A kinetic model of RNA folding

The RNA folding process is represented as a Markov process with states corresponding to RNA secondary structures and transition probabilities corresponding to transformations of a secondary structure caused by formation or disintegration of a helix. Transition probabilities (kinetic constants) are determined. A notion of a group of structures is introduced, and it allows to reduce the state space. Energetic and kinetic parameters of pseudoknots are estimated. Algorithms for computation of a kinetic ensemble for structures and groups of structures are presented, as well as their modifications that take into account pseudoknots. The described algorithms are implemented as a procedure for prediction of RNA secondary structure that is included in the package DNA-SUN.     

A Stochastic Metapopulation Model with Variability in Patch Size and Position

Analytically tractable metapopulation models usually assume that every patch is identical, which limits their application to real metapopulations. We describe a new single species model of metapopulation dynamics that allows variation in patch size and position. The state of the metapopulation is defined by the presence or absence of the species in each patch. For a system of n patches, this gives 2ⁿ possible states. We show how to construct and analyse a matrix describing transitions between all possible states by first constructing separate extinction and colonisation matrices. We illustrate the model′s application to metapopulations by considering an example of malleefowl, Leipoa ocellata, in southern Australia, and calculate extinction probabilities and quasi-stationary distributions. We investigate the relative importance of modelling the particular arrangement of patches and the variation in patch sizes for this metapopulation and we use the model to examine the effects of further habitat loss on extinction probabilities.     

Deer and elk hunter recruitment,retention, and participation trends in Montana

Big game hunting is the most popular type of hunting in the United States, and deer and elk hunting are the most popular type of hunting in Montana. Similar to other states, deer and elk hunting also generates most of the revenue spent on wildlife conservation by the state of Montana. Although nationwide trends indicate a concerning decline in hunter participation, the trends in license sales and hunter participation within most states have not received as much attention. We investigated trends in resident deer and elk license sales in Montana using existing licensing databases. We then estimated hunter recruitment, hunter participation, and license purchasing probabilities using hunter education and licensing databases. We employed a multi-state mark–recapture model and 248,819 records of deer and elk license purchasing habits for individual Montana residents during 2002–2007. We used matrix population models to examine the relative influence of these parameters on trends in license sales and hunter participation. Resident deer and elk license sales increased 4% in Montana during 2002–2007. We found that males had greater recruitment rates, retention rates, and license purchasing probabilities than females, and that young adults had lesser license purchasing probabilities than other age classes. Based on analyses of matrix population models, trends in license sales in Montana are most influenced by middle-aged and baby boomer male license purchase probabilities. Trends in hunter participation are positively influenced by recruitment and retention in all male age classes, with the smallest predicted effects arising from recruitment of young adult males. Our results suggest that a focus on older age class males with programs designed to increase hunter recruitment, retention, and license purchase probabilities may have similar or larger effects on trends in license sales and hunter participation in Montana than programs directed at youth. Our analyses also provide a framework by which trends in hunter recruitment, retention, and license purchasing habits can be objectively quantified in order to inform and evaluate hunter recruitment, retention, and license purchase habit programs. © 2011 The Wildlife Society.     

On the classification of regular systems of inbreeding

Regular systems of inbreeding are defined as those with discrete, nonoverlapping generations and with the same number of individuals and mating pattern in every generation. Given the number of individuals in a generation, there are many possible regular mating systems. A notion of when two such mating systems are equivalent is introduced, and several necessary conditions are given for such an equivalence. The use of these conditions is illustrated for N = 2, 3, 4 and 5 individuals, and a complete enumeration has been found for these cases: the numbers of inequivalent mating systems are 1, 5, 57 and 858, respectively. The maximal eigenvalue of the matrix q that specifies the recursion relations satisfied by the probabilities of identity have also been found for these cases. For N = 3 and 4 (and 2 trivially), circular mating gives the slowest rate of approach to genetic uniformity of those systems that do evolve to uniformity, but for N = 5 there are two other mating systems that have a slower rate of convergence, and for N = 6 partial results show that there are many such examples.Deceased     

Some Extensions to the Stochastic Study of the Life Table

This article discusses the application of statistical techniques in the analysis of the life table. Using a piece-wise continuous model for the mortality pattern, the maximum likelihood estimates of the probabilities of dying, qi in a life table are obtained. From the form of the covariance matrix it is deduced that the estimates are asymptotically independent. The distribution of qi and its large sample variance are also derived.     

