Result Of Stochastic Processes Research Articles

When are extinctions simply bad luck? Rarefaction as a framework for disentangling selective and stochastic extinctions

Abstract A key challenge in conservation biology is that not all species are equally likely to go extinct when faced with a disturbance, but there are multiple overlapping reasons for such differences in extinction probability. Differences in species extinction risk may represent extinction selectivity, a non‐random process by which species’ risks of extinction are caused by differences in fitness based on traits. Additionally, rare species with low abundances and/or occupancies are more likely to go extinct than common species for reasons of random chance alone, that is, bad luck. Unless ecologists and conservation biologists can disentangle random and selective extinction processes, then the prediction and prevention of future extinctions will continue to be an elusive challenge. We suggest that a modified version of a common null model procedure, rarefaction, can be used to disentangle the influence of stochastic species loss from selective non‐random processes. To this end we applied a rarefaction‐based null model to three published data sets to characterize the influence of species rarity in driving biodiversity loss following three biodiversity loss events: (a) disease‐associated bat declines; (b) disease‐associated amphibian declines; and (c) habitat loss and invasive species‐associated gastropod declines. For each case study, we used rarefaction to generate null expectations of biodiversity loss and species‐specific extinction probabilities. In each of our case studies, we find evidence for both random and non‐random (selective) extinctions. Our findings highlight the importance of explicitly considering that some species extinctions are the result of stochastic processes. In other words, we find significant evidence for bad luck in the extinction process. Policy implications. Our results suggest that rarefaction can be used to disentangle random and non‐random extinctions and guide management decisions. For example, rarefaction can be used retrospectively to identify when declines of at‐risk species are likely to result from selectivity, versus random chance. Rarefaction can also be used prospectively to formulate minimum predictions of species loss in response to hypothetical disturbances. Given its minimal data requirements and familiarity among ecologists, rarefaction may be an efficient and versatile tool for identifying and protecting species that are most vulnerable to global extinction.

Abstract P2-05-02: Age-related genetic and epigenetic changes in estrogen-receptor positive breast cancer

Abstract Background: Age is the main risk factor for developing breast cancer (BC) in women. The increase in incidence with age is dominated by estrogen receptor positive (ER+) BC despite the >90% reduction of estrogen levels during menopause and later life. Recent models suggest the lifetime risk of BC is correlated with the number of stem cell divisions with random mutations arising during each division and driving cancer development. However, only two genes are mutated in more than 20% of BC while several recurrent copy number alterations (CNAs) occur in more than 50%. New models of age-related risk factors need to be developed that incorporate mutations, CNAs, epigenetics, and other biological factors. As data of this type is limited in normal breast tissue, factors correlated with age of diagnosis in ER+ BC were identified to understand which variables changed with age and might impact risk of developing BC. Methods: In silico analysis of public databases was used to identify factors in ER+ primary BC and normal adjacent tissue (NT) that are correlated with age of diagnosis including DNA mutations, CNAs, DNA methylation and gene/protein expression (TCGA n=599ER+,113NT; METABRIC n=1435ER+,144NT). Results: DNA mutations accumulated with age in ER+ BC with the median mutation count below 28 in primary tumors diagnosis in patients <50yr and rising to more than 43 in patients >80yr. However, the two most frequently mutated genes (PIK3CA and TP53) showed no significant correlation with age. As previously reported, GATA3 mutation rate was nearly twice as high in younger patients (<50yr=0.25,>80yr=0.12). There was little evidence of a general accumulation of CNAs with age, but there were higher rates of gain in 16p (<50yr=0.42,>80yr=0.51) and loss of 1p (<50yr=0.18,>80yr=0.37) in older patients and lower rates of loss in 6q (<50yr=0.34,>80yr=0.24). The most significant correlations with age related to ESR1 including expression of ESR1 mRNA (rho=0.39,P=1.2e-23 Spearman), ERα protein (rho=0.35,P=1.7e-15 Spearman), and demethylation of ESR1 promoter (rho=-0.36,P=1.6e-13 Spearman). The levels of the activated form of ERα (pS118) also correlated with age but to a much lesser extent than total ERα (rho=0.12,P=0.01 Spearman). Demethylation and expression of ESR1 were highly correlated (rho=-0.50,P<1e-16 Spearman). Analysis of data from NT revealed correlation of age of diagnosis, expression of ESR1 (rho=0.34,P=0.001 Spearman) and demethylation of the ESR1 promoter (rho=-0.22,P=0.03 Spearman) but not with ERα expression (rho=0.32,P=0.19 Spearman) although only 19 NT had protein data. Conclusions: Analysis of DNA mutations and CNAs fit previous theoretical models with both the result of stochastic processes. In these models, the low impact on fitness from individual mutations allows the accumulation over time while the high fitness costs of CNAs prevent accumulation and are likely acquired in a single catastrophic event. The ability of ER+ BC to progress in the presence of very low postmenopausal estrogen levels may be partly explained by demethylation leading to higher ESR1 expression and maintenance of ERα activation. In theory, changes in expression and demethylation can be targeted to reduce the age-related increase in risk for developing BC. Citation Format: Schuster EF, Dowsett M. Age-related genetic and epigenetic changes in estrogen-receptor positive breast cancer [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr P2-05-02.

