Download Population Biology of the First Replicators: On

AMER. ZOOL., 23:5-14 (1983)
Population Biology of the First Replicators: On the
Origin of the Genotype, Phenotype and Organism'
RICHARD E. MICHOD
Department of Ecology and Evolutionary Biology,
University of Arizona, Tucson, Arizona 85721
SYNOPSIS. Prebiotic synthesis of short length macromolecules from precursor molecules
results in a dynamic of spontaneous creation, which allows for growth from zero density.
At this prereplicator stage in the evolution of life there is no life history, since the birth
and death processes are intimately coupled through the physical chemistry of a single
reaction. With the emergence of nonenzymatic, template-directed replication, the birth
and death processes could diverge for the first time, since selection could act differently
on the birth and death rates of the replicating molecule. Thus, with replication, natural
selection and life-history evolution began. The genotype, or nucleotide sequence, of the
replicating molecule gave rise to several phenotypic properties, the most important of
which was its three-dimensional structure which in turn affected the birth and death
processes. However, at this stage of nonenzymatic template replication, the phenotype
was the physical structure of the genotype, nothing more: For the divergence of the
phenotype from the genotype it was necessary for the replicator to produce a protein. It
is shown here that the evolution of enzyme production is facilitated by the existence of
population structure in the distribution of the macromolecules associated with replication.
Initially, this structure was created passively by the localization of the macromolecules in
rock crevices, suspended water droplets, etc. Ultimately, the replicator along with its
proteins were localized in a protocellular structure and this became the first organism.
Thus, initially, the organism was one extreme of the population structure of the macromolecules associated with life. The organism was the culmination of the encapsulation
phase of evolution which proceeded through initial phases of passive localization.
INTRODUCTION
At one stage in the history of life the
cellular organism did not exist, and the genotype and phenotype were one and the
same. This is the stage of simple molecules,
similar to extant DNA or especially RNA,
replicating nonenzymatically via templatedirected synthesis. The purpose of this article is to study the selective pressures responsible for the divergence of the phenotype from the genotype, and the origin
of the cellular organism. This work stems
from the work of Bernstein et al. (1983)
and Eigen and co-workers (Eigen 1971; Eigen and Schuster 1977, 1978a, b; Eigen et
al., 1981), which studies the process of natural selection in molecular replicators. The
reader is referred to Bernstein et al. (1983)
for the general background to the present
paper. Schuster (1980) has reviewed much
of the relevant evidence for the prebiotic
chemistry assumed implicitly in what follows.
PREREPLICATOR DYNAMIC
Let X, be the abundance of a particular
nucleotide sequence i. Under conditions
thought to be reasonable for prebiotic evolution, short-length oligonucleotides form
spontaneously from more primitive precursor molecules (see, for example, Schuster, 1980). The dynamic associated with
the change in abundance of such an entity
is (X s dX/dt)
s
= ft - iiXi,
(1)
where # and <$, are the rates of the forward
and backward reactions, respectively (Fig.
la). Such a dynamic is properly labelled
spontaneous creation, since it describes
growth from zero density. The ft term in
equation (1) incorporates the abundance
of precursor molecules. However the important
point is that the abundance of nu1
From the Symposium on The Inter-face of Life-Hiscleotide i does not enter into the rate of
tory Evolution, Whole-Organism Ontogeny and Quantita- the forward reaction. From the point of
tive Genetics presented at the Annual Meeting of the
view of a population biologist, it is temptAmerican Society of Zoologists, 27-30 December
ing to think of # as the "birth" rate and
1981, at Dallas, Texas.
RICHARD E. MICHOD
SPONTANEOUS - CREATION CbirtlT and "d
V
REPLICATOR (birth and death
V
oupled)
FIG. 1. Diagram of chemical reactions associated with
spontaneous creation and replication. These single
reactions are probably a simplification of many intermediated steps; however, the qualitative points made
in the text would not be affected by this. See text for
further discussion.
Si as the "death" rate of this nonreplicating
nucleotide sequence. However, this would
be misleading. The parameters 0t and <5, are
intrinsically related, since both ultimately
stem from the activation in energy between
the precursor molecules and the oligonucleotide product. There are no independent birth and death processes for such an
entity. There is no life history.
REPLICATOR DYNAMIC
At some point a molecule arose which
possessed the property of replicating itself.
This was probably the most fundamental
event in the history of life. Initially, the
replicating mechanism was some form of
template activity, probably involving electrostatic interactions, similar to those involved in extant base pairing. Schuster
(1980, p. 29) notes that electrostatic interactions have an intrinsic complementarity
(+, —), which can form the basis for template (+, —) replication. Enzyme-free, template-directed polymerization of nucleotides of length 30-50 has been reported
(Lohrmann and Orgel, 1980; Lohrmann et
al, 1980; Van Roode and Orgel, 1980).