Dynamical consequences of harvest in discrete age-structured population models

The role of harvest in discrete age-structured one-population models has been explored. Considering a few age classes only, together with the overcompensatory Ricker recruitment function, we show that harvest acts as a weak destabilizing effect in case of small values of the year-to-year survival probability P and as a strong stabilizing effect whenever the survival probability approaches unity. In the latter case, assuming n=2 age classes, we find that harvest may transfer a population from the chaotic regime to a state where the equilibrium point (x₁*, x₂*) becomes stable. However, as the number of age classes increases (which acts as a stabilizing effect in non-exploited models), we find that harvest acts more and more destabilizing, in fact, when the number of age classes has been increased to n=10, our finding is that in case of large values of the survival probabilities, harvest may transfer a population from a state where the equilibrium is stable to the chaotic regime, thus exactly the opposite of what was found in case of n=2. On the other hand, if we replace the Ricker relation with the generalized Beverton and Holt recruitment function with abruptness parameter larger than 2, several of the conclusions derived above are changed. For example, when n is large and the survival probabilities exceed a certain threshold, the equilibrium will always be stable.Revised version: 18 September 2003     

Making use of multiple surveys: Estimating breeding probability using a multievent‐robust design capture–recapture model

Increased environmental stochasticity due to climate change will intensify temporal variance in the life‐history traits, and especially breeding probabilities, of long‐lived iteroparous species. These changes may decrease individual fitness and population viability and is therefore important to monitor. In wild animal populations with imperfect individual detection, breeding probabilities are best estimated using capture–recapture methods. However, in many vertebrate species (e.g., amphibians, turtles, seabirds), nonbreeders are unobservable because they are not tied to a territory or breeding location. Although unobservable states can be used to model temporary emigration of nonbreeders, there are disadvantages to having unobservable states in capture–recapture models. The best solution to deal with unobservable life‐history states is therefore to eliminate them altogether. Here, we achieve this objective by fitting novel multievent‐robust design models which utilize information obtained from multiple surveys conducted throughout the year. We use this approach to estimate annual breeding probabilities of capital breeding female elephant seals (Mirounga leonina). Conceptually, our approach parallels a multistate version of the Barker/robust design in that it combines robust design capture data collected during discrete breeding seasons with observations made at other times of the year. A substantial advantage of our approach is that the nonbreeder state became “observable” when multiple data sources were analyzed together. This allowed us to test for the existence of state‐dependent survival (with some support found for lower survival in breeders compared to nonbreeders), and to estimate annual breeding transitions to and from the nonbreeder state with greater precision (where current breeders tended to have higher future breeding probabilities than nonbreeders). We used program E‐SURGE (2.1.2) to fit the multievent‐robust design models, with uncertainty in breeding state assignment (breeder, nonbreeder) being incorporated via a hidden Markov process. This flexible modeling approach can easily be adapted to suit sampling designs from numerous species which may be encountered during and outside of discrete breeding seasons.     

