A model of microbial contamination of a water reservoir

A three year record of daily fecal coliform counts in a Massachusetts water reservoir has the appearance of an irregular time series punctuated by outbursts of varying duration. The pattern is described in terms of a probabilistic model where the fluctuations in the ‘regular’ and ‘explosive’ regimes are governed by two sets of probabilities. It has been assumed that the random oscillations has a lognormal distribution, and that once an explosion threshold has been exceeded the increments or decrements in the population size have fixed probability distributions. The threshold for triggering an outburst was estimated by examining the randomness of the autocorrelation function of the record after it is filtered to eliminate peaks of progressively increasing magnitude. Once the threshold has been identified, the mean and standard deviation of the underlying lognormal distribution could be estimated directly from remains found in the record after all the peaks were removed. The probabilities of an increment and decrement during the outbursts and their relative magnitudes could also be estimated using simple formulas. These estimated parameter values were then used to generate realistic records with known threshold levels, which were subsequently used to assess the procedure’s feasibility and sensitivity.     

A Mathematical Model for Evolution and SETI

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f_l in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f_l is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually “an infinity”) of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.     

On the iterated prisoner's dilemma in a finite population

Two standard assumptions in analytical work on the iterated prisoner's dilemma are that the population is infinite, and that opponents—though randomly selected—are fixed for the duration of the game. This paper explores the consequences of relaxing both assumptions. It is shown in particular that if opponents are drawn at random throughout the game, then stable cooperation via reciprocity requires both that the probability of a further interaction be sufficiently high—higher than when opponents are fixed—and that the population not exceed a certain critical size, which depends on the probability of further interaction.     

Using the double-observer method to estimate detection probability of two cavity-nesting seabirds in Antarctica: the snow petrel (Pagodroma nivea) and the Wilson��s storm petrel (Oceanites oceanicus)

When estimating the size of seabird populations, count data may be biased due to various factors such as detection probability. Failing to account for detection probability in surveys may lead to an underestimate of population size and may compromise the ability to monitor trends if detection probability varies among surveys. Here, we use the double-observer method to estimate detection probability of cavity-nesting snow petrels (Pagodroma nivea) and Wilson’s storm petrels (Oceanites oceanicus) in East Antarctica. Estimates of single-visit detection probability of nesting/roosting adult snow petrels during the incubation stage of the breeding cycle ranged from 0.86 (SE = 0.04) to 0.87 (SE = 0.04) depending upon observers. Both observers found snow petrel chicks were easier to detect than adults, with estimated detection probability for chicks ranging from 0.92 (SE = 0.03) to 1.00 (SE = 0.34 × 10⁻⁵). Detection probability of adult and chick snow petrels increased as cavity volume increased. Compared to snow petrels, estimated detection probability was considerably lower for nesting/roosting Wilson’s storm petrels, ranging from 0.27 (SE = 0.09) to 0.50 (SE = 0.13) for each observer. These estimates of detection probability apply only to those individuals in the population that were potentially viewable or audible. Nevertheless, our results indicate that double-observer counts for ground surveys of cavity-nesting seabirds should improve estimates of population abundance in comparison with single-visit counts. Accounting for observer effects, habitat characteristics and stage of the breeding season on detection probability should also improve estimation of population trends.     

Persistence in fluctuating environments

Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations are key factors that can facilitate or disrupt coexistence. To better understand this interplay between these deterministic and stochastic forces, we develop a mathematical theory extending the nonlinear theory of permanence for deterministic systems to stochastic difference and differential equations. Our condition for coexistence requires that there is a fixed set of weights associated with the interacting populations and this weighted combination of populations’ invasion rates is positive for any (ergodic) stationary distribution associated with a subcollection of populations. Here, an invasion rate corresponds to an average per-capita growth rate along a stationary distribution. When this condition holds and there is sufficient noise in the system, we show that the populations approach a unique positive stationary distribution. Moreover, we show that our coexistence criterion is robust to small perturbations of the model functions. Using this theory, we illustrate that (i) environmental noise enhances or inhibits coexistence in communities with rock-paper-scissor dynamics depending on correlations between interspecific demographic rates, (ii) stochastic variation in mortality rates has no effect on the coexistence criteria for discrete-time Lotka–Volterra communities, and (iii) random forcing can promote genetic diversity in the presence of exploitative interactions.

