William D. Stansfield

Human Sex Ratios and Sex Distribution in Sibships of Size 2

ABSTRACT We previously analyzed data from the U.S. National Health Interview Survey (NHIS, 1998 to 2002) on families with two biological children (10 years of age and younger) and found that the distribution of families with two boys, two girls, and one boy + one girl did not statistically conform to a binomial distribution regardless of the boy/girl sex ratio used. Using the best estimate of the sex ratio from the data, we found that there were significantly more families with opposite-sex siblings than families with same-sex siblings. No biological mechanism could explain these results at the time. In the present study we conducted an analysis of the first two children in sibships of size 3 from the same data source and found that there are significantly more same-sex sibships than unlike-sex sibships. Combining the two sets of data for the first two children produced observed numbers in close agreement with the expected numbers. A hypothesis of parental choice (family planning) appears to be strongly supported as an explanation for the discrepancies in the two sets of data individually. For example, parents who have a boy and a girl (either order) as their first two children are more likely to stop having children (“stopping rule”) than are parents whose first two children are of the same sex.

Making Babies by the Flip of a Coin

Many probability and genetics textbooks pose standard questions about eye color, birth defects, sexes of children, and so on. Solutions to these questions, specifically about sexes, generally make two assumptions: first, that a randomly selected embryo is equally likely to be male or female; second, that the sexes of successive children from the same parents are independent. In other words, probabilists (and some geneticists) treat sexes of children like flips of a fair coin: two possible outcomes, each equally likely, with outcomes independent from trial to trial. But are these assumptions realistic? Demographic data suggest that neither a balance of sexes nor true independence exist in nature. Yet most textbooks, both in genetics and probability theory, continue to use the binomial distribution as an acceptable approximation for solving genetics problems involving live-birth sex ratios in species where sex is determined by an XX versus XY chromosome mechanism. We look at a widely circulated article in Parade magazine regarding the gender distribution in human families with two children and analyze comparable data from federal sources to show that such families do not conform to any binomial distribution. The sequence of investigations we take here could be followed in an introductory or intermediate probability and statistics course.

Textbooks: Expectations vs. Reality: The DNA story.

In reality, what we unavoidably often get from our textbooks is less than complete satisfaction. Whatever is in our textbooks should at least be correct and free from errors in the content provided; errors of omission (failure to mention specific topics) are often merely subjective opinions of the individual reviewer. We also want texts that are easy to read, and understand, but some teachers might object that this goal has been achieved through oversimplifications and/or the misuse of metaphors. Our textbooks should be well illustrated by pictures or diagrams whenever they would aid in comprehension and retention of complex subjects. We want to challenge our students to think critically, evaluate data, and reach unbiased, well-reasoned conclusions. Our textbooks can help here by providing multiple examples of how the methods of science, logic, and reason have been applied to solving specific biological problems. Both authors and publishers of scientific textbooks are aware of the breadth vs. depth problem. Textbooks cannot be encyclopedias. Largely because of curriculum demands, most textbooks tend to superficially cover more topics rather than select fewer topics and explore each of them in greater detail. It thus often becomes the teachers responsibility to provide important details that students need to really understand complex biological topics such as ecology and evolution. Another dilemma facing textbook authors is the amount of attention that should be given to subjects of historical interest versus the space allotted to the latest research. New discoveries in biology can stimulate interest and excitement in both student and teacher, and sometimes may even force us to reconsider well-established beliefs. Overthrowing paradigms is one way that science progresses. However, without historical perspectives, students will be deprived of a well-rounded education and cannot be expected to develop a better understanding of, and appreciation for, how we have attained our present level of scientific knowledge (Stansfield, 2000).

