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PubMed2000

Applying the saddlepoint approximation to bivariate stochastic processes.

The problem of moment closure is central to the study of multitype stochastic population dynamics since equations for moments up to a given order will generally involve higher-order moments. To obtain a Normal approximation, the standard approach is to replace third- and higher-order moments by zero, which may be severely restrictive on the structure of the p.d.f. The purpose of this paper is therefore to extend the univariate truncated saddlepoint procedure to multivariate scenarios. This has several key advantages: no distributional assumptions are required; it works regardless of the moment order deemed appropriate; and, we obtain an algebraic form for the associated p.d.f. irrespective of whether or not we have complete knowledge of the cumulants. The latter is especially important, since no families of distributions currently exist which embrace all cumulants up to any given order. In general the algorithm converges swiftly to the required p.d.f.; analysis of a severe test case illustrates its current operational limit.

Algorithms↗
PubMed1986

Dependent competing risks: a stochastic process model.

Analyses of human mortality data classified according to cause of death frequently are based on competing risk theory. In particular, the times to death for different causes often are assumed to be independent. In this paper, a competing risk model with a weaker assumption of conditional independence of the times to death, given an assumed stochastic covariate process, is developed and applied to cause specific mortality data from the Framingham Heart Study. The results generated under this conditional independence model are compared with analogous results under the standard marginal independence model. Under the assumption that this conditional independence model is valid, the comparison suggests that the standard model overestimates by 4% the effect on life expectancy at age 30 due to the hypothetical elimination of cancer and by 7% the effect for cardiovascular/cerebrovascular disease. By age 80 the overestimates were 11% for cancer and 16% for heart disease. These results suggest the importance of avoiding the marginal independence assumption when appropriate data are available--especially when focusing on mortality at advanced ages.

Adolescent↗
PubMed1989

Cellular senescence involves stochastic processes causing loss of expression of differentiated function genes: transfection with SV40 as a means for dissociating effects of senescence on growth and on differentiated function gene expression.

In the accompanying work we demonstrated that the decline in expression of steroid 17 alpha-hydroxylase in mass cultures and clones of adrenocortical cells is the result of a stochastic switching process which yields mixtures of expressing and nonexpressing cells. There is an apparent positive correlation between the replicative potential of adrenocortical cell cultures and the number of cells in the culture that can express 17 alpha-hydroxylase. We investigated this by extending the cells' replicative potential by transfecting them with cloned SV40 virus. Cells from a senescent subclone, with very limited remaining replicative potential, were transfected. The cell population showed a progressive increase in growth rate and gave rise to a line of cells that expressed T antigen and which was apparently immortalized. Induction of mRNA for 17 alpha-hydroxylase by cyclic AMP was absent in this line of cells, as it was in the senescent cells prior to transfection. The cells remained responsive to gene induction by cyclic AMP as evidenced by increases in mRNA and activity for cholesterol side-chain cleavage. The absence of 17 alpha-hydroxylase expression in this line was not the result of interference by SV40 T antigen. When early passage cells were transfected with pSV3neo, which contains the early region of SV40 and neo, and were selected with G418, SV40 T antigen-expressing lines were derived which showed high levels of expression of 17 alpha-hydroxylase after induction with cyclic AMP. These cells maintained high levels of expression of 17 alpha-hydroxylase through four successive recloning events, over a period of replication much longer than that achievable by nontransfected cells. Thus, transfection by SV40 can be used to dissociate effects of senescence on growth and differentiated gene expression. T antigen expression selectively affects growth, but preserves the state of expression of a differentiated function gene as it was prior to transfection.

Adrenal Cortex↗
PubMed2002

The distribution of species range size: a stochastic process.

The major role played by environmental factors in determining the geographical range sizes of species raises the possibility of describing their long-term dynamics in relatively simple terms, a goal which has hitherto proved elusive. Here we develop a stochastic differential equation to describe the dynamics of the range size of an individual species based on the relationship between abundance and range size, derive a limiting stationary probability model to quantify the stochastic nature of the range size for that species at steady state, and then generalize this model to the species-range size distribution for an assemblage. The model fits well to several empirical datasets of the geographical range sizes of species in taxonomic assemblages, and provides the simplest explanation of species-range size distributions to date.

Animals↗
PubMed1994

Quantum dynamics as a stochastic process.

The quantum Liouville equation is solved in the Wigner representation using generalized Monte Carlo techniques. For small increments of time, the solution is represented as a sequential classical evolution in phase space followed by a quantum "jump" distribution in momentum space, with the latter simulated via a stochastic method. Extending the work initiated by John and Remler [Ann Phys. (N.Y.) 180, 152 (1987)] the technique is developed and validated for higher dimensions. Also, an alternative algorithm is developed and applied to study motion of a quantum system in an anharmonic quartic potential well, with significantly improved results.

Algorithms↗
PubMedDate not supplied

[Protein folding with molecular chaperones:stochastic process under control].

Protein folding in a living cell occurs with the participation of specialized proteins, molecular shaperons. The functional role and molecular mechanism of action of shaperons are discussed. It is shown that shaperons can be considered as proteins that, upon interaction with the folding peptide chain, transform the spontaneous folding to a process controlled and regulated by cellular factors. Models describing these controlled phenomena are discussed.

Animals↗
PubMed1998

Phase- and density-dependent population dynamics in Norwegian lemmings: interaction between deterministic and stochastic processes.

We analysed two 26-year long (1970-1995) time-series on annual population growth rates of Norwegian lemmings (Lemmus lemmus) from Finse, south Norway, using a threshold autoregressive (TAR) approach. We demonstrate that the population dynamics is both phase- and density-dependent. The phase-dependence accounts for the observed nonlinearity. We used the deduced stochastic model structure as a basis for evaluating the dynamic properties of this system. The dynamics is characterized either by limit cycles or chaos (the latter with a strong semi-periodic component). Stochasticity is seen to play an important role in the determination of the periodicity. The ecological implications of these statistical and mathematical results are discussed.

Animals↗
PubMed1998

Stochastic processes strongly influence HIV-1 evolution during suboptimal protease-inhibitor therapy.

It has long been assumed that HIV-1 evolution is best described by deterministic evolutionary models because of the large population size. Recently, however, it was suggested that the effective population size (Ne) may be rather small, thereby allowing chance to influence evolution, a situation best described by a stochastic evolutionary model. To gain experimental evidence supporting one of the evolutionary models, we investigated whether the development of resistance to the protease inhibitor ritonavir affected the evolution of the env gene. Sequential serum samples from five patients treated with ritonavir were used for analysis of the protease gene and the V3 domain of the env gene. Multiple reverse transcription-PCR products were cloned, sequenced, and used to construct phylogenetic trees and to calculate the genetic variation and Ne. Genotypic resistance to ritonavir developed in all five patients, but each patient displayed a unique combination of mutations, indicating a stochastic element in the development of ritonavir resistance. Furthermore, development of resistance induced clear bottleneck effects in the env gene. The mean intrasample genetic variation, which ranged from 1.2% to 5.7% before treatment, decreased significantly (P < 0.025) during treatment. In agreement with these findings, Ne was estimated to be very small (500-15,000) compared with the total HIV-1 RNA copy number. This study combines three independent observations, strong population bottlenecking, small Ne, and selection of different combinations of protease-resistance mutations, all of which indicate that HIV-1 evolution is best described by a stochastic evolutionary model.

Acquired Immunodeficiency Syndrome↗