Kriging with nonparametric variance function estimation

A method for fitting regression models to data that exhibit spatial correlation and heteroskedasticity is proposed. It is well known that ignoring a nonconstant variance does not bias least-squares estimates of regression parameters; thus, data analysts are easily lead to the false belief that moderate heteroskedasticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms can seriously bias estimated correlation functions. By modeling heteroskedasticity and standardizing by estimated standard deviations, our approach eliminates this bias in the correlations. A combination of parametric and nonparametric regression techniques is used to iteratively estimate the various components of the model. The approach is demonstrated on a large data set of predicted nitrogen runoff from agricultural lands in the Midwest and Northern Plains regions of the U.S.A. For this data set, the model comprises three main components: (1) the mean function, which includes farming practice variables, local soil and climate characteristics, and the nitrogen application treatment, is assumed to be linear in the parameters and is fitted by generalized least squares; (2) the variance function, which contains a local and a spatial component whose shapes are left unspecified, is estimated by local linear regression; and (3) the spatial correlation function is estimated by fitting a parametric variogram model to the standardized residuals, with the standardization adjusting the variogram for the presence of heteroskedasticity. The fitting of these three components is iterated until convergence. The model provides an improved fit to the data compared with a previous model that ignored the heteroskedasticity and the spatial correlation.     

Genetic diversity and multilocus genetic structure in the relictual endemic herb<Emphasis Type="Italic"> Japonolirion osense</Emphasis> (Petrosaviaceae)

Plant clonality may greatly reduce effective population size and influence management strategies of rare and endangered species. We examined genetic diversity and the extent of clonality in four populations of the monotypic herbaceous perennial Japonolirion osense, which is one of the most rare flowering plants in Japan. Allozyme analysis revealed moderate levels of genetic variation, and the proportion of polymorphic loci (P=66.7%) was higher than the value for species with similar life-history traits. With four polymorphic loci, 19 multilocus genotypes were observed among 433 aerial shoot samples and 10 (52%) were found only in single populations. The proportion of distinguishable genotypes (PD=0.10) and Simpson's index of diversity (D=0.52) also exhibited moderate levels of genotypic diversity compared to other clonal plants, with genotype frequencies at Hardy-Weinberg equilibrium. The distributions of genotypes were often localized and they were mostly found within a radius of 5 m. Spatial autocorrelation analysis showed that shoot samples located 4 m apart were expected to be genetically independent. The results suggest that the spatial extent of genets was relatively narrow and thus the clonality was not extensive.     

Sampling adequacy in an extreme environment: species richness patterns in Slovenian caves

Caves harbor a rich fauna unique to subterranean environments. Although extensive records of cave animals are available, only a small fraction of known caves in any region have been biologically assessed. We investigated the impact of incomplete sampling using one of the richest, best documented cave faunas in the world – that of the Dinaric karst of Slovenia. We utilized time snapshots (1940, 1970, and 2000) of the caves and cave fauna to analyze stability of hotspots, spatial pattern, and relationship between number of species and number of caves. Using data aggregated into 100km² hexagons, the location of hotspots, black–white joins, Moran's I, and spatial autocorrelation all remained constant, at least from 1970 on. The linear regression coefficient of the relationship between number of caves and number of species declined with time. Most hexagons had been sampled, but there was no indication that any hexagon had been sampled intensively enough for the accumulation curve of number of caves versus number of species within a hexagon to reach an asymptote. This appeared to be the result of a highly skewed distribution of species richness among caves. Number and position of hotspots can be predicted from information on these few high diversity caves.     

Herbivore effects on developmental instability and fecundity of holm oaks

Plants are able to compensate for loss of tissue due to herbivores at a variety of spatial and temporal scales, masking detrimental effects of herbivory on plant fitness at these scales. The stressing effect of herbivory could also produce instability in the development of plant modules, and measures of such instability may reflect the fitness consequences of herbivory if instability is related to components of plant fitness. We analyse the relationships between herbivory, developmental instability and production of female flowers and fruits of holm oak Quercus ilex trees by means of herbivore removal experiments. Removal of leaf herbivores reduced herbivory rates at the tree level, but had no effect on mean production of female flowers or mature fruits, whereas herbivory tended to enhance flower production and had no effect on fruit abortion at the shoot level. Differences in herbivory levels between shoots of the same branch did not affect the size and fluctuating asymmetry of intact leaves. These results indicate compensation for herbivory at the tree level and over-compensation at the shoot level in terms of allocation of resources to female flower production. Removal of insect herbivores produced an increase in the mean developmental instability of leaves at the tree level in the year following the insecticide treatment, and there was a direct relationship between herbivory rates in the current year and leaf fluctuating asymmetry the following year irrespective of herbivore removal treatment. Finally, the production of pistillate flowers and fruits by trees was inversely related to the mean fluctuating asymmetry of leaves growing the same year. Leaf fluctuating asymmetry was thus an estimator of the stressing effects of herbivory on adult trees, an effect that was delayed to the following year. As leaf fluctuating asymmetry was also related to tree fecundity, asymmetry levels provided a sensitive measure of plant performance under conditions of compensatory responses to herbivory.     