Although there are many reports of template-directed, nonenzymatic polymerization of nucleotides {op. cit. or see Schuster,
1980), there has been, to my knowledge,
no demonstration of nonenzymatic replication of polynucleotides, where replication involves separation and subsequent
template activity of the newly polymerized
strand. Such an experiment would have to
involve a cycling of conditions (van Holde,
1980; Kuhn, 1972). The dehydrating conditions, which are favorable to polymerization, are the antithesis of the conditions
favorable to strand separation and the subsequent flow of mononucleotide building
blocks into the vicinity of the polymerized
strand.
A molecule capable of template replication may enter into two very different
kinds of reactions (Fig. lb). It may serve
as a template catalyst for the polymerization of a complementary strand or it may
be degraded by hydrolysis into its mononucleotide components. The template reaction is the birth process of the replicator,
so let bt be the rate of polymerization of
complementary strands per unit time. The
hydrolysis of the molecule is the death process, so let d, be the rate of this reaction
per unit time. I assume that the spontaneous rate of formation of the replicator
(not template-directed), (3,, from precursor
molecules is negligible in comparison to b{.
Consequently for the replicator, d{ represents the same process as did $ and 8t of
spontaneous creation (Fig. 1) and is numerically equal to Sit since ft ~ 0.
By virtue of its genotype (the nucleotide
sequence), a particular replicator will have
certain phenotypic characteristics which
may adapt the replicator to an increased
replication rate and decreased rate of hydrolysis. These characteristics have been
discussed in detail by Bernstein etal.{\ 983),
Eigen (1971) and Kuhn (1972) and so only
the general phenotypic categories will be
given here. First, the free energies of base
pair formation will affect the accuracy of
base pairing as have been calculated by Eigen (1971). Second, in a molecule similar
to single-strand RNA, three dimensional
structures will form by virtue of the nucleotide sequence. Different genotypes will
give rise to different three-dimensional
phenotypes some of which, particularly
those which are tightly packed, will be more
resistant to hydrolysis than others. The
three-dimensional phenotype will also affect the birth rate, since more open structures will facilitate the separation of complementary strands and the flow of
mononucleotide resources into the vicinity
of a replicating strand. Thus there are
THE FIRST REPLICATORS
adaptive constraints on the birth and death
process even at this primitive molecular
level (Bernstein et al., 1983). Third, the
length of the molecule will affect both bt
and dj.
At this level, the phenotype directly results from the genotype in combination
with the environment. There is no promotion of the birth and death process
through derived products (such as enzymes) of the genotype. The phenotype is
simply those physical and chemical aspects
of the nucleotide sequence which determine bt and dt. Thus at this level the phenotype and genotype are physically interrelated.
By virtue of their increased rate of
growth, those replicators would increase in
frequency which optimally balanced the
demands of the birth and death processes
on the three-dimensional structure and
other traits. Thus with the emergence of
replication, life-history evolution began.
The resources utilized by the first replicators were mononucleotides which were
themselves formed from sugars, phosphates, and purine and pyrimidine bases
by prebiotic synthesis (Schuster, 1980). At
some point, the mononucleotides became
limiting. Following Eigen and co-workers
(1971-1981), assume that the total number of replicators is maintained at some
constant number XT where
XT = 2 X,.
(2)
i
This assumption simplifies greatly the
mathematics which follow: however it is
rather artificial with regards to the biology
of the situation. The implications of equation (2) for prebiotic evolution have been
discussed elsewhere along with an alternate form of density regulation (Bernstein
et al., 1983). A more satisfactory approach
ecologically would be to represent the
mononucleotide resource dynamics explicitly (see, e.g., MacArthur, 1972).
Define \p as the total productivity per
replicator of the replicator community in
the absence of density limitation,
It should be understood later on in the
paper when equation (3) is used, that the
unlimited rates of growth are to be substituted in for X,. The replicator dynamics
which result under constraint (2) are (Eigen, 1971)
% = X.Cb, - d( - *).
(4)
Equation (4) is one description of selection in a community of molecular replicators. Note that the logistic growth law satisfies equation (4) in the case of single
species growth. The consequences of equation (4) have been discussed in detail by
Eigen and co-workers (1971-1981). It is a
special case of a general dynamical law, the
"Darwinian dynamic," which can be shown
to apply to the creation of order in living
as well as certain nonliving systems (Bernstein et al., 1983). I will refer to equation
(4) as a Malthusian dynamic, since in the
absence of density regulation (\p = 0), it is
linear and predicts exponential growth. Eigen (1971) terms replicators obeying such
a linear dynamic "Darwinian" in contrast
to the inherently nonlinear dynamics to be
considered shortly. I think this terminology is unfortunate, since it would suggest
that sexually reproducing replicators are
non-Darwinian. However, it is useful to distinguish this dynamic (eq. (4)) from the other evolutionary dynamics to be considered
shortly.