One day is fine, the next is black.—The Clash     

On the evolution of pure winner and loser effects: A game-theoretic model

The persistence of linear dominance hierarchies is often attributed to higher probabilities of a win after a win or a loss after a loss in agonistic interactions, yet there has been no theory on the evolution of such prior-experience effects. Here an analytic model, based on the idea that contests are determined by subjective perceptions of resource-holding potential (RHP) which animals may revise in the light of experience, demonstrates that winner and loser effects can evolve through round-robin competition among triads of animals drawn randomly from their population, and that the probability of a hierarchy increases with the strength of the combined effect. The effects are pure, in the sense that a contestant observes neither its own RHP nor its opponent’s RHP or RHP perception or win—loss record; and so the strength of an effect is unmodified by the RHPs of particular individuals, but depends on the distribution of RHP among the population at large. The greater the difference between an individual’s and its opponent’s RHP perception, the more likely it is to win a contest; however, if it overestimates its RHP, then the cost of fighting increases with the overestimate. A winner or loser effect exists only if the fitness gain of the beta individual in a hierarchy, relative to that of the alpha, is less than 0.5. Then a loser effect can exist alone, or it can coexist with a winner effect; however, there cannot exist a winner effect without a loser effect.     

A comparison of approaches for modelling the occurrence of marine animals

Approaches for modelling the distribution of animals in relation to their environment can be divided into two basic types, those which use records of absence as well as records of presence and those which use only presence records. For terrestrial species, presence–absence approaches have been found to produce models with greater predictive ability than presence-only approaches. This study compared the predictive ability of both approaches for a marine animal, the harbour porpoise (Phoceoena phocoena). Using data on the occurrence of harbour porpoises in the Sea of Hebrides, Scotland, the predictive abilities of one presence–absence approach (generalised linear modelling—GLM) and three presence-only approaches (Principal component analysis—PCA, ecological niche factor analysis—ENFA and genetic algorithm for rule-set prediction—GARP) were compared. When the predictive ability of the models was assessed using receiver operating characteristic (ROC) plots, the presence–absence approach (GLM) was found to have the greatest predictive ability. However, all approaches were found to produce models that predicted occurrence significantly better than a random model and the GLM model did not perform significantly better than ENFA and GARP. The PCA had a significantly lower predictive ability than GLM but not the other approaches. In addition, all models predicted a similar spatial distribution. Therefore, while models constructed using presence–absence approaches are likely to provide the best understanding of species distribution within a surveyed area, presence-only models can perform almost as well. However, careful consideration of the potential limitations and biases in the data, especially with regards to representativeness, is needed if the results of presence-only models are to be used for conservation and/or management purposes. Guest editor: V. D. Valavanis Essential Habitat Mapping in the Mediterranean     

Turn designation, sampling rate and the misidentification of power laws in movement path data using maximum likelihood estimates

Many authors have claimed to observe animal movement paths that appear to be Lévy walks, i.e. a random walk where the distribution of move lengths follows an inverse power law. A Lévy walk is known to be the optimal search strategy of a particular class of random walks in certain environments; hence, it is important to distinguish correctly between Lévy walks and other types of random walks in observed animal movement paths. Evidence of a power law distribution in the step length distribution of observed animal movement paths is often used to classify a particular movement path as a Lévy walk. However, there is some doubt about the accuracy of early studies that apparently found Lévy walk behaviour. A recently accepted method to determine whether a movement path truly exhibits Lévy walk behaviour is based on an analysis of move lengths with a maximum likelihood estimate using Akaike weights. Here, we show that simulated (non-Lévy) random walks representing different types of animal movement behaviour (a composite correlated random walk; pooled data from a set of random walks with different levels of correlation and three-dimensional correlated random walks projected into one dimension) can all show apparent power law behaviour typical of Lévy walks when using the maximum likelihood estimation method. The probability of the movement path being identified as having a power law step distribution is related to both the sampling rate used by the observer and the way that ‘turns’ or ‘reorientations’ in the movement path are designated. However, identification is also dependent on the nature and properties of the simulated path, and there is currently no standard method of observation and analysis that is robust for all cases. Our results indicate that even apparently robust maximum likelihood methods can lead to a mismatch between pattern and process, as paths arising from non-Lévy walks exhibit Lévy-like patterns.     

