A diffusion based study of population dynamics: Prehistoric migrations into South Asia.

A diffusion equation has been used to study migration of early humans into the South Asian subcontinent. The diffusion equation is tempered by a set of parameters that account for geographical features like proximity to water resources, altitude, and flatness of land. The ensuing diffusion of populations is followed in time-dependent computer simulations carried out over a period of 10,000 YBP. The geographical parameters are determined from readily-available satellite data. The results of our computer simulations are compared to recent genetic data so as to better correlate the migratory patterns of various populations; they suggest that the initial populations started to coalesce around 4,000 YBP before the commencement of a period of relative geographical isolation of each population group. The period during which coalescence of populations occurred appears consistent with the established timeline associated with the Harappan civilization and also, with genetic admixing that recent genetic mapping data reveal. Our results may contribute to providing a timeline for the movement of prehistoric people. Most significantly, our results appear to suggest that the Ancestral Austro-Asiatic population entered the subcontinent through an easterly direction, potentially resolving a hitherto-contentious issue.

Population Dynamics of Early Human Migration in Britain.

BACKGROUND: Early human migration is largely determined by geography and human needs. These are both deterministic parameters when small populations move into unoccupied areas where conflicts and large group dynamics are not important. The early period of human migration into the British Isles provides such a laboratory which, because of its relative geographical isolation, may allow some insights into the complex dynamics of early human migration and interaction. METHOD AND RESULTS: We developed a simulation code based on human affinity to habitable land, as defined by availability of water sources, altitude, and flatness of land, in choosing the path of migration. Movement of people on the British island over the prehistoric period from their initial entry points was simulated on the basis of data from the megalithic period. Topographical and hydro-shed data from satellite databases was used to define habitability, based on distance from water bodies, flatness of the terrain, and altitude above sea level. We simulated population movement based on assumptions of affinity for more habitable places, with the rate of movement tempered by existing populations. We compared results of our computer simulations with genetic data and show that our simulation can predict fairly accurately the points of contacts between different migratory paths. Such comparison also provides more detailed information about the path of peoples' movement over ~2000 years before the present era. CONCLUSIONS: We demonstrate an accurate method to simulate prehistoric movements of people based upon current topographical satellite data. Our findings are validated by recently-available genetic data. Our method may prove useful in determining early human population dynamics even when no genetic information is available.

Statistical analysis of the Indus script using n-grams.

The Indus script is one of the major undeciphered scripts of the ancient world. The small size of the corpus, the absence of bilingual texts, and the lack of definite knowledge of the underlying language has frustrated efforts at decipherment since the discovery of the remains of the Indus civilization. Building on previous statistical approaches, we apply the tools of statistical language processing, specifically n-gram Markov chains, to analyze the syntax of the Indus script. We find that unigrams follow a Zipf-Mandelbrot distribution. Text beginner and ender distributions are unequal, providing internal evidence for syntax. We see clear evidence of strong bigram correlations and extract significant pairs and triplets using a log-likelihood measure of association. Highly frequent pairs and triplets are not always highly significant. The model performance is evaluated using information-theoretic measures and cross-validation. The model can restore doubtfully read texts with an accuracy of about 75%. We find that a quadrigram Markov chain saturates information theoretic measures against a held-out corpus. Our work forms the basis for the development of a stochastic grammar which may be used to explore the syntax of the Indus script in greater detail.

A Markov model of the Indus script.

Although no historical information exists about the Indus civilization (flourished ca. 2600-1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system.

Entropic evidence for linguistic structure in the Indus script.

The script of the ancient Indus civilization remains undeciphered. The hypothesis that the script encodes language has recently been questioned. Here, we present evidence for the linguistic hypothesis by showing that the script's conditional entropy is closer to those of natural languages than various types of nonlinguistic systems.