Classification into one of several populations with allowance to unequal covariances

Given m independent sets of observations from each of K-variate normal distributions, the program: (1) tests the assumption of equality of covariances among groups; (2) searches for regions with homogeneous covariances; (3) estimates discrimination parameters and allocates observations; (4) evaluates the allocation procedure by calculating the misclassification matrix whose i, j entry is the number of data points that actually belong to group i and were classified into group j(i, j = 1, ...., m).     

Estimation of Fitness Components in DROSOPHILA MELANOGASTER . I. Heterozygote Viability Indices

We examine the assumption of "dominance" with regard to viability of the Cy and Pm marker chromosomes in D. melanogaster . This assumption is often invoked for the extraction of wild-type second chromosomes from natural populations and for the calculation of relative viability indices. Significant genotypic variances for viability are found among both Cy/+_j and Pm/+_i heterozygotes in California and Japanese populations. The magnitude of the Pm/+ _i genotypic variance is substantially less than that of the Cy/+_j heterozygotes (less than one half). Significant reciprocal effects are also found to influence Cy/+_j, Pm/+_i and +_i/+_j viabilities. We conclude that viability indices of heterozygotes based on the Curly method are biased. We suggest that viability indices in the future be expressed relative to the viability of the Cy/Pm genotype (Curly-Plum method) or possibly that of the Pm/+_i genotype (Plum method).     

Reliability of gene expression ratios for cDNA microarrays in multiconditional experiments with a reference design

In a typical gene expression profiling experiment with multiple conditions, a common reference sample is used for co-hybridization with the samples to yield expression ratios. Differential expression for any other sample pair can then be calculated by assembling the ratios from their hybridizations with the reference. In this study we test the validity of this approach. Differential expression of a sample pair (i, j) was obtained in two ways: directly, by hybridizations of sample i versus j, and indirectly, by multiplying the expression ratios for hybridizations of sample i versus pool and pool versus sample j. We performed gene expression profiling using amphibian embryos (Xenopus laevis). Every sample combination of four different stages and a pool was profiled. Direct and indirect values were compared and used as the quality criterion for the data. Based on this criterion, 82% of all ratios were found to be sufficiently accurate. To increase the reliability of the signals, several widely used filtering techniques were tested. Filtering by differences of repeated hybridizations was found to be the optimal filter. Finally, we compared microarray-based gene expression profiles with the corresponding expression patterns obtained by whole-mount in situ hybridizations, resulting in a 90% correspondence.     

Ligation of EcoRI endonuclease-generated DNA fragments into linear and circular structures.

Double-stranded DNA fragments terminated at their 5′-ends by the singlestranded sequence pA-A-T-T-, generated by digestion of DNA with EcoRI restriction endonuclease, were ligated with Escherichia coli polynucleotide ligase under various conditions of temperature, concentration and time. The linear and circular products of ligation were separated by electrophoresis in agarose gel and quantitated by densitometry. The rate of ligation of (EcoRI-cleaved) simian virus (SV40) DNA at a concentration of 100 μg/ml increased from 0 °C to 5 °C to 10 °C (6-fold increase overall); raising the temperature to 15 °C did not further increase the rate of ligation. At the appropriate DNA concentrations, the predominant products of ligation are either linear concatemers that are integral multimers of the starting DNA fragment, or covalently closed circular structures of the monomeric DNA fragment. Ligating a mixture of two different length DNA fragments gives rise to all of the possible expected recombinant molecules.Linear or circular products of ligation were predicted by consideration of the total concentration of DNA termini, i, and the local concentration of one terminus in the neighborhood of the other on the same DNA molecule, j. The parameter j is a function of the length of a DNA molecule, providing this length is greater than the random coil segment of DNA. Experimentally it was found that circular structures are formed in significant amounts only under conditions when the value of j is several times greater than that of i. When j = i, equal amounts of linear and circular products would be expected, but most of the molecules were ligated into linear concatemers. No circular structure of a DNA fragment whose contour length l (6 × 10⁻² μm) is smaller than the random coil segment value b (7·17 × 10⁻² μm) was observed, while circular structures of the dimer of the same molecule (12 × 10⁻² μm) were detected.     