Influence of homoeotic genes on the aldehyde oxidase pattern in imaginal discs of Drosophila melanogaster

In a study of the regulation of enzyme patterns in imaginal discs the aldehyde oxidase pattern was determined for some homoeotic mutations of D. melanogaster. Earlier indications that suggested that this pattern follows the determinitive state of compartments within imaginal discs were confirmed by the aldehyde oxidase (AO) pattern of both the wing and haltere discs from en¹; bx³, en¹; pbx, and en¹; bx³ pbx larvae and the antennal discs from Antp^73b and ss^a larvae. We additionally analyzed whether AO activity depended on the determinative state of an entire compartment or was expressed autonomously in clones. Homozygous engrailed clones were induced by mitotic recombination. From the AO clones found in normally negative areas of the posterior compartment it was concluded that enzyme activity depended upon the determinative state of the cells and was not a function of the compartment as a whole. The results are described with reference to a scheme in which compartmental and subcompartmental selector genes are thought to determine a binary code on which AO patterns depend.     

Regular systems of inbreeding

Regular systems of inbreeding with discrete, nonoverlapping generations and the same number of individuals and mating pattern in every generation are studied. The matrix Q that specifies the recursion relations satisfied by the probabilities of identity is expressed in terms of the matrix M that describes the mating system. Necessary and sufficient conditions for convergence to genetic uniformity are given, and it is determined which probabilities of identity approach one. If the mating system has certain symmetries and these are imposed initially, then a matrix R, of lower dimension than Q, specifies the recursion relations. For such a mating system, for generic initial conditions, the condensed matrix R suffices for determining whether convergence to uniformity occurs and which probabilities of identity approach one. If Q is irreducible, the maximal eigenvalue of R is the same as that of Q. If Q is also aperiodic, this implies that the asymptotic rate of convergence to homogeneity of the condensed system is the same as that of the complete one. The above results apply to autosomal loci in monoecious (with or without selfing) and dioecious populations and to X-linked loci. As an example, all the eigenvalues and right and left eigenvectors of Q for circular mating are found.Supported by National Science Foundation Grant BSR-8512844     

A method for defining steady-state unidirectional fluxes through branched chemical, osmotic and chemiosmotic reactions

A general mathematical technique is described for deriving analytical expressions and obtaining numerical solutions for the steady-state unidirectional fluxes between two chemical states via any set of intermediate states present within any hypothetical system of unbranched or branched and overlapping elementary processes. The technique is a restricted application of the theory of Markov processes with conditional probabilities being assigned to the chemical state transitions constituting the system of reactions. While, in principle, the technique requires the summation of an infinite power series of a matrix defining the conditional probabilities of single state transitions, the power series is evaluated by means of the Taylor series expansion for matrices. As this technique allows isotopic exchange velocity equations to be derived from systems of reactions in which no distinction between the labelled and unlabelled species is required it provides a distinct and independent alternative to previously proposed methods. The technique is illustrated by application to a mechanism for second-order carrier-mediated transport.     

Use of conditional distributions in the analysis of ion channel recordings

A method to test the Markov nature of ion channel gating is proposed. It makes use of singly and doubly conditional distributions. The application of this method to recordings from single BK channels provides evidence that at least two states of the underlying kinetic scheme are left at a constant rate. Moreover, the probabilities, when leaving a state, of reaching another given state are shown to be constant for all the states of the system. Offprint requests to: D. Petracchi     

Arthropod orientation in choice chambers as a Markov chain

ABSTRACT. A Markov model of arthropod locomotor behaviour in choice chambers is presented. In the model, the compartments of the choice chamber and the movements of the animals from one compartment to another are treated as the states and the state transitions of a Markov chain, respectively. The model allows one to calculate the transition probabilities and the equilibrium distribution of animals in a choice chamber from direct measurements of displacement speeds and boundary turning reactions in each compartment. The compartment preferences (i.e. the proportion of time spent in each compartment) in two-compartment choice chambers were found to be strongly correlated with the predictions of the model. Klinokinesis is suggested to have negligible significance in some of the experiments reviewed. An equation is given to evaluate quantitatively the relative strength of kinetic and tactic components in the overall preference in the choice chamber; this assessment has not previously been possible.     