The temporal dimension of marine speciation

Speciation is a process that occurs over time and, as such, can only be fully understood in an explicitly temporal context. Here we discuss three major consequences of speciation’s extended duration. First, the dynamism of environmental change indicates that nascent species may experience repeated changes in population size, genetic diversity, and geographic distribution during their evolution. The present characteristics of species therefore represents a static snapshot of a single time point in a species’ highly dynamic history, and impedes inferences about the strength of selection or the geography of speciation. Second, the process of speciation is open ended—ecological divergence may evolve in the space of a few generations while the fixation of genetic differences and traits that limit outcrossing may require thousands to millions of years to occur. As a result, speciation is only fully recognized long after it occurs, and short-lived species are difficult to discern. Third, the extinction of species or of clades provides a simple, under-appreciated, mechanism for the genetic, biogeographic, and behavioral ‘gaps’ between extant species. Extinction also leads to the systematic underestimation of the frequency of speciation and the overestimation of the duration of species formation. Hence, it is no surprise that a full understanding of speciation has been difficult to achieve. The modern synthesis—which united genetics, development, ecology, biogeography, and paleontology—greatly advanced the study of evolution. Here we argue that a similarly synthetic approach must be taken to further our understanding of the origin of species.     

Keratinophilic fungi inhabiting floor dusts of student houses at the South Valley University in Egypt

Keratinophilic fungi include true fungi that vigorously degrade keratin as well as a number of important human pathogenic dermatophytes. We identified 41 species and one variety belonging to 19 genera in 50 floor dust samples following culture on Sabouraud’s dextrose agar medium at 28°C. Dermatophytes and closely related fungi were represented by six species—Aphanoascus fulvescens, Aphanoascus sp., Arthroderma cuniculi, Chrysosporium lucknowense, Gymnoascus uncinatus and Trichophyton rubrum. There were 35 species and one variety of other fungal species, with members of Aspergillus and Penicllium being the most prevalent. Twenty-seven species and 1 variety belonging to 14 genera were identified from 24 dust samples gathered at 2-week intervals from male student housing at El-Kenose during January–December 2005 that had been cultured on Sabauraud’s dextrose agar at 28°C. The monthly counts of keratinophilic fungi showed irregular fluctuations, with a peak in April and the lowest point in November. Dermatophytes and closely related fungi were represented by Aphanoascus fulvescens, Aphanoascus sp., Chrysosporium lucknowense, Gymnoascus uncinatus, and Trichophyton rubrum. In conclusion, the study reports the incidences of some dermatophytes found in the floor dust of student houses of South Valley University, Egypt.     

Radial bulk diffusion into heterogeneous tissue

An expression is derived which describes the transient distribution of solute diffusing into heterogeneous tissue from a fully-stirred cylindrical region in which there has been a step change in solute concentration. This is envisaged as a model for the uptake of drugs by vessel walls, although the same approach has been extended for estimating the mode of total uptake of substances by annular specimens of tissue. Tissue is regarded as effectively composed of two phases—an extracellular (continuous) phase, similar to water, and a dispersed phase comprising cells of irregular profile. In each phase the relevant mode of uptake is taken as bulk diffusion rather than the permeation of a surface membrane.     

Frequency distribution of coliforms in water distribution systems.

Nine small water distribution systems were sampled intensively to determine the patterns of dispersion of coliforms. The frequency distributions of confirmed coliform counts were compatible with either the negative-binomial or the lognormal distribution. They were not compatible with either the Poisson or Poisson-plus-added zeroes distribution. The implications of the use of the lognormal distributional model were further evaluated because of its previous use in water quality studies. The geometric means from 14 data sets ranged from 10(-6) to 0.2 coliforms per 100 ml, and the geometric standard deviations were between 10 and 100, with one exception. If the lognormal model is representative of the coliform distribution; the arithmetic mean sample count is a poor estimator of the true mean coliform density, and the probability of water in a distribution system containing small patches with large coliform densities without detection by routine monitoring is finite. These conclusions have direct bearing on the interpretation of microbiological quality standards for drinking water.     

