Further considerations on the statistical mechanics of biological associations

In this continuation of a previous report it is shown how the Volterra population dynamics, which underlies the statistical theory, can be based on a variational principle; how the dynamics can be generalized as regards both the behavior of total populations and migration phenomena; and how many directly observable data, such as amplitudes and frequencies of oscillation of a population, fit into the statistical theory and can test it. Such a test is carried out in some detail using the fox-catch data of Elton, with a clear indication that the theory is capable of comprehending the major statistical properties of population-time curves. A final section sketches an extension of the theory to cover secular variations of external conditions such as temperature of the environment.     

The Limits of Individual Identification from Sample Allele Frequencies: Theory and Statistical Analysis

It was shown recently using experimental data that it is possible under certain conditions to determine whether a person with known genotypes at a number of markers was part of a sample from which only allele frequencies are known. Using population genetic and statistical theory, we show that the power of such identification is, approximately, proportional to the number of independent SNPs divided by the size of the sample from which the allele frequencies are available. We quantify the limits of identification and propose likelihood and regression analysis methods for the analysis of data. We show that these methods have similar statistical properties and have more desirable properties, in terms of type-I error rate and statistical power, than test statistics suggested in the literature.     

Contribution to the mathematical theory of mass behavior: I. The propagation of single acts

The propagation of a single act in a large population is supposed to depend on some external circumstance and on an “imitation component”, where encounters with individuals who are performing or have already performed the act contribute to the tendency of an individual to perform it. The “tendency” to perform is supposed to be measured by the average frequency of stimuli, randomly distributed in time, impinging on the individual. The deduced equation is a relation between the fraction of the population who have performed the act and time, provided the time course of the “external circumstance” and the way in which the imitation component contributes are known. Several special cases are studied, in particular, cases without the imitation component, cases with imitation only, and various mixed cases. Examples are given of social situations in which such factors may operate and general suggestions are made for the systematization of observations and/or experiments to test the assumptions of the theory.     

Comments on the entropy-based transmission/disequilibrium test

It has recently been claimed in this journal (Zhao et al. in Hum Genet 121:357–367, 2007) that a so-called “entropy-based” TDT test has improved power over the standard TDT test of Spielman et al. (Am J Hum Genet 52:506–516, 1993). We show that this claim is contradicted by standard statistical theory as well as by our simulation results. We show that the incorrect claim arises because of inappropriate assumptions, and also show that the entropy-based statistic has various undesirable properties.     

Relating recent infection prevalence to incidence with a sub-population of assay non-progressors

We present a new analysis of relationships between disease incidence and the prevalence of an experimentally defined state of ‘recent infection’. This leads to a clean separation between biological parameters (properties of disease progression as reflected in a test for recent infection), which need to be calibrated, and epidemiological state variables, which are estimated in a cross-sectional survey. The framework takes into account the possibility that details of the assay and host/pathogen chemistry leave a (knowable) fraction of the population in the recent category for all times. This systematically addresses an issue which is the source of some controversy about the appropriate use of the BED assay for defining recent HIV infection. The analysis is, however, applicable to any assay that forms the basis of a test for recent infection. Analysis of relative contributions of error arising variously from statistical considerations and simplifications of general expressions indicate that statistical error dominates heavily over methodological bias for realistic epidemiological and biological scenarios.     

Metabolic Variability in Micro-Populations

Biological cells in a population are variable in practically every property. Much is known about how variability of single cells is reflected in the statistical properties of infinitely large populations; however, many biologically relevant situations entail finite times and intermediate-sized populations. The statistical properties of an ensemble of finite populations then come into focus, raising questions concerning inter-population variability and dependence on initial conditions. Recent technologies of microfluidic and microdroplet-based population growth realize these situations and make them immediately relevant for experiments and biotechnological application. We here study the statistical properties, arising from metabolic variability of single cells, in an ensemble of micro-populations grown to saturation in a finite environment such as a micro-droplet. We develop a discrete stochastic model for this growth process, describing the possible histories as a random walk in a phenotypic space with an absorbing boundary. Using a mapping to Polya’s Urn, a classic problem of probability theory, we find that distributions approach a limiting inoculum-dependent form after a large number of divisions. Thus, population size and structure are random variables whose mean, variance and in general their distribution can reflect initial conditions after many generations of growth. Implications of our results to experiments and to biotechnology are discussed.     