A Bayesian Approach to Upscaling and Downscaling of Aircraft Measurements of Ice Particle Counts and Size Distributions

AbstractThis study addresses the issue of how to upscale cloud-sized in situ measurements of ice to yield realistic simulations of ice clouds for a variety of modeling studies. Aircraft measurements of ice particle counts along a 79-km zigzag path were collected in a Costa Rican cloud formed in the upper-level outflow from convection. These are then used to explore the applicability of Bayesian statistics to the problems of upscaling and downscaling. Using the 10-m particle counts, the analyses using Bayesian statistics provide estimates of the probability distribution function of all possiblemeanvalues corresponding to these counts. The statistical method of copulas is used to produce an extensive ensemble of estimates of these mean values, which are then combined to derive the probability density function (pdf) of mean values at 1-km resolution. These are found to compare very well to the observed 1-km particle counts when spatial correlation is included. The profiles of the observed and simulated mean counts along the flight path show similar features and have very similar statistical characteristics. However, because the observed and the simulated counts are both the results of stochastic processes, there is no way to upscale exactly to the observed profile. Each simulation is a unique realization of the stochastic processes, as are the observations themselves. These different realizations over all the different sizes can then be used to upscale particle size distributions over large areas.

The linked units of 5S rDNA and U1 snDNA of razor shells (Mollusca: Bivalvia: Pharidae)

The linkage between 5S ribosomal DNA and other multigene families has been detected in many eukaryote lineages, but whether it provides any selective advantage remains unclear. In this work, we report the occurrence of linked units of 5S ribosomal DNA (5S rDNA) and U1 small nuclear DNA (U1 snDNA) in 10 razor shell species (Mollusca: Bivalvia: Pharidae) from four different genera. We obtained several clones containing partial or complete repeats of both multigene families in which both types of genes displayed the same orientation. We provide a comprehensive collection of razor shell 5S rDNA clones, both with linked and nonlinked organisation, and the first bivalve U1 snDNA sequences. We predicted the secondary structures and characterised the upstream and downstream conserved elements, including a region at -25 nucleotides from both 5S rDNA and U1 snDNA transcription start sites. The analysis of 5S rDNA showed that some nontranscribed spacers (NTSs) are more closely related to NTSs from other species (and genera) than to NTSs from the species they were retrieved from, suggesting birth-and-death evolution and ancestral polymorphism. Nucleotide conservation within the functional regions suggests the involvement of purifying selection, unequal crossing-overs and gene conversions. Taking into account this and other studies, we discuss the possible mechanisms by which both multigene families could have become linked in the Pharidae lineage. The reason why 5S rDNA is often found linked to other multigene families seems to be the result of stochastic processes within genomes in which its high copy number is determinant.

Automatic signal detection in noise using entropy.

Automatic detection of signals in noise is a common problem in many areas of acoustics. In the field of passive acoustic monitoring of marine mammals, the signals to be detected are vocalizations. The noise originates from natural (wind, waves, and rain) and man‐made sources (e.g., shipping, construction, and seismic surveys). Signal characteristics vary broadly: frequency ranges from a few Hz to 200 kHz, duration from milliseconds to seconds to hours. Noise characteristics vary by similar orders of magnitude. While specific automatic detectors have been designed to successfully find specific calls in specific environments, the challenge is to find a large variety of calls in a large variety of noise. An exploitable difference between calls and noise is that most noise is a result of stochastic processes (wind, waves, rain, cavitating propellers + seismics generate gas bubbles underwater of varying size + resonance frequency), while many animal signals are a result of deterministic processes (vibrating st...