Slight differences among individuals and the unified neutral theory of biodiversity

The unified neutral theory of biodiversity provides a very simple and counterintuitive explanation of species diversity patterns. By specifying speciation, community size and dispersal, and completely ignoring differences among individual organisms and species, it generates biodiversity patterns that remarkably resemble natural ones. Here I show that adding even slight differences among organisms generates very different patterns and predictions. In large communities with widespread dispersal, heritable differences in viability among individual organisms lead to biodiversity patterns characterised by the overdominance of a single species comprising organisms with relatively high fitness. In communities with local dispersal, the same differences produce rapid community extinction. I conclude that the unified neutral theory is not robust to slight deviations from its most controversial assumption.     

Dispersal-mediated coexistence of competing predators

Models of metapopulations have often ignored local community dynamics and spatial heterogeneity among patches. However, persistence of a community as a whole depends both on the local interactions and the rates of dispersal between patches. We study a mathematical model of a metacommunity with two consumers exploiting a resource in a habitat of two different patches. They are the exploitative competitors or the competing predators indirectly competing through depletion of the shared resource. We show that they can potentially coexist, even if one species is sufficiently inferior to be driven extinct in both patches in isolation, when these patches are connected through diffusive dispersal. Thus, dispersal can mediate coexistence of competitors, even if both patches are local sinks for one species because of the interactions with the other species. The spatial asynchrony and the competition-colonization trade-off are usual mechanisms to facilitate regional coexistence. However, in our case, two consumers can coexist either in synchronous oscillation between patches or in equilibrium. The higher dispersal rate of the superior prompts rather than suppresses the inferior. Since differences in the carrying capacity between two patches generate flows from the more productive patch to the less productive, loss of the superior by emigration relaxes competition in the former, and depletion of the resource by subsidized consumers decouples the local community in the latter.     

Competition between near and far dispersers in spatially structured habitats

Competitive interactions and invasibility between short- and long-distance dispersal was investigated in a population on a heterogeneous landscape with spatial correlations in habitat types, and where the driving interaction between individuals is competition for space. Stochastic spatially explicit simulations were used, along with differential equation models based on pair approximations. Conditions under which either dispersal strategy can successfully invade the other were determined, as a function of the amount and clustering of suitable habitat and the relative costs involved in the two dispersal strategies. Long-distance dispersal, which reduces intraspecific competition, is sometimes advantageous even where aggregation of suitable habitat would otherwise favor short-distance dispersal, although certain habitat distributions can lead to either strategy being dominant. Coexistence is also possible on some landscapes, where the spatial structure of the populations partitions suitable sites according to the number of suitable neighboring sites. Mutual competitive exclusion, where whichever strategy is established first cannot be invaded, is also possible. All of these results are observed even when there is no intrinsic difference in the two strategies' costs, such as mortality or competitive abilities.     

Roles of oxytocin in spatial learning and memory in the nucleus basalis of Meynert in rats

The present study was performed to explore the role of oxytocin (OT) in spatial learning and memory in the nucleus basalis of Meynert (NBM) of rats. The latency, distance and swimming path to find the platform were tested by Morris water maze and recorded by a video camera connected to a computer. Intra-NBM injections of 2 or 10 nmol of OT, but not 0.2 nmol of OT, induced significant increase on the latency of spatial learning. Rats receiving intra-NBM administrations of 2 or 10 nmol of OT showed a more random search pattern. There were no significant changes in the swimming speed in Morris water maze test after the injection of OT. Furthermore, the impaired effect of OT on the latency of spatial learning was blocked by intra-NBM injection of the selective OT antagonist Atosiban, indicating that the effect of OT was mediated by OT receptor in the NBM of rats. Moreover, there were no influences of OT or Atosiban on the retention performance in rats. The results suggest that OT plays an inhibitory role in spatial learning in the NBM; the effect is mediated by OT receptor.     

Spatial and population genetic structure of microsatellites in white pine

We evaluated the population genetic structure of seven microsatellite loci for old growth and second growth populations of eastern white pine (Pinus strobus). From each population, located within Hartwick Pines State Park, Grayling, Michigan, USA, 120-122 contiguous trees were sampled for genetic analysis. Within each population, genetic diversity was high and inbreeding low. When comparing these populations, there is a significant, but small (less than 1%), genetic divergence between populations. Spatial distance between populations or timber harvest at the second growth site were reasonable explanations for the observed minor differences in allele frequencies between populations. Spatial autocorrelation analysis suggested that, for the old growth population, weak positive structuring at 15 m fits the isolation by distance model for a neighbourhood size of about 100 individuals. In comparison, genotypes were randomly distributed in the second growth population. Thus, logging may have decreased spatial structuring at the second growth site, suggesting that management practices may be used to alter natural spatial patterns. In addition, the amount of autocorrelation in the old growth population appears to be lower for some of the microsatellites, suggesting higher numbers of rare alleles and that higher mutation rates may have directly affected spatial statistics by reducing structure.