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Eörs Szathmáry's "stochastic corrector" model

Tim Tyler · 2003-12-30T12:22:30+00:00

I've written a brief essay about Eörs Szathmáry's influential "Stochastic corrector" model - and my view of its relevance to the origin of life. The essay includes a diagram - which is *very* useful for assisting understanding Szathmáry's basic idea. The diagram doesn't transfer well to ASCII - and I've made no attempt to transfer it. So - to experience the article complete with the relevant audio-visual aids - I encourage you to read the article at its home - at: http://originoflife.net/stochastic_corrector/ If you are already intimately familiar with Szathmáry's idea - and just want to hear my take on it - then I *suppose* you /might/ be able make do with the article as reprinted below: As a very brief synopsis, I think Szathmáry's idea has useful elements - but is probably more relevant to the origin of life if applied in a somewhat broader context than by considering the origin of cells. Stochastic corrector -------------------- Eörs Szathmáry's "Stochastic corrector" model is seen by some is making the error catastrophe problem faced by early organisms less pressing. Here I discuss the relevance of this model to the origin of life. Motivation for the model ------------------------ Szathmáry's model deals with a population of distinct self- replicating entities in dividing cells. It deals with the problem of how information could be transmitted in the form of the ratio between the constituent replicators - despite the fact that they are not joined together - and thus: * Stochastic forces present when the cell divides distributing them unevently in offspring; * Differences in the rate of reproduction of each sort of replicator within the cell; Explanation of the model ------------------------ The model is best explained with a diagram: [important diagram which goes here can be seen on http://originoflife.net/stochastic_corrector/ ] Organisms are composed of a small number of different types of self-replicating agents: R1 and R2. The organisms work best if there is some specified ratio between the replicators: in the diagram the preferred ratio is 1:1. The cells grow and eventually split into two - with the replicators being distributed randomly between the offspring. Then selection acts - destroying any cells that deviate too far from the optimal ratio of replicators within each cell. The result is that the information content represented by the replicators - and their proportions in the cell - is preserved between generations. The model can still work - even if some of the replicators reproduce faster than other ones - and thus there is between-replicator selection within each cell. Good points ----------- The model is useful - since it shows how a small collection of small molecules - none of which may be capable of independent replication could co-exist in a community - and help catalyse each others replication, and be inherited without being physically connected together or having their division orchestrated by some sort of controller. Not so good points ------------------ However the model doesn't scale up very well - the more of each sort of replicator is involved the greater the chance that stochastic variations will result in one type of replicator being omitted from any children - and the stronger selection is needed to maintain verbatim transmission of information between the generations. Rewriting the model ------------------- I think the model makes a lot more sense if it is rephrased a bit. Rather than consider the diagram as representing different sorts of replicator in a cell, consider it as representing different sorts of replicator in an ecosystem: The intention is to make the model more relevant to the origin of life (though it makes it less relevant to the origin of cells). For example, if you have a whole "pool" filled with replicators, then the species in it may colonise another pool downstream. If key species get wiped out - or fail to get transmitted to the new environment - then the new ecosystem will not flourish. The idea that the proportion of replicators in each "cell" is significant is abandoned in this model. That information is no longer strongly inherited. However, the collective genomes of all the important species still get transmitted - i.e. information about the existence of the different species is preserved. This phrasing retains a key feature of the model - namely the possibilty of inheriting a lot more information than is present in any individual replicator. It also still leaves open the possibility of a community of interdependent symbiotes surviving in an environment where none of them could exist alone. Overcoming differential reproductive rates ------------------------------------------ What about the possibilty that one sort of replicator will wipe out the other ones? Rather than invoking selection between ecosystems to explain this, I suggest considering the possibilities of: * Independent niches If the different replicators do not compete significantly for resources then they can probably co- exist peacefully - without one wiping the other out. Niches might be independent if - for example - the replicators were made of different stuff - and had different resource needs. * Frequency-dependent selection Frequency-dependent selection is the reason why foxes don't wipe out rabbits - (when the rabit population goes low, the fox food supply decreases) and similarly why rabits don't out-reproduce foxes (when there are lots of rabits around, the fox has an easy time of feeding and reproducing). These sorts of forces will act within most ecosystems anyway - there is no need to invoke selection between ecosystems to explain how a diverse range of species is maintained within them. The membrane-free corrector --------------------------- The other attraction of this reformulation is that it no longer depends in any way on the notion of a membrane or cell - instead, the role of container is played by the environment - which could be as simple as a rock pool. Membranous material is unlikely to be involved in the earliest living systems - since the organic material that composes most membranes tends to form sticky messes - that are incompatible with the process of crystallisation that is likely to be responsible for the replication of the genomes of the first organisms. Notes ----- The main idea presented here owes an obvious debt to the model presented in my earlier "Increasing Complexity" essay [ http://originoflife.net/complexity/ ] - i.e. it is basically much the same idea wrapped up in different terminology. References ---------- Eörs Szathmáry and J. Maynard Smith - The Major Transitions in Evolution. Oxford, 1995. Eörs Szathmáry and J. Maynard Smith - The Origins of Life, Oxford University Press, 1999; Eörs Szathmáry and László Demeter - Group selection of early replicators and the origin of life. Journal of Theoretical Biology 128, 463-486, 1987; Enjoy, -- __________ |im |yler http://timtyler.org/ [email hidden] Remove lock to reply.