Another possible dynamic, of particular
relevance to the divergence of the phenotype as will be discussed shortly, is
j = Xi(bi - d; +
(5)
which contains a nonlinear term £X,2 even
in the absence of density regulation. Such
a dynamic has been termed "hypercyclic"
by Eigen (1971). Hypercyclic growth could
result from the production of a protein
catalyst by a nonencapsulated, molecular
replicator. Assume, for example, that concentration of the enzyme is directly proportional to the concentration of the enzyme-producing replicator, X,. Then the
probability per unit time of interacting with
a protein is proportional to X,2, because at
this stage there is no cellular structure to
keep the protein near the replicator. The
variable B represents the beneficial effect
of protein mediated replication. In addition, the term B includes the production
of the enzyme from the replicator.
RICHARD E. MICHOD
With the production of a protein, it was
possible for the first time for the phenotype to diverge from the direct physical
structure of the nucleotide sequence, or
genotype. This, of course, was a major
event in the evolution of life, allowing for
the physical decoupling of function from
the information which codes for the function. Previous to this event, function was
inextricably tied to the genotype and its
physicochemical properties. With their
decoupling, increased flexibility would result in the promotion of replication and the
protection of the replicator from hydrolytic decay. The remainder of the paper
considers the selective pressures responsible for the production of proteins and the
encapsulation of the genotype-protein
complex in a proto-organism.
MALTHUSIAN VS. HYPERCYCLIC
REPLICATORS
frequency-independent and paid in the
Malthusian term, (6; — d,), while the benefits are frequency-dependent and only accrue if the protein-producer exists in appreciable frequency.
An important characteristic of Malthusian dynamics is that there always exists a
condition which allows a mutant replicator
to invade a community of other replicators.
The exact conditions depend upon the explicit form of density regulation. For Eigen
and co-worker's mechanism of resource
regulation (2), one obtains rj > r, (where
r, = bj — d,) as the condition for increase of
a mutant replicator of type j in a population initially dominated by i. Different conditions are obtained for different forms of
resource limitation (see, for example,
Bernstein et al., 1983); however the essential characteristic is the existence of some
condition on the adaptive capacities for
spread of a mutant type. Now consider the
following single-membered hypercycle
(Fig. 2) with only enzyme mediated replication (r, = 0)
Eigen and co-workers (1971-1981) argue that the dynamical properties of hypercyclic replicators (eq. (5)) compared with
Malthusian replicators (eq. (4)) is the cenX, = (BiX, - ^)Xi.
(6)
tral issue in the emergence of enzyme catalyzed replication. According to Eigen and In this case, no similar mutant can increase
co-workers (1971-1981), an important as- when rare. Consider, for example, two
pect of hypercycles is their explosive growth competitors obeying (6):
which gives rise to the "once-forever" conX, = (B,X, dition for evolution of hypercycles discussed below. However, there are several
X2 = (B2X2 problems with hypercycle (and hence protein) evolution which their work does not with Eigen's (1971) form of density reguaddress. The basic problem concerns the lation (eqs. (2) and (3))
initial stages of evolution of protein cata_ B,X t 2 + B 2 (X T - X,)2
lyzed replication. In particular, the repli(8)
cator which produces a protein will suffer
some cost in its nonenzymatic, template- An equilibrium point of equations (7) is
directed replication rate if only because of X, = XT, X2 = 0, which is always stable (prothe time it takes to polymerize the pro- vided B, > 0). Consequently nomutant.no
tein—time which could be spent on tem- matter what its hypercyclic rate of inplate replication. In addition, as Eigen and crease, B2, can increase when rare. Eigen
co-workers (1971-1981) stress, the bene- (1971) describes this evolutionary result as
fits which derive from the protein are pro- a "once-forever" decision, since once a
portional to X,2. While this does give rise, replicator is fixed the population can never
again as Eigen and co-workers stress, to be invaded by another replicator of similar
explosive growth as the protein-producer type.
becomes common, it also creates problems
A two-membered hypercycle with both
when the protein-producer is rare. In sum- enzyme and template mediated replication
mary, the costs of protein production are (Fig. 2) has growth equations
T H E FIRST REPLICATORS
X , = (r, + B 2 X 2 - «//)X,
X 2 = (r 2 + B , X ! — t//)X2,
4> =
l^Vj
i
1J 2 ^VJ^V 2 ~r D ] A j A 2
,g.
i
MALTHUSIAN
T2-X.2
A T
with
In equations (9), it is assumed that the enzyme concentration follows X( directly. The
effect of replicator 2's enzyme on the realized growth rate of replicator 1 is B2.
