Introduction
This site proposes a new mathematical theory of natural selection, enhanced by using a new 'Darwinian' model of molecular evolution.
The new theory is needed to solve many paradoxes of evolution, where the existing theory fails. The paradoxes include how life evolved from non-life, why sex evolved, the advantage of the chromosome, and if fitness always rises. The new theory is also able to show why a standard model can only prove a frequency gain for adaptation within species, but not for transition, into new ways to reproduce. Finally, the new theory is able to solve the famous Schrodinger Paradox, to prove how life evolves against its usual thermodynamic direction.
Of course, many evolutionists insist that these paradoxes are already solved. Others admit that these are not solved, but question if frequency methods can even solve them. The new theory uses a frequency solution, but with an enhancement, concerning molecular change over millions of years, and across the huge scales of life.
To explain, frequency methods work best for evolution on a small-scale, but fail on huge scales, and no one knows why. The reason is that when selection on a small scale accumulates over huge times, it does not just alter organisms, but it alters the molecular background of life as well. This is known, except there is no theory for how to emulate molecular change as a frequency, so a simplification is made. Instead of trying to solve it, a standard model assumes that over short times the molecular background of life will seem "fixed" or static, apart from odd mutations. Mostly this works, except over billions of years, molecular change is not static, and this causes paradoxes.
For example, in the transition to sex, frequency fell from 100% to 50%, which is a paradox, how a 50% loss was an advantage. The answer is that the 50% loss was for the cellular pathway, but along the molecular pathway genes gained frequency far more, I will shortly prove how. Sex is one example, but each paradox, even for Schrodinger direction, can be solved this way. From this, anyone who thinks that the paradoxes are already solved can assess how the new theory solves the same problem. Only by comparing each solution, and testing each answer against many facts, can we reach a fair conclusion.
The Basic Model
Even so, despite giving testable answers, the new theory challenges two paradigms, at the core of evolution theory.
The first paradigm is the 'mutation-centric' view of why genes gain frequency, and "mutations are considered the driving force of evolution". In the new theory, genes still gain frequency by mutating into varieties useful to the cell, but it is the cellular gain, which is not the only way for genes to gain distribution. Instead, once an adaption is proven, the gene will conserve sequence (resist mutation), and genes that conserve proven sequences for millions of generations, distribute that sequence widely across life. If anything, the simplification that the molecular background seems fixed (static), even for short times, could only work if some genes were infinitely conserved, which is not correct either. Instead, across all of life, no gene is infinitely conserved, but genes that conserve sequence more than rivals do, distribute wider across life, over genes that mutate to adapt. To settle any doubts, this rule can be tested, and if tests prove that conserved genes do distribute widest, this is pathway of natural selection. Along this pathway, genes compete for molecular gain, to maximize their distribution, across all the populations of life.
If there were two pathways, along which genes gain frequency, via cellular gain in one population, and molecular gain across life, we should be able to combine both pathways in one frequency model, to compute the total gain of frequency for any gene, in any population, in the history of life (say, when sex evolved). Except, to do this would confute another paradigm of evolution, concerning probability theory.
To explain, frequency is a probability, and one early triumph of the frequency method was proving that evolution uses a simple probability, like in a game of cards. However, if genes can gain frequency two ways, then one probable event will have two probable outcomes, which is not the same as a game of cards. Especially, there is no theory how this could work, so in Fig 0.1 below, and Fig 0.2 next, let me clarify.
See Fig 0.1
Usually, any probable outcome is a single number, between 0 and 1, or 0 and 100%. For evolution, it is the same, except events unfold over time. Fig 0.1 shows a probable outcome, xi, of a gene that begins from 0% frequency at 0% time, but then increases gain under natural selection. Growth increases naturally to 50%, but beyond 50%, the population fills with the new variety, so growth slows. Finally, growth ceases at 100% frequency after 100% time, when the model must stop. This is a standard "growth" (or logistic) curve, but gain need not follow this curve exactly. For the evolution of sex, say, we might expect a curve to settle at 50% gain in 100% time, and so on.
