Sunday, January 15, 2012


In this post I will materialize the importance of the Abstraction’s Environmental Process referred in the previous post. One of the ways this process become a reality is trough the chromosomal Crossing Over, as part of the Meiosis event.

In 1866, Mendel published his now famous paper entitled Experiments in Plant Hybridisation. In this time, evolutionists were attached to the blending kind of hereditary. This blending paradigm is one of the main reasons to the continuous view of evolution. Mendel, and his laws, brings a discrete and independent view of hereditary. However, in the same way only in 1900 his work was really appreciated (more than 30 years later), nowadays; the continuous view of evolution hasn’t yet been substituted by the discrete one. There are always people that simple don’t get it, and get stuck in details, in the following writing, details like not fully independent, or exotic disputes about other details, don’t change the point taken.

The Mendel laws are the base of the Hardy–Weinberg equilibrium, and because of that, this equilibrium, are only applicable to Eukaryotes and not to Prokaryotes. Now, what do you call, to the idea that all life is equally evolving, in a continuous and unstopping way like in Prokaryotes, and then, your examples are invariably involving Eukaryotes? You call it a delusion. Now, what it happens, when you ask to a deluded, if; are we still Evolving? If for the deluded, evolution is an unstoppable continuous process; he has the problem in conciliating the evolutionary force with his unstoppable and continuous concept. This difficulty makes the deluded a treasure hunter, where the treasure is the motive of the Natural Selection bias. If evolution has to be, the motive has to be found. As if it were not enough, you have the sticking species, and the respective speciation process undermining the continuous view of evolution. Now the delusion becomes denial, the denial of species’ existence, transformed in nothing more than a classification.

There is a question that until now hasn’t been well answered. What is the inbreeding effect on the genome quality? Charles Darwin was very concern with this issue, because he rightly suspected, that he and his family was victim of it. In a study entitled Was the Darwin/Wedgwood Dynasty Adversely Affected by Consanguinity?, by Tim M Berra, Gonzalo Alvarez, Francisco C Ceballos, it’s concluded that:
“(...) the high childhood mortality experienced by the Darwin progeny (...) might be a result of increased homozygosity of deleterious recessive alleles produced by the consanguineous marriages within the Darwin/Wedgwood dynasty.”

The experienced mortality wasn’t due exclusively to contagious diseases as many try to prove, but also to pure congenital ones, like the case of the last sun of Charles Darwin named Charles Waring. Many still see this as lack of diversity, as a mean to response to fast genetic change in infectious diseases. The name of this view was coined the Red Queen’s hypothesis.

Here I will give other explanation for the importance of Crossing Over, and show you that the so called arms races has nothing to do with it.

First of all, we will consider the two laws of Mendel. Those laws are:
  1. Law of Segregation – every individual possesses a pair of alleles (assuming diploidy) for any particular trait and that each parent passes a randomly selected copy (allele) of only one of these to its offspring;
  2. Law of Independent Assortment – separate genes for separate traits are passed independently of one another from parents to offspring.
Another thing to have in mind in the next simulations is that we will only consider the crossing over process in meiosis, and consequently; we will always consider haploid genomes for the sake of simplicity.

To help us to see what happens, we will construct an analogy with a picture made by pixels. In the next picture we have our Little Joe. We will consider the genes as the colors in each pixel of his picture. In this way, our analogy has the following meanings:

Original Picture of Little Joe

From the previous full picture we may zoom in to visualize each pixel.