An index for microcarrier dispersion inside a horizontally rotating bioreactor for animal cell culture

An index of particle dispersion is used to quantify the degree of particle dispersion inside the horizontally rotating bioreactor. Resin particles were suspended inside a horizontally rotating cylinder. The states of particle dispersion were observed and recorded on video, from which data the index of particle dispersion was calculated. The effect of the operating parameters particle concentration and cylinder rotational speed on the state of particle dispersion were described using the index. By comparing the quantitative and qualitative classifications of particle dispersion it was confirmed that the new index does reflect the degree of particle dispersion. From the comparison it can also be concluded that if the index is greater than 0.96, the particle distribution can be considered uniform.     

Analysis of tracer experiments: VII. General multi-compartment systems imbedded in non-homogeneous inaccessible media

An integral equation analysis of generaln compartment steady state systems imbedded in static media of arbitrary complexity has been developed. A set of initial entry functions can be found which serve to determine a corresponding set of partitioned initial entry functions. The partitioned functions, in turn, can be used to predict the probabilities and time courses of various transport histories and to determine all steady state rates of flow between measured compartments. The method is quite general, being completely applicable, for example, to closed systems, to cyclic systems and to systems in which relatively rapid (but finite) exchange between compartments occurs.     

Feature selection environment for genomic applications

Background  

Feature selection is a pattern recognition approach to choose important variables according to some criteria in order to distinguish or explain certain phenomena (i.e., for dimensionality reduction). There are many genomic and proteomic applications that rely on feature selection to answer questions such as selecting signature genes which are informative about some biological state, e.g., normal tissues and several types of cancer; or inferring a prediction network among elements such as genes, proteins and external stimuli. In these applications, a recurrent problem is the lack of samples to perform an adequate estimate of the joint probabilities between element states. A myriad of feature selection algorithms and criterion functions have been proposed, although it is difficult to point the best solution for each application.     

Projected status of the Pacific walrus (Odobenus rosmarus divergens) in the twenty-first century

Extensive and rapid losses of sea ice in the Arctic have raised conservation concerns for the Pacific walrus (Odobenus rosmarus divergens), a large pinniped inhabiting arctic and subarctic continental shelf waters of the Chukchi and Bering seas. We developed a Bayesian network model to integrate potential effects of changing environmental conditions and anthropogenic stressors on the future status of the Pacific walrus population at four periods through the twenty-first century. The model framework allowed for inclusion of various sources and levels of knowledge, and representation of structural and parameter uncertainties. Walrus outcome probabilities through the century reflected a clear trend of worsening conditions for the subspecies. From the current observation period to the end of century, the greatest change in walrus outcome probabilities was a progressive decrease in the outcome state of robust and a concomitant increase in the outcome state of vulnerable. The probabilities of rare and extirpated states each progressively increased but remained <10% through the end of the century. The summed probabilities of vulnerable, rare, and extirpated (P(v,r,e)) increased from a current level of 10% in 2004 to 22% by 2050 and 40% by 2095. The degree of uncertainty in walrus outcomes increased monotonically over future periods. In the model, sea ice habitat (particularly for summer/fall) and harvest levels had the greatest influence on future population outcomes. Other potential stressors had much smaller influences on walrus outcomes, mostly because of uncertainty in their future states and our current poor understanding of their mechanistic influence on walrus abundance.     

Premelting thermal fluctuational interbase hydrogen-bond disrupted states of a B-DNA guanine-cytosine base pair: significance for amino and imino proton exchange.

Modified self-consistent phonon theory when applied to the DNA double helix indicates the existence of fairly long-lived states in which single interbase H bonds are disrupted. One can then postulate a number of situations in which particular disrupted H bonds can enhance particular proton exchange. In this paper we postulate a number of such partially open states for a B-conformation GC base pair and calculate the probability of each of these states for a B-conformation poly(dG).poly(dC). We compare these probabilities to those probabilities needed to explain various observed proton exchange rates. We propose that, for a GC base pair in B conformation, there are two amino proton exchangeable states--a cytosine amino proton exchangeable state and a guanine amino proton exchangeable state; both require the disruption of only the corresponding interbase H bond. The imino proton exchange, however, requires the disruption of all three interbase H bonds and this defines a third open state. Our calculated probabilities for a GC base pair in these three states are in fair agreement with available experimental estimates from measurements of amino and imino proton exchange.     

