Human Reproductive Ratios

Jacobson et al in the journal Human Reproduction conducted a study in 1999 that showed that the sex ratios of children born in a study group had a schewed sex ratio. Normally a 1 to 1 ratio of boys to girls is expected, since there is a 50 percent chance that a male parent will pass on either one of the sex determining chromosomes. When this ratio is schewed, explanations are needed. Jacobson showed that the sex ratio decreased with increased number of chiren per plural birth and with paternal age, for example. This meant that there were more girls born than expected.
Sex allocation theory hypothesises that parents will increase their fitness by controlling the sex ratio of their offspring, schewing it torwards producing more of the rarer sex. Lumma et al are an adaptive feature and can change as the adaptive environment requires. Lummaa et al showed that this occured in a set of pre-industrial humans living between 1175-1850 in Finland. Where males were rare, more sons were produced. Mackenzie et al studied a population of Canadian aboriginees and showed that their sex ratio had declined from a stable ratio to a very low one, and hypothesised that this was due largely to the influx of industrial pollutants in the river that the aboriginees lived in close association with.
When considering what affects the human sex ratio, there are pre-fertilization factors to consider, and post-fertilization factors to consider.
Rex-Kiss in Act.Biol.Hung. found that fetal-maternal blood group incompatibility will lead to a higher newborn sex ratio, iow more males than expected. That researcher felt that the blood group incompatibility has an effect on the X chromosome, and that whatever this effect is the elimination rate of the zygotes fertilized by Y chromosome-carrying sperm will decrease .
Rex-Kiss also found that incompability within the Rh-factor system also increased the sex ratio.

Andersson and Bergstrom foundd that short maternal stature and obesity in African populations of the C.A.R. were related to a lower sex ratio at birth, meaning that more females were produced than males. Experiments in animals indicated that this was a result of maternal malnutrition on the male fetuses. TM Allan in the journal Reproduction studied, along with many others, the effects of blood type upon the at birth sex ratio. Allan found that AB mothers tend to have boys, and that if a baby is type A, it will tend to be a girl. More specifically, he found that the ratio is low for AB babies of AB mothers, and also for A babies of A mothers. The ratio was high for O babies of O mothers B babies of B mothers. He hypothesised that the ratio schewing is caused by "sex-differential mortality caused by interaction of the ABO genes, and some o the sex-determining genes, with oestrogen and progesterone".
Environmental factors such as pollutants can affect the sex ratio by affecting the already formed zygote, or they can also affect the parents in such a way, pre-fertilization, as to change the ratio. Moracelli et al in Lancet in 2000 studied the paternal concentrations of the highly dangerous industrial poison Dioxin on this. The 2000 study was a continuation of a previous study examing a population exposed to a dioxin release in Italy in 1976. They showed that there was an increasing probability of producing female offspring with increasing concentrations of dioxin in the fathers. Furthermore, fathers exposed when they were less than 19 years old produced a sgnificantly greater number of girls than boys (with a ratio of 0.38, as opposed to 0.5). They also quantized their study and found that the median concentration of dioxin that produced this effect was similar to doses that induced epididymal impairments in rats. Many people have hypothesized that this might explain the sex ratio schewing that is occuring in industrialized nations, however they found that the media dose in their study was twenty times the average estimated concentration in people in industrialized nations.
Another important pre-fertilization factor to consider is meiotic drive. This is where whole chromosomes will have one effect or another and cause themselves to be represented in the gametes in higher than normally expected amounts. This can occur with autosomal chromosomes, but also with sex chromosomes. Jaenike in Evolution in 1999, for example, noted that a particular species of Drosophila is polymorphic for X-chromosome meiotic drive, and that matings with males who have a 'sex-ratio' X chromosome (designated XSR) result in the production of strongly female-biased ratios, and also that there was variation amoung the species for suppression of this drive. In humans, Jaenike in Annual Review of Ecology and Systematics showed in 2001 the presence of driving sex chromosomes can reduce fitness within a population, and even bring about intragenomic conflict between the X, Y, and autosome chromosomes.
A theoretical study conducted by Norberg in 2004 and published under the NBER Working Paper Series found that sex determination can actually be affected by the pressence or absence of two-parent care. Norberg found that, from a sample population, 51.5% of respondants who were living with a partner before the child's conception or birth reported male births. 49.9% of those who were not reported male births.
And finally Grech et al in BMJ reported on "unexplained differences in sex ratios at birth in Europe and North America", noting that mammals in general have more males than females born, and that in humans the actual ratio is expected to be 0.515. In their study it also was found that statistically more boys were born in soutern countries than in central europe or the nordic countries. A low ratio was found in mexico, higher in teh US, and even higher in Canada. In a reply however, Voracek and Fisher reanalysed the data and found that the ratio was varying with latitude, and by virtue of that varying seasonal changes in the climate and varying photoperiods. Sheilds et al also responded to the Grech study, noting that maternal infection with the cytomegalovirus also influenced the sex ratio torwards more males, and that this infection was also associated with "social deprivation and unmarried status"
So studies have shown that the sex ratio is offset from the expected 50:50, in many animals, by adaptive and non-adaptive traits, and by pre and post zygotic factors, ranging from biochemical incompatibility to environmental pollutants and climate.

