Ensembles of Atoms, Ensembles of Species: Comparative Statistical Mechanics.

The methods of statistical physics are exemplified in the classical perfect gas-each atom is a single dynamical entity. Such methods can be applied in ecology to the distribution of cosmopolitan species over many sites. The analogue of an atom is a class of species distinguished by the number of sites at which it occurs, hardly a material entity; yet, the methods of statistical physics nonetheless seem applicable. This paper compares the application of statistical mechanics to the distribution of atoms and to the vastly different problem of distribution of cosmopolitan species. A number of different approaches show that these distributed entities must be in some sense equivalent; the dynamics must be controlled by interaction between species and the global environment rather than between species and many uncorrelated local environments.

Endemics and Cosmopolitans: Application of Statistical Mechanics to the Dry Forests of Mexico.

Data on the seasonally dry tropical forests of Mexico have been examined in the light of statistical mechanics. The results suggest a division into two classes of species. There are drifting populations of a cosmopolitan class capable of existing in most dry forest sites; these have a statistical distribution previously only observed (globally) for populations of alien species. We infer that a high proportion of species found only at a single site are specialists, endemics, and that these prefer sites comparatively low in species richness.

On the statistical mechanics of species abundance distributions.

A central issue in ecology is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to species abundance distributions (SADs) shows that simple ecological properties could account for the near universal features observed. These properties are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth and death rates. They underpin the neutral theory of Hubbell (2001), the master equation approach of Volkov et al. (2003, 2005) and the idiosyncratic (extreme niche) theory of Pueyo et al. (2007); they result in an underlying log series SAD, regardless of neutral or niche dynamics. The success of statistical mechanics in this application implies that communities are in dynamic equilibrium and hence that niches must be flexible and that temporal fluctuations on all sorts of scales are likely to be important in community structure.

Measurement of the equilibrium relative humidity for common precipitant concentrations: facilitating controlled dehydration experiments.

The dehydration of crystals of macromolecules has long been known to have the potential to increase their diffraction quality. A number of methods exist to change the relative humidity that surrounds crystals, but for reproducible results, with complete characterization of the changes induced, a precise humidity-control device coupled with an X-ray source is required. The first step in these experiments is to define the relative humidity in equilibrium with the mother liquor of the system under study; this can often be quite time-consuming. In order to reduce the time spent on this stage of the experiment, the equilibrium relative humidity for a range of concentrations of the most commonly used precipitants has been measured. The relationship between the precipitant solution and equilibrium relative humidity is explained by Raoult's law for the equilibrium vapour pressure of water above a solution. The results also have implications for the choice of cryoprotectant and solutions used to dehydrate crystals. For the most commonly used precipitants (10-30% PEG 2000-8000), the starting point will be a relative humidity of 99.5%.

The statistical mechanics of community assembly and species distribution.

• Theoretically, communities at or near their equilibrium species number resist entry of new species. Such 'biotic resistance' recently has been questioned because of successful entry of alien species into diverse natural communities. • Data on 10,409 naturalizations of 5350 plant species over 16 sites dispersed globally show exponential distributions both for species over sites and for sites over number of species shared. These exponentials signal a statistical mechanics of species distribution, assuming two conditions. First, species and sites are equivalent, either identical ('neutral') or so complex that the chance a species is in the right place at the right time is vanishingly small ('idiosyncratic'); the range of species and sites in our data disallows a neutral explanation. Secondly, the total number of naturalizations is fixed in any era by a 'regulator'. • Previous correlation of species naturalization rates with net primary productivity over time suggests that the regulator is related to productivity. • We conclude that biotic resistance is a moving ceiling, with resistance controlled by productivity. The general observation that the majority of species occur naturally at only a few sites, and only a few species occur at many sites, now has a quantitative (exponential) character, offering the study of species' distributions a previously unavailable rigor.

Investigating the role of enemies in temporal dynamics: Differential sensitivity, competition and stable coexistence.

The impact of herbivores and other pests on plants varies greatly from year to year. Here we develop an analytical model of a temporal niche dynamic as a tool to examine how natural fluctuations in pest (enemy) levels may determine coexistence in competing annual plant species when one but not the other is affected by the pest. We show that the probability and speed with which the resistant drives out the sensitive species, coexists with it, or is driven out by its sensitive competitor depends on the cost of pest-resistance to the unaffected species, the frequency of high pest levels in the habitat and the competitive advantage of the sensitive species when the pest is not actively present. The interaction is regulated primarily by pest impact on relative seedling survival of the two, with relative yield per capita of seeds viable into the following season (effective fecundity) the next most vulnerable life-cycle stage.

Phylogeny, niches, and relative abundance in natural communities.

