Measuring mast seeding behavior: relationships among population variation,individual variation and synchrony

Mast seeding, or masting, is the variable production of flowers, seeds, or fruit across years more or less synchronously by individuals within a population. A critical issue is the extent to which temporal variation in seed production over a collection of individuals can be viewed as arising from a combination of individual variation and synchrony among individuals. Studies of masting typically quantify such variation in terms of the coefficient of variation (CV). In this paper we examine mathematically how the population CV relates to the mean individual CV and synchrony, concluding that the relationship is a complex one which cannot isolate an overall measure of synchrony, and involves additional factors, principally the number of plants sampled and the mean productivity per plant. Our development suggests some simple approximate relationships of population CV to individual variability, synchrony and the number of individuals. These were found to fit quite well when applied to data from 59 studies which included seed production at the individual level.     

Scintillation proximity assay of inositol phosphates in cell extracts: high-throughput measurement of G-protein-coupled receptor activation

The phosphatidylinositol turnover assay is used widely to measure activation, and inhibition, of G(q)-linked G-protein-coupled receptors. Cells expressing the receptor of interest are labeled by feeding with tritiated myo-inositol. The label is incorporated into cellular phosphatidylinositol 4,5-bisphosphate, which, upon agonist binding to the receptor, is hydrolyzed by phospholipase C to inositol 1,4,5-trisphosphate (IP(3)) and diacylglycerol. In the presence of Li(+), dephosphorylation of IP(3) to inositol is blocked, and the mass of soluble inositol phosphates is a quantitative readout of receptor activation. Current protocols for this assay all involve an anion-exchange chromatography step to separate radiolabeled inositol phosphates from radiolabeled inositol, making the assay cumbersome and difficult to automate. We now describe a scintillation proximity assay to measure soluble inositol phosphate mass in cell extracts, thus obviating the need for the standard chromatography step. The method uses positively charged yttrium silicate beads that bind inositol phosphates, but not inositol. We have used this assay to measure activation of recombinant and endogenous muscarinic acetylcholine receptors and activation of recombinant neuropeptide FF2 receptor coupled to IP(3) production by coexpression of a chimeric G protein. Further, we demonstrate the use and functional validity of this assay in a semiautomated, 384-well format, by characterizing the muscarinic receptor antagonists pirenzepine and atropine.     

Sensitivity analyses for ecological regression

In many ecological regression studies investigating associations between environmental exposures and health outcomes, the observed relative risks are in the range 1.0-2.0. The interpretation of such small relative risks is difficult due to a variety of biases--some of which are unique to ecological data, since they arise from within-area variability in exposures/confounders. The potential for residual spatial dependence, due to unmeasured confounders and/or data anomalies with spatial structure, must also be considered, though it often will be of secondary importance when compared to the likely effects of unmeasured confounding and within-area variability in exposures/confounders. Methods for addressing sensitivity to these issues are described, along with an approach for assessing the implications of spatial dependence. An ecological study of the association between myocardial infarction and magnesium is critically reevaluated to determine potential sources of bias. It is argued that the sophistication of the statistical analysis should not outweigh the quality of the data, and that finessing models for spatial dependence will often not be merited in the context of ecological regression.     

Testing for spatial correlation in nonstationary binary data, with application to aberrant crypt foci in colon carcinogenesis

In an experiment to understand colon carcinogenesis, all animals were exposed to a carcinogen, with half the animals also being exposed to radiation. Spatially, we measured the existence of what are referred to as aberrant crypt foci (ACF), namely, morphologically changed colonic crypts that are known to be precursors of colon cancer development. The biological question of interest is whether the locations of these ACFs are spatially correlated: if so, this indicates that damage to the colon due to carcinogens and radiation is localized. Statistically, the data take the form of binary outcomes (corresponding to the existence of an ACF) on a regular grid. We develop score-type methods based upon the Matern and conditionally autoregressive (CAR) correlation models to test for the spatial correlation in such data, while allowing for nonstationarity. Because of a technical peculiarity of the score-type test, we also develop robust versions of the method. The methods are compared to a generalization of Moran's test for continuous outcomes, and are shown via simulation to have the potential for increased power. When applied to our data, the methods indicate the existence of spatial correlation, and hence indicate localization of damage.     

A geostatistical analysis of small-scale spatial variability in bacterial abundance and community structure in salt marsh creek bank sediments

Small-scale variations in bacterial abundance and community structure were examined in salt marsh sediments from Virginia's eastern shore. Samples were collected at 5 cm intervals (horizontally) along a 50 cm elevation gradient, over a 215 cm horizontal transect. For each sample, bacterial abundance was determined using acridine orange direct counts and community structure was analyzed using randomly amplified polymorphic DNA fingerprinting of whole-community DNA extracts. A geostatistical analysis was used to determine the degree of spatial autocorrelation among the samples, for each variable and each direction (horizontal and vertical). The proportion of variance in bacterial abundance that could be accounted for by the spatial model was quite high (vertical: 60%, horizontal: 73%); significant autocorrelation was found among samples separated by 25 cm in the vertical direction and up to 115 cm horizontally. In contrast, most of the variability in community structure was not accounted for by simply considering the spatial separation of samples (vertical: 11%, horizontal: 22%), and must reflect variability from other parameters (e.g., variation at other spatial scales, experimental error, or environmental heterogeneity). Microbial community patch size based upon overall similarity in community structure varied between 17 cm (vertical) and 35 cm (horizontal). Overall, variability due to horizontal position (distance from the creek bank) was much smaller than that due to vertical position (elevation) for both community properties assayed. This suggests that processes more correlated with elevation (e.g., drainage and redox potential) vary at a smaller scale (therefore producing smaller patch sizes) than processes controlled by distance from the creek bank.     