A proposal for re-defining the way the aetiology of schizophrenia and bipolar human psychiatric diseases is investigated

“The two big problems — the nature of development and the nature of the mind — are being subdued. I don’t know whether there will be beautiful, general theories to come out of this — something really nice like Watson and Crick’s double helix — or whether there will be an accumulation of more and more details. I’ll confess to a secret hope for the former” (Crow 2000).     

Genetic structure of farmer-managed varieties in clonally-propagated crops

The relative role of sexual reproduction and mutation in shaping the diversity of clonally propagated crops is largely unknown. We analyzed the genetic diversity of yam—a vegetatively-propagated crop—to gain insight into how these two factors shape its diversity in relation with farmers’ classifications. Using 15 microsatellite loci, we analyzed 485 samples of 10 different yam varieties. We identified 33 different genotypes organized in lineages supported by high bootstrap values. We computed the probability that these genotypes appeared by sexual reproduction or mutation within and between each lineage. This allowed us to interpret each lineage as a product of sexual reproduction that has evolved by mutation. Moreover, we clearly noted a similarity between the genetic structure and farmers’ classifications. Each variety could thus be interpreted as being the product of sexual reproduction having evolved by mutation. This highly structured diversity of farmer-managed varieties has consequences for the preservation of yam diversity.     

The use of microscopy and three-dimensional visualization to evaluate the structure of microbial biofilms cultivated in the calgary biofilm device

Microbes frequently live within multicellular, solid surface-attached assemblages termed biofilms. These microbial communities have architectural features that contribute to population heterogeneity and consequently to emergent cell functions. Therefore, three-dimensional (3D) features of biofilm structure are important for understanding the physiology and ecology of these microbial systems. This paper details several protocols for scanning electron microscopy and confocal laser scanning microscopy (CLSM) of biofilms grown on polystyrene pegs in the Calgary Biofilm Device (CBD). Furthermore, a procedure is described for image processing of CLSM data stacks using amira™, a virtual reality tool, to create surface and/or volume rendered 3D visualizations of biofilm microorganisms. The combination of microscopy with microbial cultivation in the CBD — an apparatus that was designed for highthroughput susceptibility testing — allows for structure-function analysis of biofilms under multivariate growth and exposure conditions.     

Random Phenotypic Variation of Yeast (Saccharomyces cerevisiae) Single-Gene Knockouts Fits a Double Pareto-Lognormal Distribution

Background

Distributed robustness is thought to influence the buffering of random phenotypic variation through the scale-free topology of gene regulatory, metabolic, and protein-protein interaction networks. If this hypothesis is true, then the phenotypic response to the perturbation of particular nodes in such a network should be proportional to the number of links those nodes make with neighboring nodes. This suggests a probability distribution approximating an inverse power-law of random phenotypic variation. Zero phenotypic variation, however, is impossible, because random molecular and cellular processes are essential to normal development. Consequently, a more realistic distribution should have a y-intercept close to zero in the lower tail, a mode greater than zero, and a long (fat) upper tail. The double Pareto-lognormal (DPLN) distribution is an ideal candidate distribution. It consists of a mixture of a lognormal body and upper and lower power-law tails.

Objective and Methods

If our assumptions are true, the DPLN distribution should provide a better fit to random phenotypic variation in a large series of single-gene knockout lines than other skewed or symmetrical distributions. We fit a large published data set of single-gene knockout lines in Saccharomyces cerevisiae to seven different probability distributions: DPLN, right Pareto-lognormal (RPLN), left Pareto-lognormal (LPLN), normal, lognormal, exponential, and Pareto. The best model was judged by the Akaike Information Criterion (AIC).

Results

Phenotypic variation among gene knockouts in S. cerevisiae fits a double Pareto-lognormal (DPLN) distribution better than any of the alternative distributions, including the right Pareto-lognormal and lognormal distributions.

