Neutral stability in many-species food webs

The predator-prey systems of Lotka and Volterra are modified to include efficiencies e_ij of converting prey biomass to predator biomass. For three or more species, it is shown that neutral stability results if e_ik = e_ije_jk for all transfers. When the number of species is odd, consistency of the differential equation system for changes in logarithms of biomass is also required.     

Cellular sodium transport in arterial wall - summary of studies by digital computer simulation

The distribution of electrolytes between extracellular and intracellular compartments is of greater functional significance in biological tissues than the total amount. A method commonly employed for the study of a substance distribution among different spaces is the continuous outflow and radioisotope counting of a fragment of tissue previously incubated with a radioactive tracet (here ²²Na⁺). The experimental data can be analyzed within the frame of a compartmental analysis system which is defined by transport rate constants (k_ij) and solved when all k_ij are numerically determined.In practical applications the direct solution requires measurements in different compartments or knowledge of the initial condition for each compartment, but this is not possible in most biological tissues where the experimentally observable data represent the summation of tracer in all compartments at each point in time. The availability of the SAAM (Simulation, Analysis And Modelling) computer program allows for a powerful simulation procedure to arrive at values for k_ij. Experimental data and specifications for a chosen model are entered in the SAAM format. A simulated ‘inflow’ experiment is mde by the computer by assigning to k_ij some estimate values. All initial conditions are now zero, since at the beginning there is no radioactive tracer in any compartment. After a time equivalent in the experimental realm to achieving constant specific activity, a ‘time change’ programmed into the computer takes place so that the outflow part of the experiment is developed with the same k_ij as for the inflow part, the final conditions for the inflow before the time change being the initial conditions for the outflow. An iterative procedure modifies the initial estimates of k_ij to seek the best fit.By coupling a powerful simulation procedure to an advanced radionuclide tracer biological methodology, we have been able to find effects of the hormone aldosterone and of experimental hypertension on Na⁺ distribution in arterial wall years before such effects were demonstrated by purely conventional experimental techniques. This computer simulation procedure may be suited to other experimental situations in which outflow data are the only available.     

The Rücker–Markov invariants of complex Bio-Systems: Applications in Parasitology and Neuroinformatics

Rücker's walk count (WC) indices are well-known topological indices (TIs) used in Chemoinformatics to quantify the molecular structure of drugs represented by a graph in Quantitative structure–activity/property relationship (QSAR/QSPR) studies. In this work, we introduce for the first time the higher-order (kth order) analogues (WC_k) of these indices using Markov chains. In addition, we report new QSPR models for large complex networks of different Bio-Systems useful in Parasitology and Neuroinformatics. The new type of QSPR models can be used for model checking to calculate numerical scores S(L_ij) for links L_ij (checking or re-evaluation of network connectivity) in large networks of all these fields. The method may be summarized as follows: (i) first, the WC_k(j) values are calculated for all jth nodes in a complex network already created; (ii) A linear discriminant analysis (LDA) is used to seek a linear equation that discriminates connected or linked (L_ij = 1) pairs of nodes experimentally confirmed from non-linked ones (L_ij = 0); (iii) The new model is validated with external series of pairs of nodes; (iv) The equation obtained is used to re-evaluate the connectivity quality of the network, connecting/disconnecting nodes based on the quality scores calculated with the new connectivity function. The linear QSPR models obtained yielded the following results in terms of overall test accuracy for re-construction of complex networks of different Bio-Systems: parasite–host networks (93.14%), NW Spain fasciolosis spreading networks (71.42/70.18%) and CoCoMac Brain Cortex co-activation network (86.40%). Thus, this work can contribute to the computational re-evaluation or model checking of connectivity (collation) in complex systems of any science field.     

