Lars Nørvang Andersen

Insights into hominid evolution from the gorilla genome sequence.

Gorillas are humans’ closest living relatives after chimpanzees, and are of comparable importance for the study of human origins and evolution. Here we present the assembly and analysis of a genome sequence for the western lowland gorilla, and compare the whole genomes of all extant great ape genera. We propose a synthesis of genetic and fossil evidence consistent with placing the human–chimpanzee and human–chimpanzee–gorilla speciation events at approximately 6 and 10 million years ago. In 30% of the genome, gorilla is closer to human or chimpanzee than the latter are to each other; this is rarer around coding genes, indicating pervasive selection throughout great ape evolution, and has functional consequences in gene expression. A comparison of protein coding genes reveals approximately 500 genes showing accelerated evolution on each of the gorilla, human and chimpanzee lineages, and evidence for parallel acceleration, particularly of genes involved in hearing. We also compare the western and eastern gorilla species, estimating an average sequence divergence time 1.75 million years ago, but with evidence for more recent genetic exchange and a population bottleneck in the eastern species. The use of the genome sequence in these and future analyses will promote a deeper understanding of great ape biology and evolution.

A new isolation with migration model along complete genomes infers very different divergence processes among closely related great ape species

We present a hidden Markov model (HMM) for inferring gradual isolation between two populations during speciation, modelled as a time interval with restricted gene flow. The HMM describes the history of adjacent nucleotides in two genomic sequences, such that the nucleotides can be separated by recombination, can migrate between populations, or can coalesce at variable time points, all dependent on the parameters of the model, which are the effective population sizes, splitting times, recombination rate, and migration rate. We show by extensive simulations that the HMM can accurately infer all parameters except the recombination rate, which is biased downwards. Inference is robust to variation in the mutation rate and the recombination rate over the sequence and also robust to unknown phase of genomes unless they are very closely related. We provide a test for whether divergence is gradual or instantaneous, and we apply the model to three key divergence processes in great apes: (a) the bonobo and common chimpanzee, (b) the eastern and western gorilla, and (c) the Sumatran and Bornean orang-utan. We find that the bonobo and chimpanzee appear to have undergone a clear split, whereas the divergence processes of the gorilla and orang-utan species occurred over several hundred thousands years with gene flow stopping quite recently. We also apply the model to the Homo/Pan speciation event and find that the most likely scenario involves an extended period of gene flow during speciation.

An algebraic approach to signaling cascades with N layers.

Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple signaling cascade consisting of n layers of modification cycles such that the modified protein of one layer acts as modifier in the next layer. Assuming mass-action kinetics and taking the formation of intermediate complexes into account, we show that the steady states are solutions to a polynomial in one variable and in fact that there is exactly one steady state for any given total amounts of substrates and enzymes.We demonstrate that many steady-state concentrations are related through rational functions that can be found recursively. For example, stimulus-response curves arise as inverse functions to explicit rational functions. We show that the stimulus-response curves of the modified substrates are shifted to the left as we move down the cascade. Further, our approach allows us to study enzyme competition, sequestration, and how the steady state changes in response to changes in the total amount of substrates.Our approach is essentially algebraic and follows recent trends in the study of posttranslational modification systems.

On Computing the Coalescence Time Density in an Isolation-With-Migration Model With Few Samples

IN a recent article, [Wang and Hey (2009)][1] consider estimation of the parameters in an isolation-with-migration (IM) model for two species. For each locus, the data X consist of two samples, and therefore the probability of the data depends only on the time to the most recent common ancestor (

Efficient computation in the IM model

In this paper we analyze the isolation-with-migration model in a continuous-time Markov chain framework, and derive analytical expressions for the probability densities of gene tree topologies with an arbitrary number of lineages. We combine these densities with both nucleotide-substitution and infinite sites mutation models and derive probabilities for use in maximum likelihood estimation. We demonstrate how to apply lumpability of continuous-time Markov chains to achieve a significant reduction in the size of the state-space under consideration. We use matrix exponentiation and spectral decomposition to derive explicit expressions for the case of two diploid individuals in two populations, when the data is given as alignment columns. We implement these expressions in order to carry out a maximum likelihood analysis and provide a simulation study to examine the performance of our method in terms of our ability to recover true parameters. Finally, we show how the performance depends on the parameters in the model.

Local Time Asymptotics for Centered Lévy Processes with Two-Sided Reflection

The present paper is concerned with the local times of a Lévy process reflected at two barriers 0 and K > 0. The reflected process is decomposed into the original process plus local times at 0 and K and a starting condition, and we study ℓ K , the mean rate of increase of the local time at K when the reflected process is started in stationarity. We derive asymptotics (K → ∞) for ℓ K when the Lévy process has mean zero. The precise form of the asymptotics depends on the existence or non-existence of a finite second moment, paralleling the difference between the normal and the stable central limit theorem.

Parallel Computing, Failure Recovery, and Extreme Values

A task of random size T is split into M subtasks of lengths T1, …, TM, each of which is sent to one out of M parallel processors. Each processor may fail at a random time before completing its allocated task, and then has to restart it from the beginning. If X1, …,XM are the total task times at the M processors, the overall total task time is then ZM = max1,…,MXi. Limit theorems as M → ∞ are given for ZM, allowing the distribution of T to depend on M. In some cases the limits are classical extreme value distributions, in others they are of a different type.

Lévy Processes with Two-Sided Reflection

Let X be a Levy process and V the reflection at boundaries 0 and b > 0. A number of properties of V are studied, with particular emphasis on the behaviour at the upper boundary b. The process V can be represented as solution of a Skorokhod problem V (t) = V (0) + X(t) + L(t) − U(t) where L, U are the local times (regulators) at the lower and upper barrier. Explicit forms of V in terms of X are surveyed as well as more pragmatic approaches to the construction of V, and the stationary distribution π is characterised in terms of a two-barrier first passage problem. A key quantity in applications is the loss rate l b at b, defined as \(\mathbb{E}_{\pi }U(1)\). Various forms of l b and various derivations are presented, and the asymptotics as \(b \rightarrow \infty \) is exhibited in both the light-tailed and the heavy-tailed regime. The drift zero case \(\mathbb{E}X(1) = 0\) plays a particular role, with Brownian or stable functional limits being a key tool. Further topics include studies of the first hitting time of b, central limit theorems and large deviations results for U, and a number of explicit calculations for Levy processes where the jump part is compound Poisson with phase-type jumps.

Towards Asymptotically Optimal One-to-One PDP Algorithms for Capacity 2+ Vehicles

We consider the one-to-one Pickup and Delivery Problem (PDP) in Euclidean Space with arbitrary dimension

Structural properties of reflected Lévy processes

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