Generalization of Human Fear Acquisition and Extinction within a Novel Arbitrary Stimulus Category

Adaptive anxiety relies on a balance between the generalization of fear acquisition and fear extinction. Research on fear (extinction) generalization has focused mostly on perceptual similarity, thereby ignoring the importance of conceptual stimulus relations in humans. The present study used a laboratory procedure to create de novo conceptual categories of arbitrary stimuli and investigated fear and extinction generalization among these stimuli. A matching-to-sample task produced two four-member categories of abstract figures. Next, a member from one category was coupled with an aversive electrical stimulation, while a member from the other category was presented alone. As expected, conditioned fear responses generalized to the other members of the first category (skin conductance and online shock-expectancy). Subsequent extinction of the conditioned member also generalized to the other members. However, extinguishing a non-conditioned member failed to reduce fear of the conditioned member itself. We conclude that fears generalize readily across conceptually related stimuli, but that the degree of extinction generalization depends on the stimulus subjected to extinction.     

Linear Diagonals‐Parameter Symmetry and Quasi‐Symmetry Models for Cumulative Probabilities in Square Contingency Tables with Ordered Categories

For the analysis of square contingency tables with ordered categories, Caussinus (1965) considered the quasi‐symmetry (QS) model, Goodman (1979) considered the diagonals‐parameter symmetry (DPS) model, and Agresti (1983) considered the linear diagonals‐parameter symmetry (LDPS) model. These models show the structures of symmetry for cell probabilities. Tomizawa (1993) proposed another DPS model which has a similar multiplicative form for cumulative probabilities that an observation will fall in row (column) category i or below and column (row) category j (>i) or above. This paper proposes another LDPS and QS models that have the corresponding similar multiplicative forms for cumulative probabilities instead of cell probabilities. Special cases of the proposed models include symmetry. Two kinds of unaided distance vision data and endometrial cancer data are analyzed using these models. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hierarchical structure and the influence of individual attributes in the captive squirrel monkey (<Emphasis Type="Italic">Saimiri collinsi</Emphasis>)

The dominance structure of primate social groups varies widely. In addition to the groups’ composition, intrinsic attributes such as sex, body size and life experience are important factors that can affect hierarchical dominance relations. All primates are social animals, and the social environment has a direct influence on the physiological conditions of vital systems such as immunological, reproductive and cardiovascular systems. In this study, we analyze the hierarchical structure of Saimiri collinsi in captivity, including the hierarchical structure type, the influence of individual intrinsic characteristics (sex, age, weight and origin—born in captivity or in the wild) based on the prior-attributes model, the relation between agonistic behavior frequency and hierarchical position, and hierarchy steepness, which represents the dominance gradient. We found that the group order was characterized by a partial hierarchy: a dominance position could be occupied by more than one individual simultaneously, including individuals of both sexes. Intrinsic characteristics had no influence on hierarchical structure, with the exception of the male in the highest hierarchical position, which had a markedly larger body than all other group members. Thus, the prior-attributes model did not apply to hierarchical formation of S. collinsi in captivity. Only the frequency of agonistic behavior of males correlated with their hierarchical position, and they differed from all other group members in their more aggressive behavior. The steepness between adjacent positions along the dominance gradient was significant only between the dominant male and the next individual in the group, with a smooth gradient between the other positions in the rank. As the access to resources is directly related to hierarchical dominance, a smooth dominance gradient is to be expected in species that form very large groups, such as wild Saimiri populations.     

Specialization in phagocytosis

When phagocytes have been incubated with a mixture of two types of particles (say A and B), a microscopic count can be made of cells having ingested iA-particles and jB-particles, for various i and j. Simple assumptions (the validity of which has been checked in a previous work) allow derivation of formulae that give a fair account of experimental results.Only such a quantitative study can determine whether there is a specialization among phagocytic cells, which question is of great immunological interest.     