Looking forwards or looking backwards in avian phylogeography? A comment on Zink and Barrowclough 2008

Looking forwards or looking backwards in avian phylogeography? A comment on Zink and Barrowclough 2008

Universal oscillations in counting statistics.

Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants n(m) of the number n of passed charges to very high orders (up to m = 15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factorially with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data.

Evolutionary significance of differential species longevity in Osagean–Meramecian (Mississippian) crinoid clades

Abstract The pattern of differential species longevities among five Osagean–Meramecian crinoid clades is analyzed for its evolutionary significance. Differences in mean species longevity between clades may have resulted from species sorting based on eurytopy (niche breadth). In order to test the relationship between longevity and eurytopy it was first necessary to recognize generalists (eurytopes) vs. specialists (stenotopes) objectively. Three different approaches were used: (1) the “Eurytopy Index” (EI), which is a measure of mean number of facies per species; (2) analysis of crinoid functional morphology; and (3) use of canonical discriminant analysis to analyze species distributions between facies in order to separate generalists from specialists. Mean species longevity for each clade was evaluated by four different approaches: (1) rarefaction was used to control for differences in sample size, including both species richness and number of occurrences, between clades; (2) potential facies control of species longevity was evaluated by a bootstrap that compared the observed data to a null model where species longevity was limited only by the actual occurrences of each species known facies through time; (3) uniformity of clade species richness through time was evaluated by the “Index of Uniformity for Species Richness” based on the standard deviation of clade species richness across the time intervals; and (4) potential species range truncations were evaluated by a biostratigraphic gap analysis based on the binomial distribution. The general order of increasing longevity and eurytopy is (from least to most): flexibles, advanced cladids, camerates, disparids, and primitive cladids. In general the pinnulate crinoids (advanced cladids and camerates) were specialists with lower mean species longevity, and the non-pinnulate crinoids (disparids and primitive cladids) were generalists with higher mean species longevity. Pinnulate crinoids were specialized for feeding in high-energy currents and, thus, were limited in their facies distribution and presumably more extinction-prone. The non-pinnulates could feed in both low- and high-energy currents and, thus, were less limited in their facies distribution and presumably less extinction-prone. The flexibles were the exception in that they were non-pinnulate but had the lowest mean species longevity, apparently because they were specialized for deeper-water clastic environments. On average, generalist clades have mean species longevities that at a minimum are up to 45% (≈1.0 ± 0.7 m.y.) longer than specialist clades. However, greater mean species longevity did not necessarily confer long-term advantages to a clade. The specialist advanced cladids became the dominant crinoid clade of the late Paleozoic and gave rise to the articulate crinoids of the post-Paleozoic. This may have resulted from the more rapid species turnover of stenotopes creating adaptive evolutionary novelties for their clade. Alternatively, it could simply be the result of stochastic processes. The finer subdivision of niche space by specialists has led previous workers to predict that specialist clades should have higher species richness than generalist clades. The present study supports this prediction.

Genetic studies of free‐ranging macaques of Cayo Santiago II. 6‐Phosphogluconate dehydrogenase and NADH‐methemoglobin reductase (NADH‐diaphorase)

AbstractFor the population of 395 semi‐free‐ranging rhesus macaques (Macaca mulatta) that inhabited Cayo Santiago in 1976, 6‐phosphogluconate dehydrogenase phenotypes of 378 animals were determined. Three phenotypes, controlled by two autosomal codominant alleles,PGDA andPGDB, were found by electrophoretic methods. The frequencies of the alleles are 0.898 and 0.102, respectively. The population, composed of five troops and peripheral males, is in Hardy‐Weinberg equilibrium at this locus. The allele frequencies at the 6‐phosphogluconate dehydrogenase locus in the population in 1976 were compared with frequencies in 1973; a statistically significant difference was found in one troop. The phenotypes of NADH‐methemoglobin reductase (NADH‐diaphorase) were determined electrophoretically for 372 animals. These phenotypes are probably the products of two autosomal codominant alleles,Dia1 andDia2, with frequencies of 0.786 and 0.214, respectively. The population is in equilibrium at this locus also. Tests of homogeneity at the dehydrogenase and reductase loci indicate that the allele frequencies are significantly different among the five troops in the population. Observed and expected phenotypic ratios in progeny were compared at the dehydrogenase and the reductase loci. The only significant deviation from expectation occurs among offspring of mothers heterozygous at the reductase locus. The observed distributions of alleles at the 6‐phosphogluconate dehydrogenase locus and the NADH‐methemoglobin reductase locus are probably the results of stochastic processes.