Statistics of seismic cluster durations

Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of events triggered by a given main shock of fixed magnitude m that occurred at the origin of time, at times larger than some present time t. Using the technology of generating probability function (GPF), we derive the explicit expressions for the GPF of the number of future offsprings in a given temporal seismic cluster, defining, in particular, the statistics of the cluster's duration and the cluster's offsprings maximal magnitudes. We find the remarkable result that the magnitude difference between the largest and second largest event in the future temporal cluster is distributed according to the regular Gutenberg-Richer law that controls the unconditional distribution of earthquake magnitudes. For earthquakes obeying the Omori-Utsu law for the distribution of waiting times between triggering and triggered events, we show that the distribution of the durations of temporal clusters of events of magnitudes above some detection threshold \nu has a power law tail that is fatter in the non-critical regime $n<1$ than in the critical case n=1. This paradoxical behavior can be rationalised from the fact that generations of all orders cascade very fast in the critical regime and accelerate the temporal decay of the cluster dynamics.Comment: 45 pages, 15 figure

Within-individual changes in DNA methylation with age.

Age tracking for the final age estimation model. Predictions for individuals containing at least two blood samples collected over time in the data set (S1 Table). The final model was able to correctly predict 71% (20/28) cases of which samples collected from an individual at a later date were from an older sample. The dashed line represents the overall simple regression analysis between predicted and chronological age. There was a consistent significant relationship between predicted age and chronological age, even with samples collected over time (R2 = 0.86, p <0.001).</p

Correlation between methylation rate and chronological age.

Correlation between methylation rate and chronological age for (A) RALYL (cor = 0.52, p TET2 (cor = −0.60, p <0.001) in Asian elephants.</p

Graphical representation of the methodology.

Workflow to build an age estimation model using methylation-sensitive high-resolution melting (MS-HRM).</p

List of supplementary tables.

Age is an important parameter for bettering the understanding of biodemographic trends—development, survival, reproduction and environmental effects—critical for conservation. However, current age estimation methods are challenging to apply to many species, and no standardised technique has been adopted yet. This study examined the potential use of methylation-sensitive high-resolution melting (MS-HRM), a labour-, time-, and cost-effective method to estimate chronological age from DNA methylation in Asian elephants (Elephas maximus). The objective of this study was to investigate the accuracy and validation of MS-HRM use for age determination in long-lived species, such as Asian elephants. The average lifespan of Asian elephants is between 50–70 years but some have been known to survive for more than 80 years. DNA was extracted from 53 blood samples of captive Asian elephants across 11 zoos in Japan, with known ages ranging from a few months to 65 years. Methylation rates of two candidate age-related epigenetic genes, RALYL and TET2, were significantly correlated with chronological age. Finally, we established a linear, unisex age estimation model with a mean absolute error (MAE) of 7.36 years. This exploratory study suggests an avenue to further explore MS-HRM as an alternative method to estimate the chronological age of Asian elephants.</div

Primer information and polymerase chain reaction (PCR) conditions.

Primer information and polymerase chain reaction (PCR) conditions.</p

Final age estimation model.

Analysis of estimation accuracy and model performance on the final age estimation model combining RALYL and TET2. (A) SVR model before leave-one-individual-out cross-validation (LOIOCV) analysis (R2 = 0.82, p R2 = 0.74, p <0.001).</p

Influence of sex on the final age estimation model.

Δage residuals, defined as the residual from regressing predicted age on chronological age was calculated. Chronological age was adjusted as a covariate. (A) Compares the distribution of Δage residuals between females and males. The boxplots show group medians (solid line), inter-quartile range (box outline) and spread of data with outliers (whiskers) for each group. (B) The relationship between Δage residuals and chronological age. Linear regression analysis indicated that sex did not affect Δage residuals significantly (p = 0.99).</p

Details on samples and individuals.

Summary of blood sample information (n = 53) taken from the studied captive Asian elephants (n = 25) between 2004 and 2022 from Japanese zoos. (DOCX)</p

Probe coverage on chicken chromosome 1 for array comparative genomic hybridization.

<p>Probes are designed in 3 regions (>60 Mb) where significant <i>F</i>-values have been identified by previous quantitative trait loci analysis. Genome-wide <i>F</i>-values for tonic immobility duration (thick line) and induction attempts (thin line) are quoted from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080205#pone.0080205-Schtz1" target="_blank">[7]</a>.</p