A probability distribution model of small -scale species richness in plant communities

We devised a probability distribution model that best expressed species richness per quadrat in grassland communities, and clarified the mechanism by which the mean richness per quadrat was always larger than the variance among quadrats. Our model will aid in the understanding of community structures, and allow comparisons among different communities. The model was constructed based on relatively simple theoretical assumptions about the mechanisms in play in target communities. We assumed in the model that the number of species occurring in an actual quadrat, j, is the sum of “the fundamental number of species”, k (constant), and “a fluctuating number of species”, i (a Poisson variate with the mean of μ); that is, j = k + i, where i, j and k are non-negative integers. The probability that j species occur in a quadrat is given by a Poisson-like distribution (extended Poisson), with two parameters k and μ. The mean species richness in the probability distribution is expressed by λ (= k + μ), and the variance is λ − k. The proposed model afforded a good fit for the observed frequency distribution of species richness per quadrat. If even one species is common among many quadrats, the mean number of species per quadrat is greater than the variance. The greater the number of common species among quadrats is, the larger is the value of k, and then the more pronounced is the difference between the mean and the variance (although the variance does not change). We fitted the model to 55 datasets collected by ourselves from grasslands in various locations (Tibet, Inner Mongolia, Slovakia, or Japan), with varying quadrat size (0.25, 0.0625, or 0.01 m²), and under differing management status (various stocking densities).     

Fixation probabilities and effective population numbers in diploid populations with overlapping generations

A finite diploid population, observed at times t = 0, 1, 2,…, is studied. An individual is said to be in age group i at time t if its age is between i and i + 1 units at that time, where i ? 1. It is assumed that the number of individuals in a particular age-sex class is the same for every t and that the probability that a male offspring was produced by a mating of a male in age group i and a female in age group j is p_ij^m (with a corresponding probability p^f_ij for a female offspring), regardless of when the individual is born. The probability of ultimate fixation of an allele A₁ and the inbreeding effective number, for large populations, is calculated under the further assumptions that A₁ is neutral and that mating is random, given the ages of the mates.     

Searching and gradualness

Consider the elements of the power set S as the alternatives in a search space. Each element of the set has a value and the goal of a search is to find an element with near-minimum value. If high-valued elements of cardinality i (recall that elements of S are themselves sets) are subsets of high-valued elements of cardinality i + 1, then the search space has a king of gradualness that should facilitate search.A search algorithm might generate a series, S′(1), … S′(k) of samples in S, where all the elements in S′ (i) have cardinality i. I propose a class of search algorithms, where each algorithm A(j) generates S′(i + 1) by emphasizing the j lowest-valued elements in S′(i). I then define search space gradualness and search algorithm performance and formally relate gradualness and performance.     

The functional responses of adaptive consumers of two resources

This article investigates some aspects of the shape of the functional responses of consumers that utilize two resources. Adaptive variation in consumption behavior is shown to have a major effect on the relationship between amount of resource available and its rate of consumption by an average consumer individual. The effects of adaptive variation are dependent on the nutritional status of the two resources. If the resources are linearly substitutable, increases in the density of resource i will usually increase the quantity, functional response on i divided by density of i, and increases in the density of resource j will decrease this quantity. The result is that the functional response to resource i will generally decrease with the density of resource j, and will increase faster than it would otherwise have increased with the density of resource i. If resources are nonsubstitutable, an adaptive functional response to resource i will increase with the density of resource j, and it will increase more slowly with the density of resource i than it would have without adaptive change. If resources are both complementary and substitutable, the functional response will exhibit ranges of smooth change separated by rapid jumps between values, and different ranges of resource densities will result in a functional response with the characteristics of linearly substitutable or of non-substitutable resources. Adaptive functional response shape is dependent upon the tradeoff involved in raising each functional response. These results have implications for the types of indirect interactions that occur between resources as the result of a common consumer's functional response. They also suggest that the adaptive response of competing consumers to each other will differ depending on the nutritional status of the resources for which they are competing. Implications of these findings for consumer growth isocline shape and several other issues are explored.     