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Published: 30 December 2003
Last activity: 30 December 2003
Original author: Tim Tyler
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Original post
Tim Tyler
Archived post

30 December 2003, 12:22 UTC #1

I've written a brief essay about Eörs Szathmáry's influential "Stochastic corrector" model - and my
view of its relevance to the origin of life.
The essay includes a diagram - which is *very* useful for assisting understanding Szathmáry's
basic idea.
The diagram doesn't transfer well to ASCII - and I've made no attempt to transfer it.
So - to experience the article complete with the relevant audio-visual aids - I encourage you to
read the article at its home - at:
originoflife.netstochastic corrector
If you are already intimately familiar with Szathmáry's idea - and just want to hear my take on it -
then I *suppose* you /might/ be able make do with the article as reprinted below:
As a very brief synopsis, I think Szathmáry's idea has useful elements - but is probably more
relevant to the origin of life if applied in a somewhat broader context than by considering the
origin of cells.
Stochastic corrector
--------------------
Eörs Szathmáry's "Stochastic corrector" model is seen by some is making the error catastrophe
problem faced by early organisms less pressing.
Here I discuss the relevance of this model to the origin of life.
Motivation for the model
------------------------
Szathmáry's model deals with a population of distinct self- replicating entities in dividing cells.
It deals with the problem of how information could be transmitted in the form of the ratio between
the constituent replicators - despite the fact that they are not joined together - and thus:
* Stochastic forces present when the cell divides
distributing them unevently in offspring;
* Differences in the rate of reproduction of each sort of replicator within the cell;
Explanation of the model
------------------------
The model is best explained with a diagram:
[important diagram which goes here can be seen on
originoflife.netstochastic corrector ]
Organisms are composed of a small number of different types of self-replicating agents: R1 and R2.
The organisms work best if there is some specified ratio between the replicators: in the diagram the
preferred ratio is 1:1.
The cells grow and eventually split into two - with the replicators being distributed randomly
between the offspring.
Then selection acts - destroying any cells that deviate too far from the optimal ratio of
replicators within each cell.
The result is that the information content represented by the replicators - and their proportions in
the cell - is preserved between generations.
The model can still work - even if some of the replicators reproduce faster than other ones - and
thus there is between-replicator selection within each cell.
Good points
-----------
The model is useful - since it shows how a small collection of small molecules - none of which may
be capable of independent replication could co-exist in a community - and help catalyse each others
replication, and be inherited without being physically connected together or having their division
orchestrated by some sort of controller.
Not so good points
------------------
However the model doesn't scale up very well - the more of each sort of replicator is involved the
greater the chance that stochastic variations will result in one type of replicator being omitted
from any children - and the stronger selection is needed to maintain verbatim transmission of
information between the generations.
Rewriting the model
-------------------
I think the model makes a lot more sense if it is rephrased a bit. Rather than consider the diagram
as representing different sorts of replicator in a cell, consider it as representing different sorts
of replicator in an ecosystem:
The intention is to make the model more relevant to the origin of life (though it makes it less
relevant to the origin of cells).
For example, if you have a whole "pool" filled with replicators, then the species in it may colonise
another pool downstream. If key species get wiped out - or fail to get transmitted to the new
environment - then the new ecosystem will not flourish.
The idea that the proportion of replicators in each "cell" is significant is abandoned in this
model. That information is no longer strongly inherited. However, the collective genomes of all the
important species still get transmitted -
i.e. information about the existence of the different species is preserved.
This phrasing retains a key feature of the model - namely the possibilty of inheriting a lot more
information than is present in any individual replicator.
It also still leaves open the possibility of a community of interdependent symbiotes surviving in an
environment where none of them could exist alone.
Overcoming differential reproductive rates
------------------------------------------
What about the possibilty that one sort of replicator will wipe out the other ones? Rather than
invoking selection between ecosystems to explain this, I suggest considering the possibilities of:
* Independent niches
If the different replicators do not compete significantly for resources then they can probably co-
exist peacefully - without one wiping the other out.
Niches might be independent if - for example - the replicators were made of different stuff - and
had different resource needs.
* Frequency-dependent selection
Frequency-dependent selection is the reason why foxes don't wipe out rabbits - (when the rabit
population goes low, the fox food supply decreases) and similarly why rabits don't out-reproduce
foxes (when there are lots of rabits around, the fox has an easy time of feeding and reproducing).
These sorts of forces will act within most ecosystems anyway - there is no need to invoke
selection between ecosystems to explain how a diverse range of species is maintained within them.
The membrane-free corrector
---------------------------
The other attraction of this reformulation is that it no longer depends in any way on the notion of
a membrane or cell - instead, the role of container is played by the environment - which could be as
simple as a rock pool.
Membranous material is unlikely to be involved in the earliest living systems - since the organic
material that composes most membranes tends to form sticky messes - that are incompatible with the
process of crystallisation that is likely to be responsible for the replication of the genomes of
the first organisms.
Notes
-----
The main idea presented here owes an obvious debt to the model presented in my earlier "Increasing
Complexity" essay [ originoflife.netcomplexity ] - i.e. it is basically much the same idea
wrapped up in different terminology.
References
----------
Eörs Szathmáry and J. Maynard Smith - The Major Transitions in Evolution. Oxford, 1995.
Eörs Szathmáry and J. Maynard Smith - The Origins of Life, Oxford University Press, 1999;
Eörs Szathmáry and László Demeter - Group selection of early replicators and the origin of life.
Journal of Theoretical Biology 128, 463-486, 1987;
Enjoy,
--
__________
|im |yler timtyler.orgtimtyler.org [email hidden] Remove lock to reply.