Parental contribution and coefficient of coancestry among maize inbreds: pedigree, RFLP, and SSR data

The genetic relationship between inbreds i and j can be estimated from pedigree or from molecular marker data. The objectives of this study were to: (1) determine whether pedigree, restriction fragment length polymorphism (RFLP), and simple sequence repeat (SSR) data give similar estimates of parental contribution and coefficient of coancestry (f _ij ) among a set of maize (Zea mays L.) inbreds, and (2) compare the usefulness of RFLP and SSR markers for estimating genetic relationship. We studied 13 maize inbreds with known pedigrees. The inbreds were genotyped using 124 RFLP and 195 SSR markers. For each type of marker, parental contributions were estimated from marker similarity among an inbred and both of its parents, and were subsequently used to estimate f _ij . Estimates of parental contribution differed significantly (α<0.05) between pedigree data and either type of marker, but not between the marker systems. The RFLP estimates of parental contribution failed to sum to 1.0, reflecting a higher frequency of non-parental bands with RFLP than with SSR markers. The f _ij estimated from pedigree, RFLP, and SSR data were highly correlated (r=0.87–0.97), although significant differences were found among the three sets of f _ij estimates. We concluded that pedigree and marker data often lead to different estimates of parental contribution and f _ij , and that SSR markers are superior to RFLP markers for estimating genetic relationship. A relevant question is whether or not the inbreds previously genotyped with an older marker system (e.g., RFLP) need to be re-analyzed with a newer marker system (e.g., SSR) for the purpose of estimating genetic relationship. Such re-analysis seems unnecessary if data for the same type of marker are available for a given inbred and both of its parents. Received: 2 June 1999 / Accepted: 30 July 1999     

Estimation of a Conditional Mean in a Linear Regression Model

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_il X_ij + ε_ij,j = 1,2,…,n_i, i = 1,2, where ε_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The estimated value of a mean of Y₁ for a given value of X₁ is made to depend on a preliminary test of significance of the hypothesis β₁₁ = β₂₁. The bias and the mean square error of the estimator for the conditional mean of Y₁ are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.     

Statistical Distance as a Measure of Physiological Dysregulation Is Largely Robust to Variation in Its Biomarker Composition

Physiological dysregulation may underlie aging and many chronic diseases, but is challenging to quantify because of the complexity of the underlying systems. Recently, we described a measure of physiological dysregulation, D_M, that uses statistical distance to assess the degree to which an individual’s biomarker profile is normal versus aberrant. However, the sensitivity of D_M to details of the calculation method has not yet been systematically assessed. In particular, the number and choice of biomarkers and the definition of the reference population (RP, the population used to define a “normal” profile) may be important. Here, we address this question by validating the method on 44 common clinical biomarkers from three longitudinal cohort studies and one cross-sectional survey. D_Ms calculated on different biomarker subsets show that while the signal of physiological dysregulation increases with the number of biomarkers included, the value of additional markers diminishes as more are added and inclusion of 10-15 is generally sufficient. As long as enough markers are included, individual markers have little effect on the final metric, and even D_Ms calculated from mutually exclusive groups of markers correlate with each other at r~0.4-0.5. We also used data subsets to generate thousands of combinations of study populations and RPs to address sensitivity to differences in age range, sex, race, data set, sample size, and their interactions. Results were largely consistent (but not identical) regardless of the choice of RP; however, the signal was generally clearer with a younger and healthier RP, and RPs too different from the study population performed poorly. Accordingly, biomarker and RP choice are not particularly important in most cases, but caution should be used across very different populations or for fine-scale analyses. Biologically, the lack of sensitivity to marker choice and better performance of younger, healthier RPs confirm an interpretation of D_M physiological dysregulation and as an emergent property of a complex system.     

Limiting similarity and the form of the competition coefficient

The question of whether there is a limit to the similarity of competing species has previously been investigated by a number of authors. These studies have all used the Lotka-Volterra model of competition, and have assumed that the competition coefficient α_ij may be calculated using the expression, α_ij = ∝ U_i(R) U_j(R) dR/∝ (U_i(R))² dR. In this paper, the generality of this formula is questioned and two alternative expressions for α_ij are proposed. When these expressions are used in an analysis of limiting similarity, qualitatively different conclusions emerge regarding the existence and nature of this limit, using either deterministic or stochastic models. The relevance of these findings to theories of character convergence and similarity barriers is discussed. The available field evidence does not strongly support the validity of the formula for α_ij used in previous studies. Since a given method of calculating α_ij must be derived from a higher level model, it is suggested that the Lotka-Volterra model is not sufficient in an investigation of limiting similarity.     