Mendelian Genetic Laws

The Law of Independant Assortment



This simply states that during the formation of gametes that pairs of alleles will segregate independantly of one another. This means that when considering two genes (with 2 alleles each, therefore 4 alleles all together), all combinations of gametes genotypes will occur.

The Product Rule
This permits one to calculate the probability of two independent events both occuring. Simply multiply the probability of one event by the other. The probability of an individual having a genotype of yy is therefore
1/2 X 1/2 = 1/4

However, the probability of an individual having a genotype of Yy is not as simple, as these are two mutually exclusive events; because one parent must give Y and another must give y and not anything else.

The Sum Rule
To calculate the probability of two mutually exclusive events both occuring, you add the individual probabilities.. So the Probability of having Yy is
1/2 + 1/2 = 1/4

Multiple traits can be analyzed via these methods. Consider two individuals heterozygous for 3 traits being crossed

AaBbCc X AaBbCc

The Probability that the offspring will have a genotype of aaBBcc is

1/4 x 1/4 x 1/4 = 1/64

Because the events are independent and thus only the Product Rule applies.

The probability of having the phentoype ABc can also be calculated

3/4 X 3/4 X 1/4 = 9/64

Chi-square Analysis
This type of analysis allows one to determine how close to the theoretical results one's experimental results are, and if something other than statistical chance is creating unexpected results. The formulae is


Where E is the expected results and O is what is actually observed. The answer to the equation is then compared to a chi-squared table, using the degrees of freedom and the above value to determine the 'p' or proability for the experiment. For genetic analyses, if there are two phenotypic classes then there is one degree of freedom. The p values inform you as to theprobability that the variations were due to chance, and usually p values lower than 0.05 are considered a cut off. That p value would mean that there is a less than 0.05 percent chance that the variations were statistically insignificant.

Patterns of Inheritance and Pedigrees


A pedigree is a diagram showing the inheritance patterns of traits. A horizontal pattern of inheritance indicates that a trait is rae and recessive. It occurs in several members of any particular generation, but doesn't tend to occur generation to generation. A vertical pattern of inheritance is where the trait is in every generation. Often these are dominant traits, however a very common recessive allel can give the same pattern. Approximately half of the family will get the trait when its within the family, and everyone that is affected will have an affected parent.

Incomplete Dominance

The appearance of the intermedaite pink trait is a result of gene dosage, gene A produces a red pgiment, gene 'a' produces a white pigment. Homozygotes are either red or white, but heterozygotes are pink, because they have both a red and a white pigment. This is called Incomplete Dominance and is sometimes called 'blending inheritance'

Co-Dominance

Human blood types illustrate the concept of co-dominance. There are three alleles, Ib, Ia, and i. Regardless of what other alleles are part of teh genotype, so long as allele Ib is present, a particular sugar is added to the coats of red blood cells. If Ia is present, then a different sugar is added. So when both are present, both are added, and when neither is present, and the genotype is ii, no sugars are added.

A child with type A blood born to a mother with type B blood could not have come from a father with types O or B blood. This is why blood typing is sometimes used in paternity testing.

Some genes are not simply dominant to each other, but infact occur ina dominance series, such that A >ax>af>a

Other alleles can infact be leathal when present in the homozygous condition.

In general, by examining the ratios of crosses, one can determin ehow the genes are acting. A 12:3:1 ration indicates that Dominant Epistasis is occuring. The 9:7 ration indicates that complementation between multiple genes is occuring.

Chromosomes

In the somatic cells of an individual, there is a fixed number of chromosomes, humans have 46 and flies have 8 for example. The chromosomes are present in pairs, this condition is called the diploid condition or the 2N condition. Gametes, however, are haploid, they posses just the 1N number of chromosomes. In humans the gametes possess 23 chromosomes.