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Jim Menegay
Archived post

30 December 2003, 12:23 UTC #2

Tim Tyler <[email hidden]> in message news:<[email hidden]> describes a theory
including the idea that an ecosystem of replicators can be thought of as a proto-organism.
Quoted message said:
originoflife.netstochastic corrector originoflife.netcomplexity
This idea seems to be identical to one published by Allen back in the 1970s. The title was something
like "Early genomes may have been integrated extrinsically". His point was that "genome
integration", by which he meant something like accurate segregation, could have been accomplished
outside the organism by partitioning the genes among the participants in an ecosystem.
But, just because an idea is not original doesn't mean it is bad. I kind of like the idea myself,
and I intend to use it. (But my ecosystems are themselves compartmentalized - that is, they start as
organisms in some sense - they don't become organisms later.)

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William Morse
Archived post

30 December 2003, 12:23 UTC #3

Tim Tyler <[email hidden]> wrote in news:brb1nu$2o6p$1
@darwin.ediacara.org:
Quoted message said:
I've written a brief essay about Eörs Szathmáry's influential "Stochastic corrector" model - and
my view of its relevance to the origin of life.
(snip)
Quoted message said:
Overcoming differential reproductive rates
------------------------------------------
What about the possibilty that one sort of replicator will wipe out the other ones? Rather than
invoking selection between ecosystems to explain this, I suggest considering the possibilities of:
Quoted message said:
* Frequency-dependent selection
Frequency-dependent selection is the reason why foxes don't wipe out rabbits - (when the rabit
population goes low, the fox food supply decreases) and similarly why rabits don't out-reproduce
foxes (when there are lots of rabits around, the fox has an easy time of feeding and
reproducing). These sorts of forces will act within most ecosystems anyway - there is no need to
invoke selection between ecosystems to explain how a diverse range of species is maintained
within them.
Assuming that your group of replicators is not competing for exactly the same precursors, and
assuming that a number of the replicators produce byproducts that are the precursors for other
replicators, then chemical equilibria will serve the same function of feedback to regulate the
overall rates of replication by chemicals in a "pool" that frequency- dependent selection does for
organisms in an ecosystem.Thus it seems quite possible that "pools" of chemicals could maintain
significant diversity. Such systems would however be more susceptible to extreme oscillations than
modern ecosystems.
Yours,
Bill Morse

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Tim Tyler
Archived post

30 December 2003, 12:24 UTC #4

Jim Menegay <[email hidden]> wrote or quoted:
Quoted message said:
Tim Tyler <[email hidden]> in message:
Quoted message said:
Quoted message said:
originoflife.netstochastic corrector originoflife.netcomplexity
This idea seems to be identical to one published by Allen back in the 1970s. The title was