Competition and overlap of Oryzaephilus surinamensis and Plodia interpunctella populations under condition of stored date fruits

Plodia interpunctella and Oryzaephilus surinamensis are found in food storehouses including dates and palm storages. The current study aimed to determine competition and overlap potentials of the two pests of date fruits. Time series models were used to study two species populations and logistic growth model to estimate the effect of density of the species. The results revealed the environmental capacities of O. surinamensis and P. interpunctella were 433 and 1610 (maximum number per 20 g), respectively, and the population growth rates (r) were 1.2 and 1.3, respectively. Ecological balances of the two species were close to each other from the first to the third week. The population of O. surinamensis decreased in the fourth week of the competition. The highest population balance of the two species was in the 14th week. The potential of exploitable ecological niches (e_ij) and the amount of non-exploited ecological niches by any species (z_ij) for O. surinamensis was higher than for P. interpunctella from the 8th week untill the end of sampling period. The overlap of ecological niches in the two species (D) ranged from 0.94 to 1, indicating a complete overlap of temporal activity in the two populations on date palm. The current results of this study can be used by integrated pest management specialists. Information over the effects of species competition on population dynamics and their coexistence can be used to predict population status and to adopt simple pest control methods.     

Dynamics of transitions between population interactions: a nonlinear interaction alpha-function defined

In nature, two populations may interact in different ways during their lifetime, and even undergo transitions from one type of interaction to another. A model for the dynamics of these transitions has been developed in this study. The interaction coefficients ɑ_ij in the Lotka–Volterra equations are re-interpreted as nonlinear functions of population densities N_i, N_j, modulated by environmental parameters, which offers the possibility of a change in sign. Transitions can take place owing to variations in population density (endogenous effect), or in the environmental parameters (exogenous effect). Models for both facultative and obligate associations are examined. Graphical stability analyses show that multiple density equilibria are possible, accounting for the occurrence of the transitions.     

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.     

Estimates of Inbreeding in a Natural Population: A Comparison of Sampling Properties

The average inbreeding coefficient f of a population can be estimated in several different ways based solely on the genotypic frequencies at a single locus. The means and variances of four different estimates have been compared. While the four estimates are equivalent when there are two alleles, the best estimates when there are three or more alleles are based upon total heterozygosity (see PDF) where x and y are the expected and observed number of heterozygotes) and the proportion of alleles that are homozygous (see PDF) where k = the number of alleles, a_ii = the number of A_iA_i homozygotes, and 2a_ij = the number of A_iA_j heterozygotes). Both are minimally biased estimates of f and have identical sampling variances when all alleles are equally frequent. However, when alleles have different frequencies, the choice between these two estimates depends on the gene frequencies and the true inbreeding coefficient of a population; f₂ is the best estimate when the true average inbreeding coefficient is suspected to be low or f = 0, while f₁ is best in populations with large average inbreeding coefficients. Approximate sampling variances of these two estimates are given for any f and any number of alleles with arbitrary gene frequencies; these approximations are accurate for samples as small as n = 100. The chi-square and maximum likelihood estimates of f are not as good for realistic sample sizes.     

Estimation of a Conditional Mean in a Linear Regression Model after a Preliminary Test on Regression Coefficient

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_ij, X_ij + E_ij = 1, 2,…, n_i, i = 1, 2, where E_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The problem of estimating the conditional mean of Y₁ for a given value of X₁ is considered when it is a priori suspected that β₁₀ = β₂₀ and β₁₁ = β₂₁. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β₁₀ = β₂₀ and β₁₁ = β₂₁.     

Repeated injection (continuous labelling) experiments in mouse epidermis

Theoretical labelling index curves for epidermis have been generated under conditions of repeated tritiated thymidine injection. These curves take into account different injection intervals, circadian fluctuations in labelling and two different models for epidermal proliferation; one based on a homogeneous basal layer with “random” loss initially (later, loss was restricted to late G₁), and the other based on a programmed sequential aging of proliferative cells in a compartment derived from a minority class of stem cells. These curves have been compared with previously published experimental results and with results from some new experiments. Both models fit the data to some extent provided a mean value of T_c of about 140 h is assumed. However, the sequential aging model provides a slightly better overall fit. A further conclusion is that it is impossible to make any accurate statements on the epidermal growth fraction from repeated labelling data.     

