What is the Mathematical Probability of Successful Reproduction in Evolution?

[allen74delval]

I am exploring the evolution discussion from many different subjects. I have thought that maybe math could provide some impact on the discussion. I would like to explore the mathmatical probability of one aspect of evolution. It would seem that the key to man's biological evolution seems to be successful reproduction. Let's assume that 5 perfect systems are needed to provide successful reproduction. (given just the male reproductive mechanism, i don't think this is beyond reality.) For the sake of this discussion, assume you are given 4 possible conditions of each system: (1)absence,(2) incomplete,(3)complete but not functioning, and finally, (4) complete and functioning. what is the probability that operation of the reproductive mechanism will be successful ( that is all 5 systems will be complete and functioning)?

 

[Janitor]

Are the four conditions assumed to have equal probability?

Does the condition of one system affect the probability of the various conditions of the other systems?

 

[allen74delval]

evolution and equal probability

I don't think at this point i want to get too biological. After all in a prepuberty individual of normal development the systems may be present but not complete or functioning. Let's just assume equal probability with the conditions. Janitor's question ? :"Does the condition of one system affect the probability of the various conditions of the other systems? " In a interdependent biological system this may be affirmed. ( consider age as a variable) But, I will answer no at this point. I am just wondering if the numbers will speak for themselves in favor of evloution?

 

[Bartholomew]

I don't know what the post has to do with the poll, but I voted for all 3 options other than the first. Mathematics is subjective because any conclusion must be derived from premises by the use of some computer, and no computer in the real world--whether it is an artifact or the human brain--can be assured 100% perfect at every step. On the other hand, mathematics is about as objective a discipline as you can get, relatively speaking. So I'd trust the results of mathematics to override just about anything else, but still remember that in the real world no computation can ever be assured perfect at every step.

 

[mapper]

Its much easier to say that the invisible man made us. And we made the woman by puttin g one of our ribs under a rock.

 

[Janitor]

Let's just assume equal probability with the conditions... But, I will answer no at this point. I am just wondering if the numbers will speak for themselves in favor of evloution?

If I understand, you are saying that the fraction of individuals who will be able to successfully reproduce is (1/4)^5, which works out to about 1 in 1,000.

If one were to, in godlike fashion, plunk down a population of some species into a suitable habitat, and assign those distributions of conditions, then all I can say is that natural selection will weed out 999 out of 1,000 of them right off the bat. The small fraction of the population which is able to reproduce might well give rise to a generation of offspring which have a much higher than 1/4 chance of possessing a unit that is complete and functioning. That is, if we figure that there is at least some heritability to functionality of reproductive systems, then as the generations roll on, an ever higher fraction of the population will be fit for reproducing.

 

[allen74delval]

Bartholomew: "Mathematics is subjective" contra. "mathematics is about as objective a discipline. . .". What do you mean? For me, evolution carries an intriguing mix of philosophy, biology and math. but in this investigation, neither of the three disciplines to me become an end in themselves. As I investigate the concept of evolution from each of the three disciplines, i would want to allow each to speak for themselves on the subject.

Unfortunately, i have not come to a conclusion on the following three questions?

(1) If the probability of successful reproduction was too high would one change his view of evolution. or low enough would he allow for evolution as an origins model? I

(2)If you built your philosophy on the presupposition of evolution would you care about the probability of successful reproduction?

(3) Can I build an investigation that remains unbiased by philosophy without producing proof of my own presupposition?

All of you who read this investigation, will be my judges and jury as to the validity of the method and its outcome. I thank you all in advance for your input.

Mapper: I would love to meet your invisible man. How old was rib-man when he put the rib under the rock? Did rock-woman develop simultaneously with rib-man? Did rib-man have any children that lived?

Jordan: thank you for your help on the matter. I would see that 1 in 1000 population would successfully reproduce. Because I am heterosexually reproduced, allow me to add that variable. In a heterosexual system, that could mean that there would need to be 1000 males and 1000 females available in order to reproduce the next generation. All stupidity aside, that would mean that a complete-functional (CF) male would have a 1 in 1000 chance of mating with the CF female on the first attempt? Or he would have to mate a possible 1000 times (once with each of the 1000 females) to successfully reproduce the next generation.