Brownian motion of helical flagella

We develops a theory of the Brownian motion of a rigid helical object such as bacterial flagella. The statistical properties of the random forces acting on the helical object are discussed and the coefficients of the correlations of the random forces are determined. The averages , and are also calculated where z and theta are the position along and angle around the helix axis respectively. Although the theory is limited to short time interval, direct comparison with experiment is possible by using the recently developed cinematography technique.     

A fundamental principle governing populations

Proposed here is that an overriding principle of nature governs all population behavior; that a single tenet drives the many regimes observed in nature—exponential-like growth, saturated growth, population decline, population extinction, and oscillatory behavior. The signature of such an all embracing principle is a differential equation which, in a single statement, embraces the entire panoply of observations. In current orthodox theory, this diverse range of population behaviors is described by many different equations—each with its own specific justification. Here, a single equation governing all the regimes is proposed together with the principle from which it derives. The principle is: The effect on the environment of a population’s success is to alter that environment in a way that opposes the success. Experiments are suggested which could validate or refute the theory. Predictions are made about population behaviors.     

Left-hand Preference for a Complex Manual Task in a Population of Wild Siamangs (<Emphasis Type="BoldItalic">Symphalangus syndactylus</Emphasis>)

Many hypotheses have been proposed linking the emergence of lateralized activities—such as handedness—in primates, with hemispheric specialization and the evolution of complex communication such as human language. Although data to test these ideas are rapidly accumulating for many primate taxa, some species are still largely unexplored, especially under natural conditions. I present the first data on a population of wild siamangs (Symphalangus syndactylus), highly arboreal small apes. Preference for the left hand is shown both at the individual and population levels for a complex manual task: collecting and drinking water from tree holes. There was no difference in hand preference between males and females, and immature individuals showed more variable patterns than adults. These results are consistent with the postural origins theory, allow a new interpretation of the findings of comparable studies, and indicate a useful behavior for future investigations of laterality in wild primates.     

Random local temporal structure of category fluency responses

The Category Fluency Test (CFT) provides a sensitive measurement of cognitive capabilities in humans related to retrieval from semantic memory. In particular, it is widely used to assess progress of cognitive impairment in patients with dementia. Previous research shows that, in the first approximation, the intensity of tested individuals’ responses within a standard 60-s test period decays exponentially with time, with faster decay rates for more cognitively impaired patients. Such decay rate can then be viewed as a global (macro) diagnostic parameter of each test. In the present paper we focus on the statistical properties of the properly de-trended time intervals between consecutive responses (inter-call times) in the Category Fluency Test. In a sense, those properties reflect the local (micro) structure of the response generation process. We find that a good approximation for the distribution of the de-trended inter-call times is provided by the Weibull Distribution, a probability distribution that appears naturally in this context as a distribution of a minimum of independent random quantities and is the standard tool in industrial reliability theory. This insight leads us to a new interpretation of the concept of “navigating a semantic space” via patient responses.     