Evaluating sample allocation and effort in detecting population differentiation for discrete and continuously distributed individuals

One of the most pressing issues in spatial genetics concerns sampling. Traditionally, substructure and gene flow are estimated for individuals sampled within discrete populations. Because many species may be continuously distributed across a landscape without discrete boundaries, understanding sampling issues becomes paramount. Given large-scale, geographically broad conservation efforts, researchers are looking for guidance as to the trade-offs between sampling more individuals within a population versus few individuals scattered across more populations. Here, we conducted simulations that address these issues. We first established two archetypical patterns of dispersion: (1) individuals within discrete populations, and (2) continuously distributed individuals with limited dispersal. We used genotypes generated from a spatially-explicit, individual-based program and simulated genetic structure in individuals from nine different population sizes across a landscape that either had barriers to movement (defining discrete populations) or isolation-by-distance patterns (defining continuously distributed individuals). Then, given each pattern of dispersion, we allocated samples across four different sampling strategies for each of the nine population sizes in various configurations for sampling more individuals within a population versus fewer individuals scattered across more populations. We assessed the population genetic substructure with both the population-based metric, F _ST, and an individual-based metric, D _PS regardless of the true pattern of dispersion to allow us to better understand the effect of incorrectly matching the metric and the distribution (e.g., F _ST with continuously distributed individuals, and vice versa). We show that sampling many subpopulations (or sampling areas), thus sampling fewer individuals per subpopulation, overestimates measures of population subdivision with the population-based metric for both patterns of dispersion. In contrast, using the individual-based metric gives the opposite results: sampling too few subpopulations, and many individuals per subpopulation, produces an underestimate of the strength of isolation-by-distance. By comparing all results, we were able to suggest a strong predictive model of a chosen genetic structure metric for elucidating the sampling design trade-offs given each pattern of dispersion and configuration on the landscape.     

Aging and the metrics of time

In contrast to clock time, which is extrinsic, universal and reversible, age is an intrinsic, directed measure of the state of a particular system. It is proposed that if the dynamical equations of a given system are cast into canonical form, a time scale intrinsic to that system can be derived. The metric which converts a given intrinsic time to clock time is derived in terms of the given system's constitutive parameters. Age becomes a question of similitude, two systems being in corresponding states (i.e. at the same age) at identical instants of intrinsic time (not clock time).It is further proposed that there is an intrinsic time associated with any dissipative process and that the coupling coefficients, L_ik, of irreversible thermodynamics are metrics which scale the passage of intrinsic time to clock time as measured by a standard harmonic oscillator. Thus in addition to the long standing conjecture that entropy production determines the direction of time's arrow there also is a sense in which it determines the rate of its flow.     

Marker-based estimates of identity by descent and alikeness in state among maize inbreds

Molecular markers are useful for determining relationships and similarity among inbreds, especially if the proportion of marker loci with alleles common to inbreds i and j is partitioned into: (1) the probability that marker alleles are identical by descent (_Mf_ij); and (2) the conditional probability that marker alleles are alike in state, given that they are not identical by descent ( _ij). Our objectives were to: develop a method, based on tabular analysis of restriction fragment length polymorphism marker data, for estimating _Mf_ij, _ij, and the parental contribution to inbred progeny; validate the accuracy of the method with a simulated data set; and compare the pedigree-based coefficient of coancestry (f_ij) and _Mf_ij among a set of maize (Zea mays L.) inbreds. Banding patterns for 73 probeenzyme combinations were determined among 13 inbreds. Iterative estimation of _Mf_ij, _ij, and the parental contribution to progeny was performed with procedures similar to a tabular analysis of pedigree data. Deviations of _Mf_ij from pedigree-based f_ij ranged from 0.002 to 0.288, indicating large effects of selection and/or drift during inbreeding for some inbreds. Differences between marker-based estimates and expected values of parental contribution to inbred progeny were as large as 0.205. Results for a simulated set of inbreds indicated that tabular analysis of marker data provides more accurate estimates of _Mf_ij and _ij than other methods described in the literature. Tabular analysis requires the availability of marker data for all the progenitors of each inbred. When marker data are not available for the parents of a given inbred, _Mf_ij and _ij may still be calculated if parental contributions to the inbred are assumed equal to their expectations.     