Community structure refers to the number of species in a community and the pattern of distribution of individuals among those species. We use a novel way of representing community structure to show that abundance within closely related pairs of co-occurring tree species in a highly diverse Mexican forest is more equitable than is abundance within more distantly related pairs. This observation is at odds with the fundamental assumption of neutral models of community structure, i.e., that species are interchangeable. The observed patterns suggest niche apportionment, in which interaction is focused pairwise between congeners but falls away from the phylogenetic structure above the genus level. Thus niche processes may significantly affect community structure through regulating relative abundance in a substantial proportion of species, which in turn potentially enhances community stability. One such mechanism of stable coexistence has already been shown to be active in this forest.

Raoult's law revisited: accurately predicting equilibrium relative humidity points for humidity control experiments.

The humidity surrounding a sample is an important variable in scientific experiments. Biological samples in particular require not just a humid atmosphere but often a relative humidity (RH) that is in equilibrium with a stabilizing solution required to maintain the sample in the same state during measurements. The controlled dehydration of macromolecular crystals can lead to significant increases in crystal order, leading to higher diffraction quality. Devices that can accurately control the humidity surrounding crystals while monitoring diffraction have led to this technique being increasingly adopted, as the experiments become easier and more reproducible. Matching the RH to the mother liquor is the first step in allowing the stable mounting of a crystal. In previous work [Wheeler, Russi, Bowler & Bowler (2012). Acta Cryst. F68, 111-114], the equilibrium RHs were measured for a range of concentrations of the most commonly used precipitants in macromolecular crystallography and it was shown how these related to Raoult's law for the equilibrium vapour pressure of water above a solution. However, a discrepancy between the measured values and those predicted by theory could not be explained. Here, a more precise humidity control device has been used to determine equilibrium RH points. The new results are in agreement with Raoult's law. A simple argument in statistical mechanics is also presented, demonstrating that the equilibrium vapour pressure of a solvent is proportional to its mole fraction in an ideal solution: Raoult's law. The same argument can be extended to the case where the solvent and solute molecules are of different sizes, as is the case with polymers. The results provide a framework for the correct maintenance of the RH surrounding a sample.

An analytical model assessing the potential threat to natural habitats from insect resistance transgenes.

We examine the role of ecological interactions on effective gene flow from genetically manipulated plants to their wild relatives. We do so by constructing and applying to oilseed rape (OSR) an analytical model for interaction between plants with and without an insect resistance (IR) allele in natural communities, incorporating documented levels of herbivore variability. We find that with reasonable values of advantage to the IR allele, little concomitant disadvantage (physiological costs of the allele) restricts it to low proportions of the natural population for large numbers of generations. We conclude that OSR IR transgenes are unlikely to pose an immediate threat to natural communities. Our model identifies those factors best able to regulate particular transgenes at the population level, the most effective being impaired viability of seeds in the period between production and the following growing season, although other possibilities exist. Because solutions rely on ratios, limiting values of regulating factors are testable under controlled conditions, minimizing risk of release into the environment and offering significant advancement on existing testing programmes. Our model addresses folivory but is easily modified for herbivory damaging the seed or directly affecting seed production by infested plants, or for pathogens altering seed survival in the seedbank.

Measurement of the intrinsic variability within protein crystals: implications for sample-evaluation and data-collection strategies.

The advent of micro-focused X-ray beams has led to the development of a number of advanced methods of sample evaluation and data collection. In particular, multiple-position data-collection and helical oscillation strategies are now becoming commonplace in order to alleviate the problems associated with radiation damage. However, intra-crystal and inter-crystal variation means that it is not always obvious on which crystals or on which region or regions of a crystal these protocols should be performed. For the automation of this process for large-scale screening, and to provide an indication of the best strategy for data collection, a metric of crystal variability could be useful. Here, measures of the intrinsic variability within protein crystals are presented and their implications for optimal data-collection strategies are discussed.

Coexistence and relative abundance in forest trees.

Contemporary acceleration of biodiversity loss makes increasingly urgent the need to understand the controls of species coexistence. Tree diversity in particular plays a pivotal role in determining terrestrial biodiversity, through maintaining diversity of its dependent species and with them, their predators and parasites. Most theories of coexistence based on the principle of limiting similarity suggest that coexistence of competing species is inherently unstable; coexistence of competitors must be maintained by external forces such as disturbance, immigration or 'patchiness' of resources in space and time. In contrast, storage theory postulates stable coexistence of competing species through temporal alternation of conditions favouring recruitment of one species over the other. Here we use storage theory to develop explicit predictions for relative differences between competitors that allow us to discriminate between coexistence models. Data on tree species from a primary forest on the Mexican Pacific coast support a general dynamic of storage processes determining coexistence of similar tree species in this community, and allow us to reject all other theories of coexistence.