Notice, the curve in Fig 0.1 looks two-dimensional, but this is only an illusion of time. Each event has a single outcome, between 0 x 100% frequency per instant, but each instant is 'unfolded' over 0 x 100% time. In the paradigm, any probable event can be solved inside a 100% x 100% frequency-time 'window'. Except, for how genes distribute, a 100 x 100% window might not be correct. If say, a gene gains 100% frequency in one population, it can still migrate into other populations beyond 100%. If a population extinguishes 100% of its time on Earth too, its genes can live on, in new populations to evolve from the parent one. No one denies that genes can distribute outside this 100% x 100% window, but experts insist that such gene distribution cannot be applied as a frequency, because no probability model exists, to emulate such effects.
However, although genes distribute across millions of years in time, they also distribute in phylogenetic 'space', and this allows us to graph, not a 100 x 100%, 'window' but a 100 x 100 x 100% 'landscape'. Fig 0.2 next, shows (on a spreadsheet) how the result will look.
See Fig 0.2
Notice, whereas Fig 0.1 was a single growth curve on a flat plane, Fig 0.2, uses two growth curves to form not a flat plane, but a landscape. In Fig 0.2, the heavy black front curve shows the standard, cellular gain, xi, as in Fig 0.1. As in Fig 0.1, gain increases from zero, to peak at 100% frequency in 100% time, which is a standard 'window'. In reality, genes at 100% can migrate into new populations, and evolution does not stop at each 100% time interval. This is shown in Fig 0.2 by another growth curve, sloping away at 90O to the cellular gain.
The second curve shows the molecular gain. In the new theory, this has the symbol Xi ("big x" as against "little x", as in xi). Molecular gain, Xi, starts from the same zero point, and increases via standard growth. Just that whereas cellular gain ends on a peak, in one population, a gene as a molecule can descend into many populations, and some genes end up 100% in every population. In reality, very few genes distribute across life 100%, but this is still shown as a horizontal grey line on the far slope of Fig 0.2. Fig 0.2 does not show Xi directly, but a formula converts Xi into an xi base, and this conversion projects the far grey line to infinity. As a result, even if a gene gains 100% on the first peak, it can gain frequency beyond that until it reaches the far slope. Yet if the far slope is at infinity, a gene can only reach it in infinite time, so the model avoids the paradox of time ever needing to stop.
The Paradox of Sex
To give some background, a standard frequency model teaches that a gene tries to maximize its frequency. Of course, genes do not act from volition, but if humans can prove why specific adaptations resulted in a gene gaining frequency, it quantifies why the adaptation was via natural selection, and not another cause. This is why the new theory also tries to prove that genes can gain frequency beyond 100%, to prove that each transition beyond 100% was also due to natural selection.
The problem with this argument though, is that the most puzzling transition in evolution was not beyond 100%. Rather, before sex evolved, duplicates passed on 100% of genes, but using sex, parents pass on only 50% of genes. Despite claims that this has been solved, no one has ever proven how a 50% loss of frequency was a gain over 100%, before sex evolved. The new model might not seem able to solve it either, but look again at the shape of the surface in Fig 0.2.
To explain, we suppose that if a gene ascends the first cellular peak to 100%, and then migrates into new populations that descend from the originating one, we assume that a gene at 100% in a first population stays at 100% in the next populations after that. As fact, some genes, such as for histones, or ubiquitin, descend that way. Another fact though (it needs verifying) is that all genes to descend 100% for their full length only do it after sex evolved. Prior to sex, only sub-genetic lengths of full genes can become 100% distributed, or ancient genes, mostly of RNA, which show evidence of being 'horizontally' transferred across life. It infers that full-length genes cannot migrate from 100% on the first peak and then across to the far slope of Fig 0.2, except via the use of sex.
Fig 0.2 might reveal the problem. In a standard model of evolution, in Fig 0.1, a gene can gain 100% frequency in 100% time, at no penalty. Yet in Fig 0.2, notice, with two pathways, there is a penalty. If a gene ascends 100% on the first peak it becomes trapped, and cannot migrate to the far slope without descending to cross a "valley" between the peak and the slope. Of course, no textbook admits there can be a valley, but a peak is unavoidable graphically (try it) from two growth curves, if one curve ends in a peak, and the other ends on in a slope. Besides, there are ways to cross the valley, which might solve several mysteries.
