vavoua focus). Estimates are derived for the low and high equilibrium values as well as the trapping rate. The estimated effect of sustained trapping is to reduce the population to low equilibrium values that are 85-87% lower than the levels without trapping. The effects of the natural intrinsic growth and of the migration flows cannot be estimated separately because in the model they are mathematically indistinguishable.     

Atlantic bluefin tuna: a novel multistock spatial model for assessing population biomass

Atlantic bluefin tuna (Thunnus thynnus) is considered to be overfished, but the status of its populations has been debated, partly because of uncertainties regarding the effects of mixing on fishing grounds. A better understanding of spatial structure and mixing may help fisheries managers to successfully rebuild populations to sustainable levels while maximizing catches. We formulate a new seasonally and spatially explicit fisheries model that is fitted to conventional and electronic tag data, historic catch-at-age reconstructions, and otolith microchemistry stock-composition data to improve the capacity to assess past, current, and future population sizes of Atlantic bluefin tuna. We apply the model to estimate spatial and temporal mixing of the eastern (Mediterranean) and western (Gulf of Mexico) populations, and to reconstruct abundances from 1950 to 2008. We show that western and eastern populations have been reduced to 17% and 33%, respectively, of 1950 spawning stock biomass levels. Overfishing to below the biomass that produces maximum sustainable yield occurred in the 1960s and the late 1990s for western and eastern populations, respectively. The model predicts that mixing depends on season, ontogeny, and location, and is highest in the western Atlantic. Assuming that future catches are zero, western and eastern populations are predicted to recover to levels at maximum sustainable yield by 2025 and 2015, respectively. However, the western population will not recover with catches of 1750 and 12,900 tonnes (the "rebuilding quotas") in the western and eastern Atlantic, respectively, with or without closures in the Gulf of Mexico. If future catches are double the rebuilding quotas, then rebuilding of both populations will be compromised. If fishing were to continue in the eastern Atlantic at the unregulated levels of 2007, both stocks would continue to decline. Since populations mix on North Atlantic foraging grounds, successful rebuilding policies will benefit from trans-Atlantic cooperation.     

The diffusion model for migration and selection in a plant population

 The diffusion approximation is derived for migration and selection at a multiallelic locus in a partially selfing plant population subdivided into a lattice of colonies. Generations are discrete and nonoverlapping; both pollen and seeds disperse. In the diffusion limit, the genotypic frequencies at each point are those determined at equilibrium by the local rate of selfing and allelic frequencies. If the drift and diffusion coefficients are taken as the appropriate linear combination of the corresponding coefficients for pollen and seeds, then the migration terms in the partial differential equation for the allelic frequencies have the standard form for a monoecious animal population. The selection term describes selection on the local genotypic frequencies. The boundary conditions and the unidimensional transition conditions for a geographical barrier and for coincident discontinuities in the carrying capacity and migration rate have the standard form. In the diallelic case, reparametrization renders the entire theory of clines and of the wave of advance of favorable alleles directly applicable to plant populations. Received 30 August 1995; received in revised form 23 February 1996