Sources of Wilhelm Johannsen’s Genotype Theory

This paper describes the historical background and early formation of Wilhelm Johannsen’s distinction between genotype and phenotype. It is argued that contrary to a widely accepted interpretation (For instance, W. Provine, 1971. The Origins of Theoretical Population Genetics. Chicago: The University of Chicago Press; Mayr, 1973; F. B. Churchill, 1974. Journal of the History of Biology 7: 5–30; E. Mayr, 1982. The Growth of Biological Thought, Cambridge: Harvard University Press; J. Sapp, 2003. Genesis. The Evolution of Biology. New York: Oxford University Press) his concepts referred primarily to properties of individual organisms and not to statistical averages. Johannsen’s concept of genotype was derived from the idea of species in the tradition of biological systematics from Linnaeus to de Vries: An individual belonged to a group – species, subspecies, elementary species – by representing a certain underlying type (S. Müller-Wille and V. Orel, 2007. Annals of Science 64: 171–215). Johannsen sharpened this idea theoretically in the light of recent biological discoveries, not least those of cytology. He tested and confirmed it experimentally combining the methods of biometry, as developed by Francis Galton, with the individual selection method and pedigree analysis, as developed for instance by Louis Vilmorin. The term “genotype” was introduced in W. Johannsen’s 1909 (Elemente der Exakten Erblichkeitslehre. Jena: Gustav Fischer) treatise, but the idea of a stable underlying biological “type” distinct from observable properties was the core idea of his classical bean selection experiment published 6 years earlier (W. Johannsen, 1903. Ueber Erblichkeit in Populationen und reinen Linien. Eine Beitrag zur Beleuchtung schwebender Selektionsfragen, Jena: Gustav Fischer, pp. 58–59). The individual ontological foundation of population analysis was a self-evident presupposition in Johannsen’s studies of heredity in populations from their start in the early 1890s till his death in 1927. The claim that there was a “substantial but cautious modification of Johannsen’s phenotype–genotype distinction” (Churchill, 1974, p. 24) from a statistical to an individual ontological perspective derives from a misreading of the 1903 and 1909 texts. The immediate purpose of this paper is to correct this reading of the 1903 monograph by showing how its problems and results grow out of Johannsen’s earlier work in heredity and plant breeding. Johannsen presented his famous selection experiment as the culmination of a line of criticism of orthodox Darwinism by William Bateson, Hugo de Vries, and others (Johannsen, 1903). They had argued that evolution is based on stepwise rather than continuous change in heredity. Johannsen’s paradigmatic experiment showed how stepwise variation in heredity could be operationally distinguished from the observable, continuous morphological variation. To test Galton’s law of partial regression, Johannsen deliberately chose pure lines of self-fertilizing plants, a pure line being the descendants in successive generations of one single individual. Such a population could be assumed to be highly homogeneous with respect to hereditary type, and Johannsen found that selection produced no change in this type. Galton, he explained, had experimented with populations composed of a number of stable hereditary types. The partial regression which Galton found was simply an effect of selection between types, increasing the proportion of some types at the expense of others.     

Differentiation and adaptation in <Emphasis Type="Italic">Brassica nigra</Emphasis> populations: interactions with related herbivores

Local adaptation and population differentiation of plants are well documented, but studies on interactions with natural enemies are rare. In particular, evidence for plant adaptation to the local biotic environment, such as herbivores remains poor. We used the black mustard Brassica nigra, an annual species of river valley and coastal habitats to (1) analyse population differentiation in plant traits and herbivory in a common garden experiment, (2) examine home versus away differences in a reciprocal transplant experiment and (3) test whether plants are adapted to local herbivores or vice versa under standard greenhouse conditions. In the common garden experiment, we found significant differentiation in plant traits, leaf damage and herbivore number among seven populations of B. nigra from France and Germany (distance 15–1,000 km). Differences were particularly strong among coastal and river valley populations and did not necessarily increase with geographical distance. A herbivore removal treatment did not change population differentiation when compared with the control allowing natural colonisation. The reciprocal transplant experiment at a scale of 15–30 km did not reveal local plant adaptation, whilst one dominant herbivore species (Meligethes aeneus) occurred in significantly higher numbers on local plants. A greenhouse experiment combining three aphid (Brevicoryne brassicae) and plant populations of the same provenance indicated herbivore adaptation to their local plants rather than plant adaptation, but overall contrasts between local and non-local combinations were not significant. The results suggest that herbivores may counteract local plant adaptation to other environmental factors. Our study has important implications for plant translocations in ecological restoration projects.     

Natural Selection with Nuclear and Cytoplasmic Transmission. III. Joint Analysis of Segregation and Mtdna in Drosophila Melanogaster

Despite the widespread use of mitochondrial DNA by evolutionary geneticists, relatively little effort has been spent assessing the magnitude of forces maintaining mtDNA sequence diversity. In this study the influence of cytoplasmic variation on viability in Drosophila was examined by analysis of second chromosome segregation. A factorial experiment with balancer chromosomes permitted the effects of cytoplasma and reciprocal crosses to be individually distinguished. The first test used six lines of diverse geographic origin, testing the segregation of all six second chromosomes in all six cytoplasms. The second and third tests were also factorial designs, but used flies from one population in central Pennsylvania. The fourth test was a large chain cross, using 28 lines from the same Pennsylvania population. Only the first test detected a significant nuclear-cytoplasmic effect. Restriction site variation in the mtDNA of all of these lines was assayed by Southern blotting, and statistical tests were performed in an effort to detect an influence of mtDNA type on fitness components. Posterior linear contrasts revealed an effect of mtDNA on segregation only among lines of diverse geographic origin. Within a population, no such influence was detected, even though the experiment was sufficiently large to have revealed statistical significance of a 0.5% segregation difference with a 57% probability.     