The first way that a gene can cross from the peak to the slope is by 'horizontal' transfer. This will appear in Fig 0.2, as if the gene leaves the surface and simply leaps across empty space (as if in hyperspace). I will later explain why it is this way, but it occurred extensively in early life. The other way across, is not to ascend the peak all the way up. Notice, a gene could avoid crossing the valley where it is deep, if the gene stopped halfway up to the cellular peak, and crossed on a flatter part of the slope. Later, I show another diagram of why a gene would stop at exactly 50% along the front curve. I will also propose tests of molecular distribution, from before until after the transition to sex, which can test independently if this is the correct explanation.
Even then, the peak, valley, and slope in Fig 0.2, is not intended to explain each biological detail of sex, or nullify other theories about its advantages. There were many steps to the evolution of sex, the book will explain. Instead, before we even come to sex, the first paradox to resolve in evolution is how the gene can gain frequency, and the model can keep running, beyond 100% limits. Without this, you cannot even prove how life evolved from non-life. The method of two pathways of selection can solve this puzzle. As correlation, this method also seems able to solve the paradox over the evolution of sex. It might also explain horizontal gene exchange, and other effects leading to sex.
The Schrodinger Paradox
Now, let me give a solution to the Schrodinger Paradox.
There is much confusion over this paradox, and many evolutionists claim that it too is solved, although most people confuse thermodynamic direction with the Second Law, but these are not the same. Instead, this paradox concerns that any equation is a closed system of information, so it can run in either direction in time. When physical systems run in either direction, we call them reversible. When systems involve conversion of energy, rules stipulate one direction, towards increasing disorder, which is irreversible. Life combines reversible (the gene) and irreversible (the cell) processes. Incredibly, though, when the gene and cell combine, the irreversible part flips direction 180O, and moves towards an increase in order, against the usual thermodynamic direction.
To be careful, the 180O change of thermodynamic direction does not violate other laws, just that rules forbid us from adding the reversible and irreversible parts of an equation to prove a result. This problem, (I think), was the paradox correctly identified by Schrodinger. Notice, however, rules forbid us from combing the reversible and irreversible parts of an equation, but in a standard frequency, it is also forbidden to combine two pathways of selection. The new model can solve how to combine the two pathways, so if this is the same problem, this approach should be able to solve the Schrodinger Paradox as well.
In a two-pathway model, the cellular pathway is irreversible, and the molecular pathway is reversible, but both pathways are emulated as a frequency, which is reversible. Now, any frequency is directionless, but in Fig 0.2, there is a 'direction', in how the 90O 'angle', between the xi and Xi axes, is faced. This could be either +90O, or –90O, and there is no rule. In a transition, however, the molecular pathway has to cross the 100% barrier first, in which case the molecular path, Xi, 'leads' (like aiming a gun) the cellular path, xi. By convention, 'lead' is a positive, +90O. This is how Fig 0.2 is drawn, but I suggest that the +90O angle is the 'positive' thermodynamic direction to evolution, which is towards increasing order. Let me give two examples of how it works.
Take the case of modern life.
If Xi 'leads' xi, it roughly means that there will be more genes as a molecular frequency, distributed across life, than the same genes will be found in just one cellular population. It seems obvious, but if you test it, this is only true if life evolves in a 'positive' direction. For instance, if a gene exists in one cellular population, and it exists in other populations, this is only possible if the other populations evolved in the past, which is only possible if life evolves in a positive direction. On the other hand, if a gene existed in just one population, the +90O means that the gene might still spread into other populations in the "future", but this too is only possible if life evolves in a positive direction.
Next, consider an example from ancient life.
Critics can object that my example of modern life is unfair, because we know the answer after the fact. Yet take an example billions of years ago, no one could know about. In a pre-biotic soup, suppose that early selection was refining self-replicating molecules and empty proto-cells. The question then arises if there must be more or less self-replicating molecules than proto-cells, for life to evolve, or if both must be of equal number. No one could know, yet if the reversible process must 'lead' the irreversible one, then there must be more self-replicating molecules than empty proto-cells, in a pre-biotic soup, to cross the first transition into life. I hope that there is a way to test this, but I make a prediction, based on the rule that a +90O angle between the xi and Xi axis, is the 'positive' direction in which life evolves.
Objections to the Theory
Finally, let me remark on the objection by experts that my solutions do not conform to standard probability rules.