Modeling of the phase equilibria of polystyrene in methylcyclohexane with semi-empirical quantum mechanical methods I

A method for calculating interaction parameters traditionally used in phase-equilibrium computations in low-molecular systems has been extended for the prediction of solvent activities of aromatic polymer solutions (polystyrene+methylcyclohexane). Using ethylbenzene as a model compound for the repeating unit of the polymer, the intermolecular interaction energies between the solvent molecule and the polymer were simulated. The semiempirical quantum chemical method AM1, and a method for sampling relevant internal orientations for a pair of molecules developed previously were used. Interaction energies are determined for three molecular pairs, the solvent and the model molecule, two solvent molecules and two model molecules, and used to calculated UNIQUAC interaction parameters, a _ij and a _ji . Using these parameters, the solvent activities of the polystyrene 90,000 amu+methylcyclohexane system, and the total vapor pressures of the methylcyclohexane+ethylbenzene system were calculated. The latter system was compared to experimental data, giving qualitative agreement. Figure Solvent activities for the methylcylcohexane(1)+polystyrene(2) system at 316 K. Parameters a _ij (blue line) obtained with the AM1 method; parameters a _ij (pink line) from VLE data for the ethylbenzene+methylcyclohexane system. The abscissa is the polymer weight fraction defined as ₂(x ₁)=(1–x ₁)M ₂/[x ₁ M ₁+(1–x ₁)M ₂], where x ₁ is the solvent mole fraction and M _i are the molecular weights of the components.An erratum to this article can be found at     

Evolution of the rate of biological aging using a phenotype based computational model

In this work I introduce a simple model to study how natural selection acts upon aging, which focuses on the viability of each individual. It is able to reproduce the Gompertz law of mortality and can make predictions about the relation between the level of mutation rates (beneficial/deleterious/neutral), age at reproductive maturity and the degree of biological aging. With no mutations, a population with low age at reproductive maturity R stabilizes at higher density values, while with mutations it reaches its maximum density, because even for large pre-reproductive periods each individual evolves to survive to maturity. Species with very short pre-reproductive periods can only tolerate a small number of detrimental mutations. The probabilities of detrimental (P_d) or beneficial (P_b) mutations are demonstrated to greatly affect the process. High absolute values produce peaks in the viability of the population over time. Mutations combined with low selection pressure move the system towards weaker phenotypes. For low values in the ratio P_d/P_b, the speed at which aging occurs is almost independent of R, while higher values favor significantly species with high R. The value of R is critical to whether the population survives or dies out. The aging rate is controlled by P_d and P_b and the amount of the viability of each individual is modified, with neutral mutations allowing the system more “room” to evolve. The process of aging in this simple model is revealed to be fairly complex, yielding a rich variety of results.     

Are two better than one? Analysis of an FtsK/Xer recombination system that uses a single recombinase

Bacteria harbouring circular chromosomes have a Xer site-specific recombination system that resolves chromosome dimers at division. In Escherichia coli, the activity of the XerCD/dif system is controlled and coupled with cell division by the FtsK DNA translocase. Most Xer systems, as XerCD/dif, include two different recombinases. However, some, as the Lactococcus lactis XerS/dif_SL system, include only one recombinase. We investigated the functional effects of this difference by studying the XerS/dif_SL system. XerS bound and recombined dif_SL sites in vitro, both activities displaying asymmetric characteristics. Resolution of chromosome dimers by XerS/dif_SL required translocation by division septum-borne FtsK. The translocase domain of L. lactis FtsK supported recombination by XerCD/dif, just as E. coli FtsK supports recombination by XerS/dif_SL. Thus, the FtsK-dependent coupling of chromosome segregation with cell division extends to non-rod-shaped bacteria and outside the phylum Proteobacteria. Both the XerCD/dif and XerS/dif_SL recombination systems require the control activities of the FtsKγ subdomain. However, FtsKγ activates recombination through different mechanisms in these two Xer systems. We show that FtsKγ alone activates XerCD/dif recombination. In contrast, both FtsKγ and the translocation motor are required to activate XerS/dif_SL recombination. These findings have implications for the mechanisms by which FtsK activates recombination.