ATTRIBUTES OF CHLOROCOCCUM SPECIES: A NUMERICAL ANALYSIS2

From previously published data, 73 characteristics of 17 species of Chlorococcum were compiled. Comparisons of character states of each character were made, and simple matching coefficients were calculated for each species by following the procedure of Sokal & Michener. From a data matrix of the matching coefficients, a phenogram was constructed according to the unweighted pair group method of Sokal & Sneath. Arithmetic averages were used in transferring data from one matrix to another. The frequency of each character state was calculated, and the character states of the highest frequency (the modes) were used to describe a “typical” Chlorococcum species. Comparisons were made between the “typical” Chlorococcum species and each of the 17 species studied. Simple matching coefficients were also calculated from these comparisons. All of the species had a relatively high affinity for the data of the calculated “typical”. Suggestions are made about the use of a “typical” taxonomic unit, and questions are raised about the taxonomic relationship among species of the genus Tetracystis and the genus Chlorococcum.     

An exact solution of transient equations describing slow axonal transport

An exact analytical solution of equations describing slow axonal transport of cytoskeletal elements (CEs) injected in an axon is presented. The equations modelling slow axonal transport are based on the stop-and-go hypothesis. The simplest model implementing this hypothesis postulates that CEs switch between pausing and running kinetic states, and that the probabilities of CE transition between these two states are described by first-order rate constants. It is assumed that initially CEs are injected such that they form a uniform pulse of a given width. All injected CEs are initially attributed to the pausing state. It is shown that within 30 s kinetic processes redistribute CEs between pausing and running states; after that the process occurs under quasi-equilibrium conditions. The parameter accessible to experiments is the total concentration of CEs (pausing plus running). As the initial rectangular-shaped pulse moves, it changes its shape to become a bell-shaped wave that spreads out as it propagates. The wave's amplitude is decreasing during the wave's propagation. It is also shown that the system forgets its initial condition, meaning that if one starts with pulses of different widths, after sometime they converge to the same bell-shaped wave.     

Markov chain analysis of sessile community dynamics in a degraded Philippine reef to support restoration of coral populations

Quantitative approaches are needed for assessing assisted recovery potential in degraded coral reefs. A lagoonal community (Bolinao, Philippines) that has experienced severe disturbances (overfishing, blast fishing and coral bleaching) in the past was observed for 26 months. Benthic state sequences in 4 × 4 cm patches were used to quantify monthly probabilities of transitions between reef states. Benthic cover distribution was consistent with a spatially heterogeneous Markov process, with high variability in transition probabilities within a subset of four states: crustose algae with cropped turf, the codominant sponge Callyspongia samarensis, articulated coralline algae and fleshy macroalgae (MA). Once a patch is dominated by any of these states, there is high likelihood of cycling within the set before escaping to the rarer invertebrate groups. The assemblage is unlikely to recover naturally given prevailing conditions. Patches dominated by juvenile and adult corals have mean turnover times of about 3 and 5 months, respectively, due to (partial) mortality and competition. Asymmetry was detected for coral–macroalgal competition, despite low fleshy algal cover (9.5%), that was more adverse for coral juveniles than adults. While competition between coral and the mat-forming C. samarensis was symmetrical, loss of coral cover through this path is relatively higher as a result of the higher interaction frequency. Articulated coralline algae do not appear as a constraint. Complementary strategies for assisted recovery were inferred from successional indices as well as the sensitivity of stationary coral cover to changes in transition probabilities. Results demonstrate that short-term, fine-scale observations of state variables can be used to resolve biotic constraints to inform restoration initiatives.