The Exact Test for Cytonuclear Disequilibria

We extend the analysis of the statistical properties of cytonuclear disequilibria in two major ways. First, we develop the asymptotic sampling theory for the nonrandom associations between the alleles at a haploid cytoplasmic locus and the alleles and genotypes at a diploid nuclear locus, when there are an arbitrary number of alleles at each marker. This includes the derivation of the maximum likelihood estimators and their sampling variances for each disequilibrium measure, together with simple tests of the null hypothesis of no disequilibrium. In addition to these new asymptotic tests, we provide the first implementation of Fisher's exact test for the genotypic cytonuclear disequilibria and some approximations of the exact test. We also outline an exact test for allelic cytonuclear disequilibria in multiallelic systems. An exact test should be used for data sets when either the marginal frequencies are extreme or the sample size is small. The utility of this new sampling theory is illustrated through applications to recent nuclear-mtDNA and nuclear-cpDNA data sets. The results also apply to population surveys of nuclear loci in conjunction with markers in cytoplasmically inherited microorganisms.     

Statistical measures on residue-level protein structural properties

The atomic-level structural properties of proteins, such as bond lengths, bond angles, and torsion angles, have been well studied and understood based on either chemistry knowledge or statistical analysis. Similar properties on the residue-level, such as the distances between two residues and the angles formed by short sequences of residues, can be equally important for structural analysis and modeling, but these have not been examined and documented on a similar scale. While these properties are difficult to measure experimentally, they can be statistically estimated in meaningful ways based on their distributions in known proteins structures. Residue-level structural properties including various types of residue distances and angles are estimated statistically. A software package is built to provide direct access to the statistical data for the properties including some important correlations not previously investigated. The distributions of residue distances and angles may vary with varying sequences, but in most cases, are concentrated in some high probability ranges, corresponding to their frequent occurrences in either α-helices or β-sheets. Strong correlations among neighboring residue angles, similar to those between neighboring torsion angles at the atomic-level, are revealed based on their statistical measures. Residue-level statistical potentials can be defined using the statistical distributions and correlations of the residue distances and angles. Ramachandran-like plots for strongly correlated residue angles are plotted and analyzed. Their applications to structural evaluation and refinement are demonstrated. With the increase in both number and quality of known protein structures, many structural properties can be derived from sets of protein structures by statistical analysis and data mining, and these can even be used as a supplement to the experimental data for structure determinations. Indeed, the statistical measures on various types of residue distances and angles provide more systematic and quantitative assessments on these properties, which can otherwise be estimated only individually and qualitatively. Their distributions and correlations in known protein structures show their importance for providing insights into how proteins may fold naturally to various residue-level structures.     

The distribution of selenium and mortality owing to acquired immune deficiency syndrome in the continental United States

A hypothesis has been proposed that Selenium (Se) concentration in the environment as measured by its uptake by alfalfa, which sorbs Se from the soil in proportion to what is present, exerted an apparent effect on incidence of (acquired immune deficiency syndrome) AIDS such that AIDS’ mortality within the conterminous United States was lower where the Se quantity in the soil was high than where the amount was low. The object of this study was to test this hypothesis for statistical significance and to discover whether the apparent pattern of AIDS mortality in relation to Se distribution holds true with respect to all ages, both races (Black and White), and both genders. The statistical analysis employed was analysis of variance. Age-specific data as well as age-adjusted data were subject to statistical analysis. Ages where AIDS mortality rates per 100,000 were greatest were in the range from 25–54 yr for low-, medium-, and high-Se areas of the US. Black mortality owing to AIDS showed highly statistically significant results for the three Se regions, both genders, and six age groups, whereas white mortality was not as significantly affected by Se. A hypothesis is proposed that the Black population during the last decade or so has been less migratory than the White population. Thus, their food supply and hence its Se content have been more stable than that of the White population, which is more prone to consume imported foods of unknown Se content and be more migratory. A second hypothesis is advanced that suggests that medical care is not equally available to the poor and especially poor Blacks. Black men and women die at a greater death rate than do Whites. This implies that a lack of medical care is the true cause. This article suggests that a pattern exists between the geographical distribution of Se using alfalfa as a dietary guide and AIDS’ mortality such that an inverse relationship persists between Se quantity in an area and AIDS’ mortality in the same area.     

