Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

Effects of Acacia seyal and biochar on soil properties and sorghum yield in agroforestry systems in South Sudan

We studied the effects of Acacia seyal Del. intercropping and biochar soil amendment on soil physico-chemical properties and sorghum (Sorghum bicolor L.) yields in a two-year field experiment conducted on a silt loam site near Renk in South Sudan. A split-plot design with three replications was used. The main factor was tree-cropping system (dense acacia + sorghum, scattered acacia + sorghum, and sole sorghum) and biochar (0 and 10 Mg ha(-1)) was the subplot factor. The two acacia systems had lower soil pH, N and higher C/N ratios compared to the sole sorghum system. Biochar significantly increased soil C, exchangeable K+ contents, field capacity and available water content, but reduced soil exchangeable Ca2+ and effective CEC, and had no effect on soil pH. Acacia intercropping significantly reduced sorghum grain yields while biochar had no significant effect on sorghum yields. The land equivalent ratio (LER) for sorghum yield was 0.3 for both acacia systems in 2011, with or without biochar, but increased in 2012 to 0.6 for the scattered acacia system when combined with biochar. The reduction in sorghum yields by the A. seyal trees was probably due to a combination of competition for water and nutrients and shading. The lack of a yield response to biochar maybe due to insufficient time or too low a dosage. Further research is needed to test for the effects of tree intercropping and biochar and their interactions on soil properties and crop yields in drylands.Peer reviewe

Use of vitamin supplements and risk of total cancer and cardiovascular disease among the Japanese general population: A population-based survey

<p>Abstract</p> <p>Background</p> <p>Despite the popular use of vitamin supplements and several prospective cohort studies investigating their effect on cancer incidence and cardiovascular disease (CVD), scientific data supporting their benefits remain controversial. Inconsistent results may be partly explained by the fact that use of supplements is an inconsistent behavior in individuals. We examined whether vitamin supplement use patterns affect cancer and CVD risk in a population-based cohort study in Japan.</p> <p>Methods</p> <p>A total of 28,903 men and 33,726 women in the Japan Public Health Center-based Prospective Study cohort, who answered questions about vitamin supplement use in the first survey from 1990-1994 and the second survey from 1995-1998, were categorized into four groups (never use, past use, recent use, and consistent use) and followed to the end of 2006 for cancer and 2005 for CVD. Sex-specific hazard ratios (HRs) and 95% confidence intervals (95% CIs) were used to describe the relative risks of cancer and CVD associated with vitamin supplement use.</p> <p>Results</p> <p>During follow-up, 4501 cancer and 1858 CVD cases were identified. Multivariate adjusted analysis revealed no association of any pattern of vitamin supplement use with the risk of cancer and CVD in men. In women, consistent use was associated with lower risk of CVD (HR 0.60, 95% CI 0.41-0.89), whereas past (HR 1.17, 95% CI 1.02-1.33) and recent use (HR 1.24, 95% CI 1.01-1.52) were associated with higher risk of cancer.</p> <p>Conclusions</p> <p>To our knowledge, this is the first prospective cohort study to examine simultaneously the associations between vitamin supplement use patterns and risk of cancer and CVD. This prospective cohort study demonstrated that vitamin supplement use has little effect on the risk of cancer or CVD in men. In women, however, consistent vitamin supplement use might reduce the risk of CVD. Elevated risk of cancer associated with past and recent use of vitamin supplements in women may be partly explained by preexisting diseases or unhealthy background, but we could not totally control for this in our study.</p

Early evolution of the LIM homeobox gene family

Background: LIM homeobox (Lhx) transcription factors are unique to the animal lineage and have patterning roles during embryonic development in flies, nematodes and vertebrates, with a conserved role in specifying neuronal identity. Though genes of this family have been reported in a sponge and a cnidarian, the expression patterns and functions of the Lhx family during development in non-bilaterian phyla are not known

Extracting key information from historical data to quantify the transmission dynamics of smallpox

<p>Abstract</p> <p>Background</p> <p>Quantification of the transmission dynamics of smallpox is crucial for optimizing intervention strategies in the event of a bioterrorist attack. This article reviews basic methods and findings in mathematical and statistical studies of smallpox which estimate key transmission parameters from historical data.</p> <p>Main findings</p> <p>First, critically important aspects in extracting key information from historical data are briefly summarized. We mention different sources of heterogeneity and potential pitfalls in utilizing historical records. Second, we discuss how smallpox spreads in the absence of interventions and how the optimal timing of quarantine and isolation measures can be determined. Case studies demonstrate the following. (1) The upper confidence limit of the 99th percentile of the incubation period is 22.2 days, suggesting that quarantine should last 23 days. (2) The highest frequency (61.8%) of secondary transmissions occurs 3–5 days after onset of fever so that infected individuals should be isolated before the appearance of rash. (3) The U-shaped age-specific case fatality implies a vulnerability of infants and elderly among non-immune individuals. Estimates of the transmission potential are subsequently reviewed, followed by an assessment of vaccination effects and of the expected effectiveness of interventions.</p> <p>Conclusion</p> <p>Current debates on bio-terrorism preparedness indicate that public health decision making must account for the complex interplay and balance between vaccination strategies and other public health measures (e.g. case isolation and contact tracing) taking into account the frequency of adverse events to vaccination. In this review, we summarize what has already been clarified and point out needs to analyze previous smallpox outbreaks systematically.</p

H2S biosynthesis and catabolism: new insights from molecular studies

Hydrogen sulfide (H2S) has profound biological effects within living organisms and is now increasingly being considered alongside other gaseous signalling molecules, such as nitric oxide (NO) and carbon monoxide (CO). Conventional use of pharmacological and molecular approaches has spawned a rapidly growing research field that has identified H2S as playing a functional role in cell-signalling and post-translational modifications. Recently, a number of laboratories have reported the use of siRNA methodologies and genetic mouse models to mimic the loss of function of genes involved in the biosynthesis and degradation of H2S within tissues. Studies utilising these systems are revealing new insights into the biology of H2S within the cardiovascular system, inflammatory disease, and in cell signalling. In light of this work, the current review will describe recent advances in H2S research made possible by the use of molecular approaches and genetic mouse models with perturbed capacities to generate or detoxify physiological levels of H2S gas within tissue