My thesis is that for life to evolve, two pathways of selection, for the gene and the cell must combine. The objection is that selection can only be emulated by a frequency, but a frequency is a probability, and it must obey strict rules. Probabilities, say, cannot exceed 100%, but in life, genes at 100% in one population can spread wider. Probabilities are also 'directionless'. Cellular migration might be 'vertical', whereas molecular migration can be 'horizontal', but probability cannot have direction. Life is also unified, because genes in a unique cellular population can belong to a larger molecular population, but that is not how probabilities work. If a cellular frequency was for one species, and a molecular frequency was for all life, these cannot be combined. It is odd, though, that cellular and molecular pathways combine for life to evolve, yet mathematics cannot allow them to combine, without breaking rules.
The solution to this paradox is as follows.
The rule says that probabilities are a one-dimensional (1D) number, between 0% and 100%, and a probability cannot exist outside this limit. For example, the curve in Fig 0.1 looks like a 2D surface, so it seems as if two dimensions were used to draw it. Yet by convention, Fig 0.1 is a single 1D frequency, xi, unfolded over 0% to 100% time. By convention too, this curve is within the rules of probability.
On the other hand, if you look at Fig 0.2, it no longer looks 2D, but three-dimensional (3D), in a landscape, so it seems it uses more than one dimension to draw it. Instead, Fig 0.2 is a single frequency (call it zi) but now projected along two eras of time. The front face of this curve shows standard time, maybe twenty generations "here and now", which repeats Fig 0.1. The difference from Fig 0.1 is that the equation to draw Fig 0.2 includes a formula to convert molecular distribution across all life, into another axis of time, but still strictly within the rules for such problems. Experts can object, of course, that the formula of gene distribution across life is wrong, or it is not true that genes can distribute in different eras of time, but that is not the mathematical dispute. If there were two eras of time, for whatever reason, it should not violate the rules for a single frequency to spread across both of them.
Besides, if this interpretation were wrong, it would be very easy to falsify any part of this theory.
For instance, just in this introduction, I have made a prediction of thermodynamic direction, no one has dared predict before, and anyone could prove it wrong. I have offered a solution to the paradox of sex, and have predicted its results as molecular distribution, which it would be easy to prove wrong. I have predicted a previously overlooked "valley", between the first peak, of 100% frequency, and how a gene distributes at 100% across all life; anyone can prove that the valley is not there. Then, contrary to the 'mutation-centric' paradigm of evolution, I predict that the most conserved (least mutated) genes spread widest across life, and that every transition that is a paradox, resulted in gain of conservation, not mutation, for core genes. Anyone could falsify this prediction, merely by measuring wide-scale molecular distribution, quite independently of any mathematical theory of how it worked.
Even so, there is one objection to my theory, which I do not think is a fair or falsifiable scientific test.
This is to argue, flatly and without evidence, that my thesis must be wrong by implication, because each paradox mentioned, including of sex and thermodynamic direction, has been solved already. No one will cite a contrary proof, but it is inferred that if the paradoxes existed once, and hundreds of scientific papers about them have been written since, surely they must be solved by now. I examine this argument in the book, but I invite readers also to check on Wikipedia, to see how the mere hope that these are already solved has become self-fulfilling.
For example, the justification of my thesis is to solve the paradoxes, yet if you check for "paradoxes of evolution" on Wikipedia, there are no references under that entry. If you then search for paradoxes well known in the literature, each entry is redirected as if each paradox is now solved. For instance, if you search for "paradox of sex", you are redirected to a paradox for the two-fold cost of sex. This paradox is allegedly easier to solve, but it only concerns how sex is maintained after it evolved, rather than the original paradox of the frequency advantage for sex to evolve. If you then look up the "evolution of sex", you are directed to descriptive theories of its origin only, without any mention of the frequency paradox, or any mathematical solution to it.
Each entry is redirected this way. The paradox of sex concerns gene frequency. Yet if you look up "gene frequency" in Wikipedia, it was not before, but now it has been changed to allele frequency. This is because gene alleles only evolved after sex, so by renaming it 'allele frequency', this avoids the need to prove the frequency advantage for sex to evolve. Apart from sex, there were other paradoxes, of the chromosome, or first life, yet all references to these are removed as well. There was a famous equation by Sir R Fisher, which caused a paradox over the rise of fitness. Yet if you search "Fisher Equation", it is redirected to "Price Equation". This equation allegedly solves the fitness paradox, although I can prove that the Price model does not solve it either.