The structuring role of free-floating versus submerged plants in a subtropical shallow lake

In shallow temperate lakes many ecological processes depend on submerged macrophytes. In subtropical and tropical lakes, free-floating macrophytes may be equally or more important. We tested the hypothesis that different macrophyte growth forms would be linked with different bottom-up and top-down mechanisms in out-competing phytoplankton. We compared experimentally the effects of submerged and free-floating plants on water chemistry, phytoplankton biomass, zooplankton and fish community structure in a shallow hypertrophic lake (Lake Rodó, 34°55S 56°10W, Uruguay). Except for the retention of suspended solids, we found no other significant bottom-up process connected with either Eichhornia crassipes or Potamogeton pectinatus. Free-floating plants had a lower abundance of medium-sized zooplankton than any other microhabitat and submerged plants were apparently preferred by microcrustaceans. Fish showed a differential habitat use according to species, size-class and feeding habits. Dominant omnivore-planktivores, particularly the smallest size classes, preferred submerged plants. In contrast, omnivore-piscivores were significantly associated with free-floating plants. The density of omnivorous-planktivorous fish, by size class, significantly explained the distribution of medium-sized zooplankton, the high number of size 0 fish being the main factor. The abiotic environment and the structure of the zooplankton community explained little of the fish distribution pattern. Our results suggest that bottom-up effects of free-floating plants are weak when cover is low or intermediate. Top-down effects are complex, as effects on zooplankton and fish communities seem contradictory. The low piscivores:planktivores ratio in all microhabitats suggests, however, that cascading effects on phytoplankton through free-floating plant impacts on piscivorous fish are unlikely to be strong.     

Metapopulation dynamics with quasi-local competition

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.     

Do migratory or demographic disruptions rule the population impact of pollution in spatial networks?

Ecotoxicology supplies environmental quality criteria mainly based on the potential effects of contaminants on demographic rates of natural populations. Possible impacts through pollutant-induced disruptions of spatial behaviors are totally neglected. Should it be significant to take into account this "second way"? We developed the example of a hypothetical brown trout population living in a river network. We analyzed how behaviors of toxic avoidance or attraction during the spawning migration alter the impact of pollution. Attraction behaviors basically enhanced the bad effect of pollution. More interesting, avoidance behaviors can weakly lift the asymptotic population growth rate, while if there is density-dependent effects on recruitment, pollutant avoidance can actually lead to a substantial drop in equilibrium size. Our model allowed comparing the relative significance of migratory and demographic disruptions for explaining the population impacts of pollution; we thus stress on the need of increasing efforts to develop knowledge relative to toxicant-induced spatial behaviors and to integrate such effects in the definition of environmental quality criteria.     

Covariances among join-count spatial autocorrelation measures

Spatial distributions of biological variables are often well-characterized with pairwise measures of spatial autocorrelation. In this article, the probability theory for products and covariances of join-count spatial autocorrelation measures are developed for spatial distributions of multiple nominal (e.g. species or genotypes) types. This more fully describes the joint distributions of pairwise measures in spatial distributions of multiple (i.e. more than two) types. An example is given on how the covariances can be used for finding standard errors of weighted averages of join-counts in spatial autocorrelation analysis of more than two types, as is typical for genetic data for multiallelic loci.     

Multi-scale variation in spatial heterogeneity for microbial community structure in an eastern Virginia agricultural field

To better understand the distribution of soil microbial communities at multiple spatial scales, a survey was conducted to examine the spatial organization of community structure in a wheat field in eastern Virginia (USA). Nearly 200 soil samples were collected at a variety of separation distances ranging from 2.5 cm to 11 m. Whole-community DNA was extracted from each sample, and community structure was compared using amplified fragment length polymorphism (AFLP) DNA fingerprinting. Relative similarity was calculated between each pair of samples and compared using geostatistical variogram analysis to study autocorrelation as a function of separation distance. Spatial autocorrelation was found at scales ranging from 30 cm to more than 6 m, depending on the sampling extent considered. In some locations, up to four different correlation length scales were detected. The presence of nested scales of variability suggests that the environmental factors regulating the development of the communities in this soil may operate at different scales. Kriging was used to generate maps of the spatial organization of communities across the plot, and the results demonstrated that bacterial distributions can be highly structured, even within a habitat that appears relatively homogeneous at the plot and field scale. Different subsets of the microbial community were distributed differently across the plot, and this is thought to be due to the variable response of individual populations to spatial heterogeneity associated with soil properties.