A theory of speech perception: II

The author’s theory of speech perception, as applied to time-dependent speech sounds, leads to many testable predictions. While some of these predictions are consistent with conventional knowledge, others are new and quite unexpected. A few are in contradiction to long accepted experimental results. A computer-aided experimental program, designed to test the theory, wholly supported these predictions. In view of this outcome, it seems desirable to test other predictions of the theory and to reexamine some conventionally accepted views in order to arrive at a more comprehensive theory of speech. The present findings indicate that, apart from categorization, consonants are similar to vowels: they exhibit parallel organizations and transformation properties. Supported by National Aeronautics and Space Administration’s Electronics Research Center, Cambridge, under Contract NAS-12-129. The first part of the work appeared inBull. Math. Biophysics, Vol.,29, 793–825, 1967.     

Local Adaptation and the Effects of Isolation and Population Size – the Semelparous Perennial <Emphasis Type="Italic">Carlina vulgaris</Emphasis> as a Study Case

We made a reciprocal transplantation experiment with Carlina vulgaris, among 12 semi-natural grassland sites situated in southwest Sweden. The fate of seeds and seedlings were followed during 2 years. Local adaptation was investigated both by native superiority over non-natives, and by comparing the observed performance of a population to the fitted value of a reduced statistical model that showed the populations’ performance at all sites and the performance of all other populations at its home site. The latter method indicates presence of local adaptation even when natives are inferior to introduced populations as long as the negative difference in fitness between the populations is smaller at the native population’s home site. The strength of local adaptation was measured as the ratio of the observed to the expected performance in reduced statistical models and regressed on the degree of isolation and population size. We found no evidence of local adaptation in terms of native superiority compared to non-natives, but with the relative method we found one of six fitness components, juvenile survival, to be 6% higher for natives at their home sites compared to how they performed at other sites and how others performed at their site. Further, our results indicate that both isolation and population size have a positive effect on the process of local adaptation. Co-ordinating editor: J. Tuomi     

Space–time patterns during the establishment of a nonindigenous species

Increasing rates of global trade and travel have the invariable consequence of an increase in the likelihood of nonindigenous species arrival, and some new arrivals are successful in establishing themselves. Quantifying the pattern of establishment of nonindigenous species across both spatial and temporal scales is paramount in early detection efforts, yet very difficult to accomplish. Previous work in epidemiology has proposed methods for assessing the space–time properties of emerging infectious diseases by quantifying the degree of space–time clustering between individual cases. I tested the applicability of one such method commonly used in epidemiology, the Knox test for space–time interaction, to analyze rare abundance data from an isolated, newly-establishing gypsy moth, Lymantria dispar, population in Minnesota, USA, and incorporated a bootstrap approach to quantify the space–time pattern in a random process that can be used to compare with results from empirical data. The use of the Knox test in assessing the establishment phase of biological invasions could potentially serve as an early warning system against new invaders, particularly for those with a known history of a repeated number of arrivals.     

Population persistence in the face of advection

Many populations live in ‘advective’ media, such as rivers, where flow is biased in one direction. In these environments, populations face the possibility of extinction by being washed out of the system, even if the net reproductive rate (R) is greater than one. We propose a formal condition for population persistence in advective systems: a population can persist at any location in a homogeneous habitat if and only if it can invade upstream. This leads to a remarkably simple recipe for calculating the minimal value for the net reproductive rate for population persistence. We apply this criterion to discrete-time models of a semelparous population where dispersal is characterized by a mechanistically derived kernel. We demonstrate that persistence depends strongly on the form of the kernel’s ‘tail’, a result consistent with previous literature on the speed of spread of invasions. We apply our theory to models of stream invertebrates with a biphasic life cycle, and relate our results to the ‘colonization cycle’ hypothesis where bias in downstream drift is offset by upstream bias in adult dispersal. In the absence of bias in adult dispersal, variability in the duration of the larval stage and in oviposition sites have a large effect of the persistence condition. The minimization calculations required in our approach are very straightforward, indicating the feasibility of future applications to life history theory.