something like "Early genomes may have been integrated extrinsically".
Which Allen?
Quoted message said:
His point was that "genome integration", by which he meant something like accurate segregation,
could have been accomplished outside the organism by partitioning the genes among the participants
in an ecosystem.
That is it in a nutshell ;-)
Quoted message said:
But, just because an idea is not original doesn't mean it is bad.
I do say on: originoflife.netcomplexity :
..."this is a fairly obvious point" ;-)
I'm not /sure/ where I got it from - but IIRC, it came out of my reaction to reading Carl Woese's
"universal ancestor" material:
pnas.org6854
The material about the "stochastic corrector" model is a bit different.
I see it as a of a hybryd between the originoflife.netcomplexity idea and Szathmáry's
model. It still mentions the possible role of selection as a "corrector" - Szathmáry's idea.
--
__________
|im |yler timtyler.orgtimtyler.org [email hidden] Remove lock to reply.

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Jim Menegay
Archived post

30 December 2003, 12:24 UTC #5

[email hidden] (Jim Menegay) wrote in message news:<[email hidden]>...
Quoted message said:
Tim Tyler <[email hidden]> in message news:<[email hidden]> describes a theory
including the idea that an ecosystem of replicators can be thought of as a proto-organism.
Quoted message said:
originoflife.netstochastic corrector originoflife.netcomplexity
This idea seems to be identical to one published by Allen back in the 1970s.
I have the exact reference now. I was seriously wrong about the date. It is Gordon Allen, "Genetic
Information Could be Integrated Extrinsically for Simplest Life Forms", Origins of Live and
Evolution of the Biosphere
18 (1988) 289-298.
Incidentally, if you are interested in celebrating the contributions to OOL of people whose
contributions are uncelebrated by the orthodox, then I think that Allen deserves at least a
footnote. You should look at his article "Reflexive Catalysis, a Possible Mechanism of Molecular
Duplication in Prebiological Evolution" which appeared in The American Naturalist in March 1957.
1957!! A few years before Eigen, Dyson, et al. Amusingly, his institutional affiliation at the time
was the New York State Psychiatric Institute.

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Tim Tyler
Archived post

30 December 2003, 12:24 UTC #6

Jim Menegay <[email hidden]> wrote or quoted:
Quoted message said:
[email hidden] (Jim Menegay) wrote in message
news:<[email hidden]>...
Quoted message said:
Tim Tyler <[email hidden]> in message
[...]
Quoted message said:
Quoted message said:
Quoted message said:
originoflife.netcomplexity
This idea seems to be identical to one published by Allen back in the 1970s.
I have the exact reference now. I was seriously wrong about the date. It is Gordon Allen, "Genetic
Information Could be Integrated Extrinsically for Simplest Life Forms", Origins of Live and
Evolution of the Biosphere
18 (1988) 289-298.
...and the network has it! ;-) I now link to it as a reference from:
originoflife.netcomplexity
--
__________
|im |yler timtyler.orgtimtyler.org [email hidden] Remove lock to reply.

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