To take this to the next step what are the chances of a male (1) being CF and (2) mating with a CF female on the first try? 1 in a milllion?

 

[selfAdjoint]

allen, an organism whose reproduction depended on your odds - one in four of getting critical system right in an offspring - would quickly go extinct. The reason we share 25% of our genome with an oak tree is that evolution is able to do literally millions of times better than that; it has preserved the basic genes for a metazoan organism since chordates and plants branched apart way back in the Cambrian.

Population genetics is all about probability; evolutionary theory is tightly linked to population genetics, this was called the "new synthesis" back in the 1930s when the links were built.

 

[Janitor]

... Jordan: thank you for your help on the matter. I would see that 1 in 1000 population would successfully reproduce. Because I am heterosexually reproduced, allow me to add that variable. In a heterosexual system, that could mean that there would need to be 1000 males and 1000 females available in order to reproduce the next generation. All stupidity aside, that would mean that a complete-functional (CF) male would have a 1 in 1000 chance of mating with the CF female on the first attempt? Or he would have to mate a possible 1000 times (once with each of the 1000 females) to successfully reproduce the next generation.

To take this to the next step what are the chances of a male (1) being CF and (2) mating with a CF female on the first try? 1 in a milllion?

The way I would put it is: If you chose a CF male from among the population, he has a 1 in 1000 chance of selecting a mate who is CF such that the pairing will produce offspring. (I am assuming that he can't tell from looking which females are fertile and which aren't, so that his choice of a mate is not biased ahead of time. And of couse I am assuming monogamy.) If instead you randomly select one male and randomly select one female, the chances they will reproduce are 1 in a million.

As I hinted at above, your model may be too simple to capture the essence of evolution, since you are not allowing for CF pairs to have more than 1 in 1,000 (!) of their offspring to be born CF, i.e. you are not allowing for CF-ness to be inherited.

 

[allen74delval]

Thanks again all for your input:

Selfadjoint, Welcome and thanks. I respect your view of evolution. But when you say that "evolution is able to do literally millions of times better than that", to what are you refering? I don't think that record keeping is the issue. Genes and DNA holds the records of who I am. In vitro experiment can identify those records and further experimentation can identify the 25% genome oak-tree similarity. But in reality my records die when i drop dead. My organism is then extinct. Only my successful heterosexual reproduction insures the viable future of my genes, species, characteristics , etc. Looking at it another way, if at some point the oak tree approaches extinction, what can i do genetically to prevent it ?

Janitor: If it was just my wife and I as the FIRST CF parents, we would have to give birth to two children, male and female who are CF [CF:complete and functioning reproductive system]. The CF would be inherited but i am not sure whether it would be dominant, yet. Any input from a geneticist might help here. It would almost be necessary to birth two sets of couples to insure successful population growth. Maybe more depending on whether CF is recessive or dominant? [ After all, where did Cain and Seth get their wives?] Is that what you mean by inherited CF-ness?

How many CF parents are needed to begin a species?

Just for a moment: Why limit monogamy and single trial to the test? Wouldn't that presume a philosophical moral code? I guess i can't help but involve the discipline of biology here. Is every animal monogamous? Let's assume 100 year life span of CF male, which assumes all other incompletes and non functionings are now absent. [after all we wouldn't his heart stopping while in the middle of trial] . He is complete and starts functioning at age 12. (88 years of trials) Let's say He is "monogamous"[sic] for 7 days with one female which could mean numerous matings over a 7 day period equalling one "trial" . (52 trials a year) (<4600 total trials over his life span). It could take him <20 years to find the CFfemale. Could he reproduce 4 children successfully in his life span? No! he could only potentially "father" three children when he is 32, 52, and 72. If CF female is same age as male he may only reproduce one CF child when they are 32 depending on CF female's biological clock. [this is going in a direction that i really think is politically dangerous. I'm sorry]

allen74delval