Mitosis is the process by which new cells are produced, the end result is two daughter cells with identical sets of chromosomes.

1. Chromosomes duplicate, with copies remaining attached to each other, these attached copies are called 'sister chromatids'
2. The Sister chromatids line up in the center of the cell
3. They seperate to opposite poles of the cell
4. The cellular cytoplasm divides, resulting in two new cells

In meiosis, there are two rounds of division and a duplication. Meiosis is often called 'reductive division'. A diploid cell that completes meiosis will yeild haploid cells.

1. The chromosomes duplicate into Sister Chromatids
2. Homologous duplicated chromostomes pair (aka synapsis).
3. Homologous chromosomes(but not sister chromatids) will exhange material (aka crossing over)
4. Paired homologous duplicated chromosomes (aka tetrads) line up independently
5. Homologous duplicated chromosomes seperate from their homolog, forming daughter cells. These cells are not identical. This is what makes up the basis of mendellian Independent Assortment)
6. Duplicated chromosomes divide (iow, sister chromatids seperate), forming 4 daughter cells overall, each with half the original chromosomal content (iow, they are now haploid).

The Chromosomal Theory of Inheritance

When chromosomes were first observed in teh stains of cells, their function was not known and their behaviour wasn't understood. Over time, their complicated and bizzare movements noted above were observed and in 1902, Sutton hypothesized that these chromosomal bodies infact carry genes. He based this hypothesis largely the fact that Mendels theoretical Laws could be explained by the movements of the chromosomal bodies.

Chromosomes:

1. Occur in pairs
2. Seperate in gametogenesis
3. But reconcile in fertilization
4. And they assort independantly

The linkage between sex determination and the chromosomes strengthened this hypothesis.

Simple Genetic Analysis

Gregor Mendel is a great person to start off with when considering the analysis of genetic traits. This is becuase not only was he the first person to systematically do this, but also because he used surprisingly 'modern' seeming methods. He was extremely thorough in choosing his paths of investigation, and also extremely detailed and systematic in recording his results.
His investigations were so successful because he used an excellent organism to study, the Pea plant. It has a short generation time, which is vital when studying the distribution of characteristics over generations. They're also easy to control in terms of breeding, he could use a small brush or tweezers to control their breeding by physically manipulating their pollen bearing and receiving structures. They also produce a large number of offspring in each generation, this means that there are large datasets on which statistical analyses can be performed. Mendel used whats called "pure breeding lines" to begin his experiments, these are lines that are the result of a long series of breedings and that 'breed true' for a characteristic or trait, such as pod shape or pea colour. He'd then mate different pure breeding lines to create hybrids. The specific traits he picked to study were clearly identifiable. In systematic-phylogenetic terms he used 'bivariate' traits, ie traits that were either one of two extremes (green coloured or yellow coloured), rather than multivariate traits where there are a number of states that can be occupied or even a smeared out spectrum (ie, red, blue, yellow, or a continuum from blue to green to yellow).
Mendel performed reciprocral crosses for his study, mating, for example, purple flowering female to white flowering male, and then white flowering female to purple flowering male.

Some of the traits Mendel studied












Monohybrid Cross

The simplest type of cross Mendel would do is called a monohybrid cross, this means that the result is a generation hybridized for a single trait, rather than multiple traits. An individual from a pure breeding line for one trait is mated with an individual from a pure breeding line with the opposite trait.

Now the whole of the new generation, called the F1 generation, is only showing one of these clear traits, such as green colour or smooth pea shape, and the other traits, yellow colour or wrinkled shape, are lost. Next, the F2 generation is obtained by self-fertilization of F1 plants. Mysteriously (at the time), the lost trait reappeared, in proportion with the other trait also. The two types show up in a 3:1 portion, the lost trait reappears as a third of the whole population. Mendel concluded that there is latent information that is not expressed in the plant. That the lost trait was preserved somehow.

The trait that appears in all of the F1 generation is called 'dominant', the trait that is lost but will reappear is called 'recessive'. Mendel reasoned that each plant contains two discrete units of inheritance. Today we call the unit a gene and the discrete and different forms alleles.

Individuals in this case are diploid, they have a 2N genotype, iow they have two alleles for each trait. In gametes however, there is only a 1N genotype, the haploid condition. During gametogenesis only one allele is packaged into the gamete. This packaging process is called Segregation. From these genotypes result phenotypes, the actual displaying of characteristics and traits. Individuals with both alleles in the dominant form or both in the recessive form are said to be homozygous, whereas individuals with a mix of the dominant and recessive alleles are heterzygous.