Conclusions and Significance

A DPLN distribution is consistent with the hypothesis that developmental stability is mediated, in part, by distributed robustness, the resilience of gene regulatory, metabolic, and protein-protein interaction networks. Alternatively, multiplicative cell growth, and the mixing of lognormal distributions having different variances, may generate a DPLN distribution.     

Quantifying Primate Food Distribution and Abundance for Socioecological Studies: An Objective Consumer-centered Method

Food abundance and distribution have played a central role in the conceptual theory of primate socioecology. This theory predicts that agonistic (contest) competition should occur when food is distributed in discrete, defensible patches; in contrast, when food sources are distributed uniformly or randomly, nonagonistic (scramble) competition is expected. Primatologists usually measure resource density and patchiness from a botanical perspective, without an explicit link to the biology of the animal being studied. Such an approach may be irrelevant to how the animals view the dispersion of resources. For studies related to feeding competition, we suggest the use of a method that provides a consumer-based index of food distribution. We then describe such an approach and apply it to understand agonistic behavior in white-faced capuchins (Cebus capucinus), at Lomas Barbudal. Instead of choosing sample plots at random, we use each actual feeding tree of a group as the center of a sample plot and we use the monkey species’ average group spread as the sampling area. This focal tree method allows us to evaluate the resource availability both within and outside of the feeding tree during a particular feeding bout. To summarize the spatial distribution of food at the level of a foraging group, we define and use an extension of Lloyd’s Dispersion Index, Lloyd’s Extended Index (LEI), designed to allow the inclusion of resources of diverse sizes and species in a single measure. We evaluate if LEI can be used to predict the frequency of aggression, if changing the area of the plot alters these results, and if calculating LEI based on fruit abundance or fruit biomass better predicts the frequency of aggression in this population of capuchins. In support of socioecological predictions, our results show that the frequency of agonism in a focal tree declines as LEI increases. This relationship is significant when LEI is calculated using a 20-m plot size and weighting tree size by fruit counts, but not when using larger plot sizes, unweighted tree counts, or weighting by fruit biomass. Our approach demonstrates the importance of carefully considering plot size and different measures of food availability when testing socioecological models relating resource distribution and quality to aggression in nonhuman primates.     

Bacteria-epiphytes of brown macro alga in oil utilization in north sea ecosystems

Using the luminescent microscopy method, an epiphytic microbial community of Fucus sp. sea macrophytes collected in the littoral zone of White Sea was investigated. The abundant colonization of macrophytes’ surface by various bacteria, yeast, and microscopic alga was revealed. Enrichment culture of microorganisms—active oxidesers of oil and its derivatives was obtained with using of fucus’ thallus fragments. In macrocosm experiments on a biological research station of Moscow State University (MSU) at the coast of White Sea at the conditions imitating that of nature, the high oxidizing ability of selected cultures of the epiphytic microbial community was demonstrated. It was shown that the rate of oil utilization depends on its concentration and amount of epiphytic microbial community biomass used for this process.     

Estimation of population density of European pine marten in central Italy using camera trapping

Evaluating presence and abundance of small carnivores is essential for their conservation. In Italy, there is scarce information on European pine marten distribution, and no data are published on its abundance. Camera traps have been widely used to estimate population density applying capture–recapture models for species in which individual recognition is possible. Here we estimate the abundance of European pine martens in central Italy using camera trapping and a model that allows the estimation of population density without the need for individual recognition Rowcliffe et al. (Anim Conserv 11:185–186, 2008). Camera trapping was also used to evaluate habitat use patterns by martens. Fifteen camera traps were deployed in 90 placements for 15 days each, for a total of 1,334 camera days. Pine martens were captured in 24% of camera trap placements with a mean trap success rate of 0.33 photographs per camera placement. Estimated pine marten population density in the study area was 0.34 individuals km⁻². Marten trap rate was not strongly associated with any habitat type, although there were trends towards lower probability of records at locations with high coverage of cultivated fields and higher probability of records at locations with high coverage of human-made woodland. The results suggest that pine martens in this area are not confined to wooded habitat. To our knowledge, this study is the first application of the Rowcliffe et al. (Anim Conserv 11:185–186, 2008) method to a wild carnivore population and, furthermore, the first estimation of population density of pine martens in Italy.