Zoom of the original picture

Next we have the generation tree for the simulation:

Stacking tree per generation

For the first simulation, we approach the merging view of the 19th century for heritably (continuous process), staring with the creation of 16 pictures resulted from the insertion of random noise, each one with the same parameters, in the original picture (Genome) for the 1/16 generation. The first obtained picture, similar in noise to the other 15, looks like this (first arrow):

Sample 1 of 16 from the generation 1/16

For the 1/8 generation, and following the generation tree, we will evenly stack each picture of the 1/16 generation by a methodology similar to focus stacking, resulting 8 pictures with reduced noise. The first obtained picture, similar in noise to the other 7, looks like this (first one of the 1/8 generation):

Sample 1 of 8 from the generation 1/8

Repeating the process for the generation 1/4, the obtained picture, similar in noise to the other 3, looks like this (first one of the 1/4 generation):

Sample 1 of 4 from the generation 1/4

Repeating the process for the generation 1/2, the obtained picture, similar in noise to the other one, looks like this (first one of the 1/2 generation):

Sample 1 of 2 from the generation 1/2

Finally, we get a single picture for the 1/1 generation, with extremely reduced noise comparably with the one on the 1/16 generation.

Final sample from the generation 1/1

In conclusion for this first simulation, the merging process clearly has the ability to reduce noise, however, this ability tend to lose strength for each new generation. This has to do with the merging nature itself. While merging we are making averages, and as many averages we make, we never get the real color of the original picture despite the approximation to with. The maximum that the merging process can provide is an Asymptote to the original color.

Animation from generation 1/16 throughout 1/1

Now we will take a different approach. We will take for granted the species. Species in the next simulation will be represented by the original picture of the Little Joe. Species, a product of Sexual Selection, is seen here as a target of systematic bombardment made by noise. In this way, our analogy has the following added meanings:
  • Original picture – Species;
  • Mask – Threshold between positive and negative allele’s feedback;
  • Mask’s white pixel – Fixed allele;
  • Mask’s black pixel – No fixed allele.

In this simulation we drop de continuous view of the noise, and adopt a Yes or No kind one. In this way, we create a Mask for the picture where is marked if there is or isn’t noise (no fixed allele). For this mask, we use the color white for the pixel without noise, and black for the pixel with noise.

Using the first 16 pictures of the previous simulation, we produce for each one of them, the white and black mask. This mask, and the resultant picture, similar to the other 15, looks like this (first arrow):

Mask sample 1 of 16 from the generation 1/16

As you can see, this mask doesn’t represent a uniform distribution of random noise; however, because it still represents a random situation it makes no difference for this simulation.

You immediately note an important difference, now, due to this discrete approach, the noise looks like sand in a surface, it almost seems like something you may literally clean instead of dimming it.

For the staking process, we consider the product of the Mask’s pixels, so, the white pixel represents 0 and the black one 1. For each pixel we have the following stacking results:

Bellow we will review the mixed staking in more detail, for now we just accept things as they are.
Applying the stacking process, the first obtained Mask, and the resultant picture, similar in noise to the other 7, look like this (first one of the 1/8 generation):

Mask sample 1 of 8 from the generation 1/8

Repeating the process for the generation 1/4, the obtained Mask, and the resultant picture, similar in noise to the other 3, look like this (first one of the 1/4 generation):

Mask sample 1 of 4 from the generation 1/4

Repeating the process for the generation 1/2, the obtained Mask, and the resultant picture, similar in noise to the other one, look like this (first one of the 1/2 generation):

Mask sample 1 of 2 from the generation 1/2

Finally, we get a single Mask and the resultant picture for the 1/1 generation, with practically no noise comparably with the one on the 1/16 generation.

Final mask sample from the generation 1/1

Unlike the merging simulation, here there is no continuity restriction, and so, convergence can be total without any kind of Asymptote, and more importantly, there is no losing strength in reducing noise.

Animation from generation 1/16 throughout 1/1

As told before, we considered the result of a mixed stack, Heterozygous, as always White (0). You may think that it is an over simplification, however is not far from reality.

Firstly, while a no fixed allele will frequently encounter a mixed stacking (Heterozygous), a fixed allele, on the contrary, it will frequently encounter an equal allele (Homozygous), so, in terms of chances and accordingly with the first law of Mendel, a no fixed allele sees his probabilities of being carried on reduced by 1/2 per generation (Exponential decay), while the fixed one, only sporadically gets in that situation.