The Most Widely Publicized Gender Problem in Human Genetics

Abstract In two-child families containing at least one boy, the expected probability that such a family has two boys is 1/3, provided that the boy/girl (B/G) ratio is 1.0 and the population to which they belong has a binomial distribution of BB, (BG + GB), and GG families. It is commonly known that in most human populations the sex ratio at birth (i.e., the ratio of the number of boys to the number of girls) is greater than 1.0. Teachers and textbook writers seldom discuss the more realistic expected distributions in populations where the sex ratio is greater than 1.0. We present data from two federal surveys with sex ratios greater than 1.0 and find that the observed proportions of two boys in families of size 2 with at least one boy range from 0.3335 to 0.3941. It has been reported in the literature that the probability (p) of a male birth is subject to both within-sibship variation (Poisson variation), for which our data are suggestive, and possibly also between-sibship variation (Lexis variation). These deviations (biases) from the assumptions of a simple binomial distribution are involved in the calculation of values of p and standard 95% confidence intervals, thereby foiling attempts to make reliable statistical inferences from the data. Analysis of the data is also complicated by family planning that falsifies the assumption of randomness in the binomial gender distribution model. Families of size 2 (and their sex composition) are often discussed in a wider context. Overpopulation in some parts of the world has caused mass starvation and threatens to do the same worldwide unless the birth rate drops to agriculturally sustainable levels. Even if every woman of fertile age has only two children on average from now on, the worlds population is predicted to continue growing toward 9 billion people by 2050. Other sociological problems are bound to follow. Although the birth rate in China has recently dropped, the average age of the population has risen, so that by 2035 it is projected that for each person over age 65 there will be just three working-age people. Furthermore, Chinas one-child policy has already led to a sex imbalance where there is a large excess of men for whom marriage and parentage is denied.

Acquired Traits Revisited

ABSTRACT Most biology texts villify Lamarcks concept of “inheritance of acquired characters” and leave the impression that all acquired characters are never transmitted to offspring. However, recent research indicates that this is not true! Some “acquired” traits are inherited. I profile some of these striking cases and their importance for evolution and for understanding a broader epigenetic context for heredity and ontogeny (the emerging field of “evo-devo”). Further, I discuss how such cases, even considered as exceptions, contribute to understanding the nature of science, both the role of general rules in biology and the occurrence of conceptual change, or paradigm shifts.

Science & the Senses: Perceptions & Deceptions

ABSTRACT Science requires the acquisition and analysis of empirical (sense-derived) data. Given the same physical objects or phenomena, the sense organs of all people do not respond equally to these stimuli, nor do their minds interpret sensory signals identically. Therefore, teachers should develop lectures on human sensory systems that include some common examples of sensory limitations, variations, deficiencies, malfunctions, and diseases (as discussed herein) because they have important implications for conducting scientific investigations, science education, and introspection that are seldom included in biology textbooks. Students need to be made aware of the human tendency to self deception in order to avoid the cognitive error of confirmation bias.

Bayesian Statistics for Biological Data: Pedigree Analysis

I n teaching biology, there may be a tendency to concentrate too much on the descriptive aspects of the subject. A well-rounded education in the biological sciences also requires experience in the gathering and statistical analysis (interpretation) of quantitative data from field or laboratory studies. There are numerous mathematical tools and computer programs to help us do this today. Introducing students to some of these tools and their practical applications should be part of every biology class. One of these tools is known as Bayesian analysis. The specific purposes of this report are to:

The Discovery of Insulin: A Case Study of Scientific Methodology

ABSTRACT The nature of scientific research sometimes involves a trial-and-error procedure. Popular reviews of successful results from this approach often sanitize the story by omitting unsuccessful trials, thus painting the rosy impression that research simply follows a direct route from hypothesis to experiment to scientific discovery. The discovery of insulin is a classical case study in this genre that begs for an explanation to our students because it is so often ignored or misrepresented even in biology and physiology textbooks.

The Truth about Models: How Well Do Mechanical Models Mimic the Observed Gender Distributions in Two-Child Families?

ABSTRACT We question the use of mechanical models, such as coin flipping, to represent the probabilities of gender distributions in sibship families consisting of two children. Both the assumptions of the models and the reliability of the data should be evaluated. Using models without these critical evaluations may tend to perpetuate myths rather than elucidate biological realities.

Teaching Evolution & the Nature of Science Via the History of Debates about the Levels at Which Natural Selection Operates

ABSTRACT Students should not graduate from high school without understanding that scientific debates are essential components of scientific methodology. This article presents a brief history of ongoing debates regarding the hypothesis that group selection is an evolutionary mechanism, and it serves as an example of the role that debates play in correcting faulty ideas and stimulating new research in the pursuit of extending scientific knowledge.