Now, consider the Schrodinger Paradox.
Again, there is much confusion over this. We know that the paradox concerns that life evolves against the usual thermodynamic direction, but this raises several issues. Wikipedia states that the paradox from this is that life does not violate the Second Law, which is easily solved, but I am sure that Schrodinger knew that, so this solution is a straw man, not the real paradox. The next paradox, not on Wikipedia, is the degradation of information over time. This is solved in my model if genes also compete to conserve sequence, but neither Schrodinger nor anyone else knew that. The final paradox about thermodynamic direction is that any equation is either reversible, or it is irreversible towards disorder, but no equation is irreversible towards an increase in order, in the 'direction' in which life is different from non-life. Surely, this paradox worried Schrodinger as well, but it is not mentioned on Wikipedia, and this paradox too has never been solved, apart from my proposal here.
I hope that there is no need to press this issue further.
People can say that this is only on Wikipedia, but even then, surely the issue is not how arguments are presented. It is whether key paradoxes in one of our most important sciences have been solved or not, yet no one is prepared to answer explicitly. Remember too, regardless how anyone claims it the underlying paradox is that the gene and the cell must both refine using natural selection, for life to evolve, but a standard frequency model cannot emulate this. In this case, ironically, it is correct that these paradoxes occur, because the model is incomplete.
This is why I prefer to state my own solutions, and let anyone who claims that this is already solved compare the answers. To me, the data needed to resolve this, is whether genes maximize distribution across all life by conserving sequencing, as my model predicts, or if genes compete only by mutating into new varieties, as the standard model teaches. If we verify this, it can be solved. The other choice is to check the equations, to verify if a frequency can enact along two pathways, and then check this against data. By contrast, if people think that this can be solved merely by "redirecting" entries on Wikipedia, or altering the names of famous paradoxes, to argue that with a different name it no longer needs solving, science cannot advance by this mean.
Summary
This then, is the new mathematical theory of how life evolves.
I have called it a mathematical theory, not because it is filled with equations, or that this topic is my specialty, it is not.
Rather, I have called it this to highlight the facet of evolution theory that not even experts suspect is the limitation. I have argued before, from many facts that across all life, contrary to the mutation-centric paradigm, genes maximize distribution by conserving sequence. I have written books on this, but critics think I am merely noting that gene conservation is important, which is already known.
It is not that gene conservation is merely important, but that this is a pathway of a natural selection. Life evolves, and it only evolves, by two forces of natural selection. One is the mutation-centric force, emulated in the standard frequency model. The other force is not gene mutation, but selection for conservation, to preserve order against thermodynamic decay. Both forces act on the gene, yet the hesitation with this thesis is not that genes can both mutate and conserve sequence at the same time, but that rules forbid a frequency from emulating two probable outcomes at the same time. Nevertheless, if life emulates this as a fact, there has to be an equation. In Fig 0.2, I drew the result on a spreadsheet to show how two probable outcomes appear, and I can already show tentative solutions from this approach. I am certain that combining both forces of selection in an equation this way, can prove how life evolves from non-life, across each transition, even sex, against thermodynamic direction, as a gain of frequency, without any paradox.
The rest is up to readers.
Anyone reading this, still convinced that all of the paradoxes are already solved, or that the mutation-centric model of evolution is already perfect and infallible, should put this book down now. No facts that I can point out can shake such confidence. On the other hand, anyone reading this not even convinced of either argument, but curious enough to realize that each approach needs further verification, might find in the following pages many new ideas to explore. Ironically, the rival theories are both "gene"-centric, in that both theories teach that successful genes act as if to maximize distribution. Just, the standard model teaches that this only needs to be emulated, and tested, in single populations at a time. The new theory is that this must be emulated and tested across all populations, but to do so, requires a new physical model, and new mathematical model of how life evolves. I can outline the equations, but this is not my specialty. Rather, the first person to grasp the concept of two pathways of selection, acting as a single frequency, could formulate his or her own equations I am sure, more elegantly than I can here.
I can do no more myself than elucidate these principles, and hope that at least one person who can research it more, tries to formulate from it a more comprehensive model of how life evolved.