In top of the exponential decreasing probability, we have the Natural and Sexual Selection, each one with the following three kinds of feedback:
  1. Positive Feedback – Increases offspring relatively to the average;
  2. Neutral Feedback – Maintains offspring relatively to the average;
  3. Negative Feedback – Decreases offspring relatively to the average.
Both Negative Feedbacks, for Natural or Sexual Selection, are the last hope killers for the “lucky” noise, which one, albeit the odds managed to remain in the genome, sees its diminished odds become even more reduced next to nothing.

In conclusion, the exponential decay of the probability of fixation for a no fixed allele, associated with the negative feedbacks of Natural and Sexual Selection, is a good base to consider that the result of the crossing over between a fixed and no fixed allele is the fixed one, mainly if the no fixed one has no evolutionary advantages (noise).

However, knowing that we are considering haploid genomes, we should not view these values as exact ones. For instance, for a new allele get fixed in a population without any inbreeding, the positive feedback of Natural Evolution had to be such, to the point of canceling the Exponential decay previously referred. In this way, that positive feedback would need to produce more than 2 times the average offspring per generation, so that 2*1/2 becomes 1 (same as the fixed allele), and to compensate the initial negative feedback from Sexual Selection.

Now you may ask, but it’s not possible the existence of Positive Feedback from Sexual Selection for the newcomer allele? For the right answer, we need to realize that the positive feedback of Sexual Selection is in the direction of the existing genome that defines the species. As you saw in the last simulation, the mask is the result of the difference between the original picture and the one with the noise, and in this way, Sexual Selection is attached to a referential, something that doesn't happen with Natural Selection. So, if positive feedback for Sexual Selection is relative to an existing referential, only Natural Selection has the ability of giving Positive Feedback for newcomers.

Some of you are in this moment thinking about the peacock's tail, and making the question if that is not an excellent example of Positive Feedback of Sexual Selection for newcomers. Thirst of all, you have to have in mind that tails per se are common in birds, so tails have a Positive Feedback from Natural Selection. What we are discussing is the ornament not the tail, and the ornament may well be explained with correlation. So, if a trait, any trait, positively correlates with some other trait or traits, which have Positive Feedbacks, either from Natural or Sexual Selection, with time, and only through Natural Selection, that trait becomes a fixed trait. When it becomes a fixed trait, and only then, it may receive Positive Feedback from Sexual Selection, simply because it becomes part of the new existing referential (species). In this way, you may think in beautiful bird singing, vibrant feathers colors, and stunning flowers as exclusive products of Natural Selection.

Giving a step forward, we will approach in detail the issue of Consanguineous or Inbreeding reproduction. Since Adam and Eve times, inbreeding reproduction becomes an inevitably, however, we will not explore the Adam and Eve reality; but instead, we will try to understand what we mean by the inexistence of inbreeding, and then, its degree.

Without inbreeding, our heritage (past generations) would follow an exponential Power of Two, and after few generations, would become greater than the existent population. To visualize this reality we will use the demography evolution of Portugal expressed in the next picture.

Numeric simulation with Portuguese population

Using a generation length of 30 years, by the year of 1410 any Portuguese born after 2010 would be relative to all the Portuguese population previous to 1410! This young Portuguese would be a direct descendent of figures like the Henry the Navigator, or even his great father, John of Gaunt. In the next graphics is possible to visualize the interception point, where the population needed for a perfect non consanguineous reproduction meets the real one.

Graphical simulation with Interception point (1410)

Now that it’s clear that inbreeding is an inevitable reality, it’s time to understand its impact in the Crossing over process. More, the real question is not, what is the impact of inbreeding, but instead, what is the impact of inbreeding’s degree. For this degree we use the distance in generations. For example, in case of brothers we have 1 generation distance, in case of first cousins 2 generations, and so on. Using our generation tree, we may construct a table with the impact of consanguineous reproduction, and see the impact in terms of genetic sampling.