In order to predict the percentages of different phenotypes and genotypes in a new generation, a Punnett Square can be used.

The outer edges of the square essentially represent individual and distinct gametes from the crossed individuals (the parental generation). The boxes within the square represent the genotypes of the individuals in the offspring generation, and from this the phenotype can also be determined. In a self-fertilization of the F1 generation, there are two phenotypes and three genotypes. Half of that generation are heterozygotes. A quarter are homozygous recessive and another quarter are homozygous dominant. This is a genotypic ratio of 1:2:1 , and a phenotypic ratio of 3:1

The Punnett Square follows two simple probability rules, the Sum and Products rules. The Product Rules states that the probability of two independant events both occuring is the probability of the first event times the probability of the second event. In a monohybrid cross (Yy X Yy), the probability of a gamete having a y allele is 1/2. The probability of a gamete having a Y allele is 1/2. So the probability of an individual having a genotype of YY or even yy is 1/4. The probability of getting the heterozygous condition is not independant. The Sum Rule states that the probability of two mutually exclusive events occuring is the sum of their individual probabilities. So the probability of one parent giving the y allele and then the other giving the Y allele is 1/2 x 1/2 = 1/4. The probability of the reverse, say the female parent giving y and the male giving Y, is also 1/4. The sum of these two events is the probability of an individual being heterozygous, Yy, which is 1/2.

Mendel then crossed his F2 generation. When he crossed F2 green peas he got all green offspring, and with F2 yellow peas he got all yellow offspring. Of this, 1/3 ended up being pure breeding. 2/3 gave rise to yellow and green peas in a ratio of 3:1 (iow they were hybrids).
To distinguish between pure breeding individual and a hybrid you perform a test cross, wherein the unknown is crossed with a known homozygous recessive. The ratios and types of offspring that result will allow one to work backwards to the parental genotypes.


<--phenotypes are all one type

phenotypes are half and half --->

For example, in cattle, the polled phenotype (which is hornless) is dominant over the horned condition. If a polled bull is crossed with

• Cow A, horned, and yields a horned calf
• Cow B, polled, and yields a horned calf
• Cow C, horned, and yeilds a polled calf

Then what are the genotypes of all those involved?

To determine, you'd consider a test cross with a homozygous recessive individual. A homozygous recessive individual is anyone who displays the recessive trait. A horned cow, such as Cow C, is therefore homozygous recessive. In order for a cross with Cow C to result in polled individuals, there must be at least a single polled allele in the bull. Thus we now know part of the polled Bull's genotype.

The cross with Cow A however results in a horned calf. Since that calf is horned, its also homozygous recessive, and that means that it has two recessive alleles, only one of which can have come from the Cow. So the other must have come from the bull, and therefore the bull has at least one recessive allele. These results taken together mean that the polled bull under consideration must be a heterozygote.

This means that in the cross with the polled Cow B, which results in a horned calf (which, again, must be homozygous recessive ), that Cow B must be heterozygous, in order for it to produce a gamete with the recessive allele.

The phenotypic ratios of offsprings from each crossing set can also be determined. Because crossing A and C is a homozygote and a heterozygote, this is the punnett square.

This results in half the offspring being polled and half being horned. A ratio of 1:1

The crossing with Cow B, which is another heterozygote, results in this Punnett Squar. Here the offspring phenotypes are in a 3:1 ratio.

Dihybrid Cross

Mendel also considered dihybrid crosses, wherein the individuals to be crossed have opposite characteristics for multiple traits. For example, in a cross of Pure breeding yellow-round peas with pure breeding green-wrinkled peas, (YYRR x yyrr), the F1 generation individuals were all yellow and round (all hybrids). In the F2 generation, he received the following:

• Yellow Round....315 (a parental type)
• Yellow Wrinkled....101 (recombinant type, new combination of characters)
• Green Round....108 (recombinant type, new combination of characters)
• Green Wrinkled...32 (the other parental type)

Notice that individual traits, such as Yellow, still appear in total in a 3:1 ratio.

In the dihybrid cross, the different pairs of alleles segregate independantly into the gametes. Thus in a YyRr individual, the possible gametes are YR, Yr, yR, yr.

The genotypes will become present in their specific ratios, as shown.

Given a mulitple cross of two heterzygous individuals for three traits (AbBbCc x AbBbCc) , what is the probability that offspring of aaBBcc genotype occuring?

1/4 x 1/4 x 1/4 = 1/64