Further, from the proof of Theorem 2.11, (mathbb{T}) can be decomposed into the union of all elements in the well-connected periodic timescale sequence ({mathbb{T}_{0}^{i}}_{iinmathbb{Z}^) and (mathbb{T}_{r}=emptyset).
If (mathbb{T}=bigcup_{i=1}^{infty}mathbb{T}_{i}), where (mathbb{T}_{i}) is (omega_{i} -periodic fomega_{i} -periodicZ}^), then there exists a well-connected timescale sequence ({mathbb{T}_{0}^{i}}_{iinmathbb{Z}^) such that (mathbb{T}=bigcup_{i=1}^{infor}mathbb{T}_{0}^{i}), wheach(mathbb{T}_{0}^{iinmathbb{ega_{0}^{i})-periodic.
Our assumption about dates meant that species counts were made using the same timescale as sequence and nucleotide variant counts.
On the fine timescale, the sequence of involvement of simultaneously recorded neurons in activity was not uniform but varied from one cycle to the other, whereby any neuron could be leading in some particular cycles (Fig. 5 e and Fig. S2 b).
Third, it might be argued that simple stochastic variation in the rate of base substitutions in LTRs can lead to a gradual decline in element numbers (on the timescale of sequence divergence) to the right of an age distribution peak, yielding a false impression of an earlier steady-state birth death process.
Our results thus demonstrate the utility of genome alignments for examining ncRNA orthology across considerable evolutionary timescales and complement sequence similarity guided approaches.
This process leads to a decreasing sequence of timescale sets: mathbb{T}supsetmathbb{T}_{1}supsetmathbb{T}_{2}supset cdotssupset mathbb{T}_{n}supsetcdots.
First, on the laboratory-experimental (Schuchert et al. 1991; Steiner et al. 2009) and inferred-historical timescales, multiple, distinct DNA sequence motifs of fission yeast promote meiotic recombination and are suicidal.
Despite the importance of reliable estimates of divergence times, our understanding of the temporal patterns of diversification remain in flux for many groups, in part because the methods for estimating evolutionary timescales from DNA sequences are being refined [ 1, 13, 14].
During these periods, the birth rates of mammalian LTR element families averaged 276 (85), again on a timescale of 1% LTR sequence divergence (equivalent to ∼0.3 1.0 My for the taxa involved) (table 1).
As defined by the exponential curves in figure 1, on a timescale of 1% LTR sequence divergence, the average genome-wide birth rate of LTR element families in invertebrates and fish from the deep past to the current time is 120 (standard error = 34), whereas that for land plants is slightly larger, 193 (76) (table 1).