Generation tree considered in the simulations

In the last simulation a consanguineous reproduction can be seen as a branch removal. From the way the simulation was carry on, based on the product of the Mask’s pixels, is applicable the concept of Absorbing element, where the White (0) pixel is the Absorbing element. One of the properties associated with the Absorbing element, is that the operation order doesn’t maters, the result is the same, the absorbing element White (0). This means that the reduction of branches is equivalent to the reduction of samples. In the simulation there were 16 samples of masks, as you can see in the next picture, depending on the generation where we have inbreeding; there is a reduced new set of samples. For instance, in the case of an inbreeding in the 1/2 generation, half of the samples are removed from the equation, meaning that only 8 samples become stacked, the same effect as stopping the reproduction series in the 1/2 generation instead the 1/1.

Unremoved noise due to consanguinity

It is possible to see in the image above; that inbreeding in the generation 1/2 has an impact in the picture, maintaining some noise that otherwise would have been removed.

Other conclusion is possible to make, as you can see in the next picture, inbreeding loses its influence in an Exponential decay way as far from the 1/1 generation it occurs. For instance, a single consanguineous has an influence of 2/16 in the 1/8 generation, and an influence of 4/16 in the 1/4 generation, or in other words, the inverse of the possible number of no consanguineous mating for a given generation.

Impact of inbreeding’s degree

Consanguinity is not worldwide equally distributed, some countries, like India and Pakistan, have high rates of consanguinity. The “rat-people” is a crude example of a mal functioning cross over, something promoting fixation of alleles that otherwise would never become fixed.

Worldwide distribution of consanguineous marriages

It’s now possible to conclude that there isn’t any kind of arms race, what we have is deleterious mutations that became easily fixed due to redundant crossing over in the respective locus. These deleterious mutations, like many other symptoms, weaken the immune system to the point of being exploited by infectious diseases. They work in somehow like AIDS, making people much more likely to get infections, including opportunistic infections and tumors that do not affect people with full working immune systems.

There is another problem with the arms race of the Red Queen’s paradigm, that problem is called blood type. Blood types varies in worldwide distribution, with A blood more frequent in Europe, Australia and North America, B blood, more frequent in Asia, and O blood bore frequent in Latin America. If this is considered an arms race, you have to consider races also the result of an arms race, because the distribution of blood type isn’t very different from other racial traits, neither in time or space. In that sense, the black skin of an African person would have to be seen as an arms race against the sun. The problem is that, like in races, there aren’t significant variances in time and space to attribute to other reasons than Natural Selection. However, this arms race is still argued as the reason for Sexual Selection, something essentially different from Natural Selection.

If blood type is no more than a polymorphism, like skin color, and if blood types play an important role in the protection from infectious diseases, there is little credit to be given to Arms Race or any other thing but the old and simple Natural Selection. What you really have in constantly change that crossing over works against it, is not any kind of virus, or bacteria, it’s instead, the old and simple noise. This noise, the product of Dissipation, root of all environmental processes, undermines the complexity in life and the possibility of greater genomes. Crossing over, and the consequent Speciation, is the working solution that no Eukaryote was ever able to be truly free of.

Dependence stacking of environmental processes

So, what crossing over really is? Crossing over is the instrument of the Environmental Abstraction process. This abstraction becomes the new entity subject to evolution. With abstraction, organisms were drained of protagonism, given to the new concept of Species and its Sexual Selection mechanism. This way, species become the real subject of Natural Selection and the consequent Evolution, or simple putted, Strains gave place to Species.

If materialization was needed, you just need to remember the heritage’s Power of Two exponential process. This form of heritage, only possible with crossing over, works like a stairs that connects species with individuals; turning them, not into children of parents, but into children of species. So, for the question, what makes us human? We may simple answer, the Species does.

Stairs connecting species with individuals

In conclusion, there are those who ask how, and those who ask why, Mendel, was one of the last kind. I will end this post with a simple sentence to bear in mind.

“The HOW represses, the WHY frees.”

Prokaryotes vs. Eukaryotes, NS - Natural Selection, SS - Sexual Selection

1 comment:

  1. No need to mention that Crossing Over (Meiosis) allows a level of fluidity with no match by any other form of reproduction!