Simulations in evolution. II. Relative fitness and the propagation of mutants.

In Neo-Darwinism, variation and natural selection are the two evolutionary mechanisms which propel biological evolution. Our previous article presented a histogram model [1] consisting in populations of individuals whose number changed under the influence of variation and/or fitness, the total population remaining constant. Individuals are classified into bins, and the content of each bin is calculated generation after generation by an Excel spreadsheet. Here, we apply the histogram model to a stable population with fitness F(1)=1.00 in which one or two fitter mutants emerge. In a first scenario, a single mutant emerged in the population whose fitness was greater than 1.00. The simulations ended when the original population was reduced to a single individual. The histogram model was validated by excellent agreement between its predictions and those of a classical continuous function (Eqn. 1) which predicts the number of generations needed for a favorable mutation to spread throughout a population. But in contrast to Eqn. 1, our histogram model is adaptable to more complex scenarios, as demonstrated here. In the second and third scenarios, the original population was present at time zero together with two mutants which differed from the original population by two higher and distinct fitness values. In the fourth scenario, the large original population was present at time zero together with one fitter mutant. After a number of generations, when the mutant offspring had multiplied, a second mutant was introduced whose fitness was even greater. The histogram model also allows Shannon entropy (SE) to be monitored continuously as the information content of the total population decreases or increases. The results of these simulations illustrate, in a graphically didactic manner, the influence of natural selection, operating through relative fitness, in the emergence and dominance of a fitter mutant.

High constant incidence rates of second primary cancers of the head and neck: a pooled analysis of 13 cancer registries.

Scanty data are available on the incidence (i.e., the absolute risk) of second cancers of the head and neck (HN) and its pattern with age. We investigated this issue using data from a multicentric study of 13 population-based cancer registries from Europe, Canada, Australia and Singapore for the years 1943-2000. A total of 99,257 patients had a first primary HN cancer (15,985 tongue, 22,378 mouth, 20,758 pharyngeal, and 40,190 laryngeal cancer), contributing to 489,855 person-years of follow-up. A total of 1,294 of the patients (1.3%) were diagnosed with second HN cancers (342 tongue, 345 mouth, 418 pharynx and 189 larynx). Male incidence rates of first HN cancer steeply increased from 0.68/100,000 at age 30-34 to 46.2/100,000 at age 70-74, and leveled off at older age; female incidence increased from 0.50/100,000 at age 30-34 to 16.5/100,000 at age 80-84. However, age-specific incidence of second HN cancers after a first HN cancer in men was around 200-300/100,000 between age 40-44 and age 70-74 and tended to decline at subsequent ages (150/100,000 at age 80-84); in women, incidence of second HN cancers was around 200-300/100,000 between age 45-49 and 80-84. The patterns of age-specific incidence were consistent for different subsites of second HN cancer and sexes; moreover, they were similar for age-specific incidence of first primary HN cancer in patients who subsequently developed a second HN cancer. The incidence of second HN cancers does not increase with age, but remains constant, or if anything, decreases with advancing age.