Allele frequencies in multidimensional Wright-Fisher models with a general symmetric mutation structure

The diffusion form of a multiple-allele Wright-Fisher model of allele frequencies of types A₁,…,A_K at a neutral locus where there are general symmetric mutation rates of M_ij (=M_ji) from A_i → A_j is studied. A convenient recurrence relationship for the moments of linear forms in the allele frequencies is found. A formula is derived for the expected homozygosity in the transient and stationary models, which is applied to general stepwise mutation models where mutation over more than one step is possible. The probability that two randomly chosen genes are j steps apart at time t in the stepwise mutation model is found to have a reasonably simple form if conditioning is on the initial allele frequencies arranged in order of magnitude. Of interest is a new geometric charge state model, mutation over several steps roughly corresponding to independent charge changes. The expected homozygosity and expected distance between two randomly chosen genes is tabulated in this model.     

To grow or not to grow? Intermediate and paratenic hosts as helminth life cycle strategies

Larval helminths in intermediate hosts often stop growing long before their growth is limited by host resources, and do not grow at all in paratenic hosts. We develop our model [Ball, M.A., Parker, G.A., Chubb, J.C., 2008. The evolution of complex life cycles when parasite mortality is size- or time-dependent. J. Theor. Biol. 253, 202-214] for optimal growth arrest at larval maturity (GALM) in trophically transmitted helminths. This model assumes that on entering an intermediate host, larval death rate initially has both time- (or size-) dependent and time-constant components, the former increasing as the larva grows. At GALM, mortality changes to a new and constant rate in which the size-dependent component is proportional to that immediately before GALM. Mortality then remains constant until death or transmission to the definitive host. We analyse linear increasing and accelerating forms for time-dependent mortality to deduce why there is sometimes growth (intermediate hosts) and sometimes no growth (paratenic hosts). Calling i the intermediate or paratenic host, and j the definitive host, conditions favouring paratenicity are: (i) high values in host i for size at establishment, size-related mortality, expected intensity, (ii) low values in host i for size-independent mortality rate, potential growth rate, transmission rate to j, and ratio of death rate in j/growth rate in j. Opposite conditions favour growth in the (intermediate) host, either to GALM or until death without GALM. We offer circumstantial evidence from the literature supporting some of these predictions. In certain conditions, two of the three possible growth strategies (no growth; growth to an optimal size then growth arrest (GALM); unlimited growth until larval death) can exist as local optima. The effect of the discontinuity in death rate after GALM is complex and depends on mortality and growth parameters in the two hosts, and on the mortality functions before and after GALM.     

A new approach to the investigation on the tonogenic groups of root cell walls

Acid-base properties of wheat, lupin, pea root cell walls were investigated. The roots of etiolated and green plants of different age were analysed by the potentiometric method. The ion exchange capacity of root cell walls (S_i) was estimated at various pH values (pH_i 2 to pH_i 12) and constant ion strength of the solution (10 mM). To analyse polysigmoid curves pH_i =f (S_i), Gregor's equation was used. It was shown that Gregor's model fits fairly well the experimental data. The total quantities of cation-exchange (S_t ^cat) and anion-exchange (S_t ^an) groups were determined in the root cell walls. It was shown that the quantity of anion exchange groups is varied through a small range (60–185 μmol/g dry wt.) in plant species tested, and that the S_t ^cat differs widely from 550 to 1300 μmol/g dry wt. For leguininous plants the quantity of acidic groups (fixed anions) is nearly twice as large as that for cereals. It was found that in seedlings as well as in plants, there are 3 cation-exchange groups and one anion-exchange group in root cell walls. The quantity of functional groups of each type (S^j) was estimated, and the corresponding values of n^j and pK_a ^j were calculated. It can be assumed that the groups with the pK_a ¹ ≈ 3.2 are amine groups, the ones with PK_a ² ≈ 5 are groups of galacturonic acid, the ones with pK_a ≈ 7.5 are the carboxyl groups of the second species, and the ones with pK_a ⁴ ≈ 40 are the phenolic groups. The values of dissociation constants (pK_a ^j) and S^j indicate that the root cell walls of wheat, lupin and pea are identical in qualitative structure of ionogenic groups but vary in the quantity of each ionogenic group. It was demonstrated that the summarized quantity of carboxyl groups (S² + S³) should be connected directly with the pH gradient in the extracellar space at the membrane surface. The gradient arises from ion-exchange reactions between cations of an outer medium and protons of the ionized carboxyl groups of the cell walls. The results suggest that, S_t ^cat and S_t ^an allow the quantitative estimation of ion exchange properties of the cell walls. The resulting parameters (S^j, pK_a ^j and n^j) allow prediction of changes in an ionic composition of a medium that bathes the cell membrane, during the first step of mineral nutrition uptake. This revised version was published online in June 2006 with corrections to the Cover Date.     

