Reincarnation and stem cell research

'Animal birth' is a state of mind, which is why monks are censured for engaging in 'animal talk'. This is why the sutta SN 56.120 says an animal can realise the four noble truths. In other words, the teaching about "reappearance" as an animal in the Pali suttas appears to be a metaphor.

Bhikkhus, these two bright principles protect the world. What are the two? Shame and fear of wrongdoing. If, bhikkhus, these two bright principles did not protect the world, there would not be discerned respect for mother or maternal aunt or maternal uncle's wife or a teacher's wife or the wives of other honored persons, and the world would have fallen into promiscuity, as with goats, sheep, chickens, pigs, dogs, and jackals. But as these two bright principles protect the world, there is discerned respect for mother... and the wives of other honored persons. AN 2.9

Then the thought occurred to the him, "These Users of BuddhismSE... are all still with fetters. What if I were to teach them the Dhamma in such a way that in this very sitting their minds, through lack of clinging, would be released from fermentations?"

So he addressed the monks: "Monks."

"Yes, lord," the monks responded.

The Blessed One said, "From an inconceivable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. What do you think, monks? Which is greater, the blood you have shed from having your heads cut off while transmigrating & wandering this long, long time, or the water in the four great oceans?"

"As we understand the Dhamma taught to us by the Blessed One, this is the greater: the blood we have shed from having our heads cut off while transmigrating & wandering this long, long time, not the water in the four great oceans."

"Excellent, monks. Excellent. It is excellent that you thus understand the Dhamma taught by me.

"This is the greater: the blood you have shed from having your heads cut off while transmigrating & wandering this long, long time, not the water in the four great oceans.

"The blood you have shed when, being cows, you had your cow-heads cut off: Long has this been greater than the water in the four great oceans.

"The blood you have shed when, being water buffaloes, you had your water buffalo-heads cut off... when, being rams, you had your ram-heads cut off... when, being goats, you had your goat-heads cut off... when, being deer, you had your deer-heads cut off... when, being chickens, you had your chicken-heads cut off... when, being pigs, you had your pig-heads cut off: Long has this been greater than the water in the four great oceans.

"The blood you have shed when, arrested as thieves plundering villages, you had your heads cut off... when, arrested as highway thieves, you had your heads cut off... when, arrested as adulterers, you had your heads cut off: Long has this been greater than the water in the four great oceans.

"Why is that? From an inconceivable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. Long have you thus experienced stress, experienced pain, experienced loss, swelling the cemeteries — enough to become disenchanted with all fabrications, enough to become dispassionate, enough to be released."

Timsa Sutta: Thirty

All of Us - Beset by birth, decay, and death

If you have ever read Don Quixote, you'll remember that he was fighting windmills. Everybody (not awakened) is doing just that, fighting windmills. Don Quixote was the figment of a writer's imagination, a man who believed himself to be a great warrior....

[Note: This is a gift of Dhamma and not meant for commercial purpose or other low wordily gains by means of trade and exchange.]

How do we apply reincarnation to phenomena such as reproduction by binary fission?

I don't.

• I don't understand it (the theory of rebirth) well, so I try not to use it nor rely on it.
• If form is not self, then I'm not sure why you expect there's any one-to-one relationship between "a being" and "a cell". A sheep is a multi-cellular organism -- do you count it as one being, or as several?

My "science" education teaches me that different theories are used for different reasons, to explain different phenomena. For example, the "theory of gravity" explains why things fall when you drop them, but the "theory of gravity" doesn't explain why water boils when you heat it.

So, part of understanding (or using) a theory is to know when and why to use it, what it's "useful" for, and what it isn't useful for.

I think the theory of reincarnation has some uses, for example:

• It teaches that causes can have an effect, even if the effect doesn't seem to be immediate
• It may help to decrease ego-centrism, e.g. the view that "Me, this life, is all-important -- and nothing else matters: no-one else, no other time".
• It may promote disenchantment (see for example the quote in Samana Johann's answer); and equanimity (if something "bad" happens, does it help to consider that this wasn't the first time it has happened?).
• It may help redirect attachment (the theory that a loved one still exists after death, though in a different form)
• And more?

However, IMO, trying to relate it to cellular biology, as you did, is completely off-topic: neither the purpose (use), nor the type of observation (phenomena), for which the theory is or was intended.

How do we apply reincarnation to phenomena such as reproduction by binary fission (amoeba) and creating animals like Dolly the sheep from a single cell?

As I understood Nagarjuna, a Being (Self) is neither the Skandhas, nor not the Skandhas; for a Being can't be obtained without the Skandhas. Then it can be said in our worldly wording that each amoeba is a Being though by binary fission; so is each Dolly an individual sheep. And life isn't created, for if it could we can assemble in lab.; even Frankentein needs that "lightening" to give it life. Therefore since life isn't created it can't be annihilated, just changes form of expression from each life-session. That's what called reincarnation, or better named rebirth. Reincarnation is specially for some Beings who are autonomous in it, or with mission.

why the population is rising in the animal kingdom including humans

Because we are now in a declining minor Kalpas, according to Sutras. Things are deteriorating, so to speak, thus more lesser Beings are born. The 6 Realms are like the pyramid, the higher the fewer. In Buddha's time, more Beings are born from the celestial realms to the human world and vice versa, now there are more from lower realms. Homo sapiens is just a vast generalization, in it carried many favours.

it cannot be other beings from different realms are coming to earth

It surely can. If the earth is only good for humans, or the earth also inhabited by non-humans? Why not? When a Being's Karma weight is right for earth, then Terra is the home. Personally I wonder if Saturn and Jupiter homes of the Asuras, maybe the Devas? For there rain diamonds. Different realms can't be seen via naked eyes, unless one has divine vision, or with special apparatus.

I'm more concerned with the "in vitro meat". In reference to the answer in the beginning, how does this lab-meat feel (Vedanā)? If I contemplate, I kind of get that it must be in constant pain. If your skin is torn and flesh exposed, how do you feel? It would be the same for this meat-being sitting only just in plain air, or in the culturing fluid - unending pain.

~§ Due to ignorant, we commit many crimes; they weigh us down, which we thought achievement. §~

There is no literal rebirth of the same "being", Janaki. All entities, including "beings" are approximate abstractions.

Reincarnation is a metaphor for continuity of information and causation, presented in a way accessible to simpleminded ancient people.

How do we apply reincarnation to phenomena such as reproduction by binary fission (amoeba) and creating animals like Dolly the sheep from a single sell?Also, why the population is rising in the animal kingdom including humans, surely, it cannot be other beings from different realms are coming to earth.

I am so confused about this although I am a practising Buddhist.

If you want to become an even more confused Buddhist, then keep pondering this :)

If not, then stop pondering this and go practice.

You might also want to take a look at the Four Imponderables:

The four imponderables are identified in the Acintita Sutta, Anguttara Nikaya 4.77, as follows:

The Buddha-range of the Buddhas [i.e., the range of powers a Buddha develops as a result of becoming a Buddha];

The jhana-range of one absorbed in jhana [i.e., the range of powers that one may obtain while absorbed in jhana];

The [precise working out of the] results of kamma;

Speculation about [the origin, etc., of] the cosmos is an imponderable that is not to be speculated about.

These imponderables the Buddha advices not to contemplate, since they will only agitate and destabilize the mind, making it less suitable for practice.