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

Transcription profiling reveals potential mechanisms of dysbiosis in the oral microbiome of rhesus macaques with chronic untreated SIV infection.

A majority of individuals infected with human immunodeficiency virus (HIV) have inadequate access to antiretroviral therapy and ultimately develop debilitating oral infections that often correlate with disease progression. Due to the impracticalities of conducting host-microbe systems-based studies in HIV infected patients, we have evaluated the potential of simian immunodeficiency virus (SIV) infected rhesus macaques to serve as a non-human primate model for oral manifestations of HIV disease. We present the first description of the rhesus macaque oral microbiota and show that a mixture of human commensal bacteria and "macaque versions" of human commensals colonize the tongue dorsum and dental plaque. Our findings indicate that SIV infection results in chronic activation of antiviral and inflammatory responses in the tongue mucosa that may collectively lead to repression of epithelial development and impact the microbiome. In addition, we show that dysbiosis of the lingual microbiome in SIV infection is characterized by outgrowth of Gemella morbillorum that may result from impaired macrophage function. Finally, we provide evidence that the increased capacity of opportunistic pathogens (e.g. E. coli) to colonize the microbiome is associated with reduced production of antimicrobial peptides

Isotopic and molecular distributions of biochemicals from fresh and buried Rhizophora mangle leaves†

Rhizophora mangle L. (red mangrove) is the dominant species of mangrove in the Americas. At Twin Cays, Belize (BZ) red mangroves are present in a variety of stand structures (tall >5 m in height, transition ~2–4 m and dwarf ~1–1.5 m). These height differences are coupled with very different stable carbon and nitrogen isotopic values[1] (mean tall δ(13)C = -28.3‰, δ(15)N = 0‰; mean tall δ(13)C = -25.3‰, δ(15)N = -10‰). To determine the utility of using these distinct isotopic compositions as 'biomarkers' for paleoenvironmental reconstruction of mangrove ecosystems and nutrient availability, we investigated the distribution and isotopic (δ(13)C and δ(15)N) composition of different biochemical fractions (water soluble compounds, free lipids, acid hydrolysable compounds, individual amino acids, and the residual un-extractable compounds) in fresh and preserved red mangrove leaves from dwarf and tall trees. The distribution of biochemicals are similar in dwarf and tall red mangrove leaves, suggesting that, regardless of stand structure, red mangroves use nutrients for biosynthesis and metabolism in a similar manner. However, the δ(13)C and δ(15)N of the bulk leaf, the biochemical fractions, and seven amino acids can be used to distinguish dwarf and tall trees at Twin Cays, BZ. The data support the theory that the fractionation of carbon and nitrogen occurs prior to or during uptake in dwarf and tall red mangrove trees. Stable carbon and nitrogen isotopes could, therefore, be powerful tools for predicting levels of nutrient limitation at Twin Cays. The δ(13)C and δ(15)N of biochemical fractions within preserved leaves, reflect sedimentary cycling and nitrogen immobilization. The δ(15)N of the immobilized fraction reveals the overlying stand structure at the time of leaf deposition. The isotopic composition of preserved mangrove leaves could yield significant information about changes in ecosystem dynamics, nutrient limitation and past stand structure in mangrove paleoecosystems

Nutrient Enrichment Increases Mortality of Mangroves

Nutrient enrichment of the coastal zone places intense pressure on marine communities. Previous studies have shown that growth of intertidal mangrove forests is accelerated with enhanced nutrient availability. However, nutrient enrichment favours growth of shoots relative to roots, thus enhancing growth rates but increasing vulnerability to environmental stresses that adversely affect plant water relations. Two such stresses are high salinity and low humidity, both of which require greater investment in roots to meet the demands for water by the shoots. Here we present data from a global network of sites that documents enhanced mortality of mangroves with experimental nutrient enrichment at sites where high sediment salinity was coincident with low rainfall and low humidity. Thus the benefits of increased mangrove growth in response to coastal eutrophication is offset by the costs of decreased resilience due to mortality during drought, with mortality increasing with soil water salinity along climatic gradients

The emergence of waves in random discrete systems

Essential criteria for the emergence of wave-like manifestations occurring in an entirely discrete system are identified using a simple model for the movement of particles through a network. The dynamics are entirely stochastic and memoryless involving a birth-death-migration process. The requirements are that the network should have at least three nodes, that migration should have a directional bias, and that the particle dynamics have a non-local dependence. Well defined bifurcations mark transitions between amorphous, wave-like and collapsed states with an intermittent regime between the latter two

Association between subclinical thyroid dysfunction and change in bone mineral density in prospective cohorts

Background Subclinical hyperthyroidism (SHyper) has been associated with increased risk of hip and other fractures, but the linking mechanisms remain unclear. Objective To investigate the association between subclinical thyroid dysfunction and bone loss. Methods Individual participant data analysis was performed after a systematic literature search in MEDLINE/EMBASE (1946–2016). Two reviewers independently screened and selected prospective cohorts providing baseline thyroid status and serial bone mineral density (BMD) measurements. We classified thyroid status as euthyroidism (thyroid-stimulating hormone [TSH] 0.45–4.49 mIU/L), SHyper (TSH < 0.45 mIU/L) and subclinical hypothyroidism (SHypo, TSH ≥ 4.50–19.99 mIU/L) both with normal free thyroxine levels. Our primary outcome was annualized percentage BMD change (%ΔBMD) from serial dual X-ray absorptiometry scans of the femoral neck, total hip and lumbar spine, obtained from multivariable regression in a random-effects two-step approach. Results Amongst 5458 individuals (median age 72 years, 49.1% women) from six prospective cohorts, 451 (8.3%) had SHypo and 284 (5.2%) had SHyper. During 36 569 person-years of follow-up, those with SHyper had a greater annual bone loss at the femoral neck versus euthyroidism: %ΔBMD = −0.18 (95% CI: −0.34, −0.02; I2 = 0%), with a nonstatistically significant pattern at the total hip: %ΔBMD = −0.14 (95% CI: −0.38, 0.10; I2 = 53%), but not at the lumbar spine: %ΔBMD = 0.03 (95% CI: −0.30, 0.36; I2 = 25%); especially participants with TSH < 0.10 mIU/L showed an increased bone loss in the femoral neck (%Δ BMD = −0.59; [95% CI: −0.99, −0.19]) and total hip region (%ΔBMD = −0.46 [95% CI: −1.05, −0.13]). In contrast, SHypo was not associated with bone loss at any site. Conclusion Amongst adults, SHyper was associated with increased femoral neck bone loss, potentially contributing to the increased fracture risk