Polyandry: the history of a revolution

We give a historic overview and critical perspective of polyandry in the context of sexual selection. Early approaches tended to obfuscate the fact that the total matings (copulations) by the two sexes is equal, neglecting female interests and that females often mate with (or receive ejaculates from) more than one male (polyandry). In recent years, we have gained much more insight into adaptive reasons for polyandry, particularly from the female perspective. However, costs and benefits of multiple mating are unlikely to be equal for males and females. These must be assessed for each partner at each potential mating between male i and female j, and will often be highly asymmetric. Interests of i and j may be in conflict, with (typically, ultimately because of primordial sex differences) i benefitting and j losing from mating, although theoretically the reverse can also obtain. Polyandry reduces the sex difference in Bateman gradients, and the probability of sexual conflict over mating by: (i) reducing the potential expected value of each mating to males in inverse proportion to the number of mates per female per clutch, and also often by (ii) increasing ejaculate costs through increased sperm allocation. It can nevertheless create conflict over fertilization and increase conflict over parental investment. The observed mean mating frequency for the population (and hence the degree of polyandry) is likely, at least in part, to reflect a resolution of sexual conflict. Immense diversity exists across and within taxa in the extent of polyandry, and views on its significance have changed radically, as we illustrate using avian polyandry as a case study. Despite recent criticisms, the contribution of the early pioneers of sexual selection, Darwin and Bateman, remains generally valid, and should not, therefore, be negated; as with much in science, pioneering advances are more often amplified and refined, rather than replaced with entirely new paradigms.     

Validation of previous computer models and MD simulations of discoidal HDL by a recent crystal structure of apoA-I

HDL is a population of apoA-I-containing particles inversely correlated with heart disease. Because HDL is a soft form of matter deformable by thermal fluctuations, structure determination has been difficult. Here, we compare the recently published crystal structure of lipid-free (Δ185-243)apoA-I with apoA-I structure from models and molecular dynamics (MD) simulations of discoidal HDL. These analyses validate four of our previous structural findings for apoA-I: i) a baseline double belt diameter of 105 Å ii) central α helixes with an 11/3 pitch; iii) a “presentation tunnel” gap between pairwise helix 5 repeats hypothesized to move acyl chains and unesterified cholesterol from the lipid bilayer to the active sites of LCAT; and iv) interchain salt bridges hypothesized to stabilize the LL5/5 chain registry. These analyses are also consistent with our finding that multiple salt bridge-forming residues in the N-terminus of apoA-I render that conserved domain “sticky.” Additionally, our crystal MD comparisons led to two new hypotheses: i) the interchain leucine-zippers previously reported between the pair-wise helix 5 repeats drive lipid-free apoA-I registration; ii) lipidation induces rotations of helix 5 to allow formation of interchain salt bridges, creating the LCAT presentation tunnel and “zip-locking” apoA-I into its full LL5/5 registration.