by Cleve Moler

Online Resources

Book Summary

Numerical Computing with MATLAB is a textbook for an introductory course in numerical methods, MATLAB, and technical computing. It emphasizes the informed use of mathematical software. Topics include matrix computation, interpolation and zero finding, differential equations, random numbers, and Fourier analysis.

Based on MATLAB, the textbook provides more than 70 M-files. Many of the more than 200 exercises involve modifying and extending these programs. The book also makes extensive use of computer graphics, including interactive graphical expositions of numerical algorithms.

Two editions of the book have been published. An electronic edition, published by The MathWorks, is available from this Web site. A traditional textbook print edition, published by the Society for Industrial and Applied Mathematics, is available from the SIAM Web site.

Mitochondrial Eve

Allan Charles Wilson (18 October 1934 – 21 July 1991) was a Professor of Biochemistry at the University of California, Berkeley, a pioneer in the use of molecular approaches to understand evolutionary change and reconstruct phylogenies, and a revolutionary contributor to the study of human evolution. He was one of the most controversial figures in post-war biology; his work attracted a great deal of attention both from within and outside the academic world. He is the only New Zealander to have won the MacArthur Fellowship.[1]

He is best known for experimental demonstration of the concept of the molecular clock (with his doctoral student Vincent Sarich), which was theoretically postulated by Linus Pauling and Emile Zuckerkandl, revolutionary insights into the nature of the molecular anthropology of higher primates and human evolution, called Mitochondrial Eve hypothesis (with his doctoral students Rebecca L. Cann and Mark Stoneking).[2][3]

Wilson joined the UC Berkeley faculty of biochemistry in 1964, and was promoted to full professor in 1972.[8] His first major scientific contribution was published as Immunological Time-Scale For Hominid Evolution in the journal Science in December 1967.[16] With his student Vincent Sarich,[17][18] he showed that evolutionary relationships of the humanspecies with other primates, in particular the Great Apes (chimpanzees, gorillas, and orangutans), could be inferred from molecular evidence obtained from living species, rather than solely from fossils of extinct creatures. Their microcomplement fixation method (see complement system) measured the strength of the immune reaction between an antigen(serum albumin) from one species and an antibody raised against the same antigen in another species. The strength of the antibody-antigen reaction was known to be stronger between more closely related species: their innovation was to measure it quantitatively among many species pairs as an “immunological distance“. When these distances were plotted against the divergence times of species pair with well-established evolutionary histories, the data showed that the molecular difference increased linearly with time, in what was termed a “molecular clock“. Given this calibration curve, the time of divergence between species pairs with unknown or uncertain fossil histories could be inferred. Most controversially, their data suggested that divergence times between humans, chimpanzees, and gorillas were on the order of 3~5 million years, far less than the estimates of 9~30 million years accepted by conventional paleoanthropologists from fossil hominids such as Ramapithecus. This ‘recent origin’ theory of human/ape divergence remained controversial until the discovery of the “Lucy” fossils in 1974.[15]

Wilson and another PhD student Mary-Claire King subsequently compared several lines of genetic evidence (immunology, amino acid differences, and protein electrophoresis) on the divergence of humans and chimpanzees, and showed that all methods agreed that the two species were >99% similar.[4][19] Given the large organismal differences between the two species in the absence of large genetic differences, King and Wilson argued that it was not structural gene differences that were responsible for species differences, butgene regulation of those differences, that is, the timing and manner in which near-identical gene products are assembled during embryology and development. In combination with the “molecular clock” hypothesis, this contrasted sharply with the accepted view that larger or smaller organismal differences were due to large or smaller rates of genetic divergence.

In the early 1980s, Wilson further refined traditional anthropological thinking with his work with PhD students Rebecca Cann and Mark Stoneking on the so-called “Mitochondrial Eve” hypothesis.[20] In his efforts to identify informative genetic markers for tracking human evolutionary history, he focused on mitochondrial DNA (mtDNA) — genes that are found in mitochondria in the cytoplasm of the cell outside the nucleus. Because of its location in the cytoplasm, mtDNA is passed exclusively from mother to child, the father making no contribution, and in the absence of genetic recombination defines female lineages over evolutionary timescales. Because it also mutates rapidly, it is possible to measure the small genetic differences between individual within species by restriction endonuclease gene mapping. Wilson, Cann, and Stoneking measured differences among many individuals from different human continental groups, and found that humans from Africa showed the greatest inter-individual differences, consistent with an African origin of the human species (the so-called “Out of Africa” hypothesis). The data further indicated that all living humans shared a common maternal ancestor, who lived in Africa only a few hundreds of thousands of years ago. This common ancestor became widely known in the media and popular culture as the Mitochondrial Eve. This had the unfortunate and erroneous implication that only a single female lived at that time, when in fact the occurrence of a coalescent ancestor is a necessary consequence of population genetic theory, and the Mitochondrial Eve would have been only one of many humans (male and female) alive at that time.[2][3] This finding was, like his earlier results, not readily accepted by anthropologists. Conventional hypothesis was that various human continental groups had evolved from diverse ancestors, over several million of years since divergence from chimpanzees. The mtDNA data, however, strongly suggested that all humans descended from a common, quite recent, African mother.[4][15]

Proc Natl Acad Sci U S A. 1969 Aug;63(4):1088-93.

A molecular time scale for human evolution.


We discuss published molecular evidence concerning the relationship of man to African apes and Old World monkeys. Quantitative comparisons of their serum albumins, transferrins, hemoglobins, and DNA show that man is genetically much more similar to the African apes than to the Old World monkeys. The amino acid sequences of hemoglobins from humans, chimpanzees, gorillas, and rhesus monkeys are consistent with the hypothesis that the probability of an amino acid substitution occurring in a given interval of time is the same for every hemoglobin lineage. This allows the use of these data as a hemoglobin evolutionary clock, just as we have previously done with the albumins. It is shown that concordance exists between the hemoglobin and albumin results and that both support the suggestion that the human lineage diverged from that leading to the African apes far more recently than is generally supposed. Considering both the albumin and hemoglobin data, we would set the most probable date at 4 to 5 million years.

[PubMed – indexed for MEDLINE]

Free PMC Article

Charles Joseph Minard

Charles Joseph Minard (French: [minaʁ]; 27 March 1781 – 24 October 1870) was a French civil engineer recognized for his significant contribution in the field of information graphics in civil engineering and statistics. Minard was among other things noted for his representation of numerical data on geographic maps.

statistical inference

A statistical hypothesis is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.[1] A statistical hypothesis test is a method of statistical inference. Commonly, two statistical data sets are compared, or a data set obtained by sampling is compared against a synthetic data set from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis that proposes no relationship between two data sets. The comparison is deemed statistically significant if the relationship between the data sets would be an unlikely realization of the null hypothesis according to a threshold probability—the significance level. Hypothesis tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance. The process of distinguishing between the null hypothesis and the alternative hypothesis is aided by identifying two conceptual types of errors (type 1 & type 2), and by specifying parametric limits on e.g. how much type 1 error will be permitted.

An alternative framework for statistical hypothesis testing is to specify a set of statistical models, one for each candidate hypothesis, and then use model selection techniques to choose the most appropriate model.[2] The most common selection techniques are based on either Akaike information criterion or Bayes factor.

Statistical hypothesis testing is sometimes called confirmatory data analysis. It can be contrasted with exploratory data analysis, which may not have pre-specified hypotheses.