Likewise for 5,. Note that this effect is assumed to be "donor" controlled with no
cost on the template replication rate of the
donor for making the protein.
Eigen and co-workers (1971-1981) have
argued that hypercycles possess intrinsic
advantages in competition with Malthusian
replicators and that (1978a, p. 41), "selection of a hypercycle is a 'once-forever' decision." It can be seen from equations (9)
for the two-membered hypercycle, that as
a hypercycle becomes rare its growth approaches that for Malthusian replicators
since the product terms get small. Thus, it
seems appropriate to study the evolution
of hypercycles vis-a-vis Malthusian replicators as a means to clarify the early advantages of enzyme mediated (i.e., hypercyclic) growth.
Consider, initially, competition between
a one-membered hypercycle and a Malthusian replicator. Let X, and X2 be the abundances of the hypercycle and Malthusian
replicator, respectively. Using Eigen's form
of resource regulation (eqs. (2) and (3)), we
have
ONE-MEMBERED HYPERCYCLE
TWO-MEMBERED HYPERCYCLE
Fie. 2. Diagram of replicators. The symbols/; stands
for replicator or "informational molecule" i, and £,
stands for the enzyme made by replicator i. The closed
loops represent self-replication, which may be assisted
by the presence of a protein which it or another replicator makes. The variable rt represents the rate of
template replication and B, the additive effect of E,
on the overall replication rate.
specificity will be removed in the next section. Returning to equations (10), it is easy
to see that the Malthusian replicator will
invade a population dominated by a onemembered hypercycle if
r2 - r, > BX,
(11)
This inequality may be difficult to satisfy,
if XT, the carrying capacity, is large, even
X, = X,(r, + BX, if B is initially small (the protein helps but
X2 = X2(r2 - t)
(10) not too much), so long as r, and rs are not
r,X, BX,2 X2r2
too different.
However, in view of the fact that enzyme
catalyzed reactions are often many orders
with X2 = XT — X,. Note that in equations of magnitude faster than their non-cata(10) it is assumed that the enzyme is already lyzed counterparts, it is likely that B itself
specific for the replicator which produced is large. Consequently, "a hypercycle once
it. This seems to me to be unlikely. I would established, can not easily be replaced by
expect the first enzyme to be some general any newcomer, since new species always
catalyst which would facilitate replication emerge as one copy" (Eigen and Schuster,
of other replicators as well as the replicator 1978a, p. 41). However, it is unlikely if the
which produced it. This assumption of protein is produced at no cost to the hy-
10
RICHARD E. MICHOD
percycle, if only because of the time in- replicators decreases and this is reflected
volved producing the protein which could in conditions (11) and (14).
be spent in template replication. Let C repSince Malthusian replication (nonenzyresent this cost, so that the realized rate of matic) presumably arose first in the evoincrease of the hypercycle is r, — C + £X, lution of life, it is more to the point to study
— \f/. The condition for increase of a Malthe increase of a hypercycle in a population
thusian replicator is then
dominated by Malthusian replicators. But
as already pointed out, when hypercycles
(12) are rare their Malthusian terms dominate,
- r, > BX. - C.
It seems reasonable that the cost/benefit since the benefits accrued through the enratio may initially be quite high, if the first zyme are small. However, the costs are fremeans of translation were inefficient and quency independent and are still paid in
time consuming. In any event, hypercycle the Malthusian terms. This would seem to
evolution is not necessarily a "once-for- present a barrier to the initial evolution of
ever" decision, but Malthusian replicators hypercycles.
may increase when rare provided (12) is
There are two possible ways to overcome
met.
the costs of protein production discussed
Consider, now, competition between the above. The first is based on Eigen's (1971)
two-membered cycle (X,, X2) given in equa- "quasispecies distribution" and for reasons
tion (9) and a Malthusian replicator (Xs). of space will not be presented here (F. Hopf
The relevant growth equations are
and R. E. Michod, unpublished results). In
this approach it is assumed that a MalthuX, = (r, + B2X2 sian replicator produces another replicator
through recurrent mutation and that the
X2 = (r2 + B ^ ! (13) mutant then produces the protein. In this
X3 = (r3 case, the original Malthusian replicator
does not pay the costs of producing the
protein. The second way to overcome the
r 2 X 2 + r3X3
costs of producing the protein is for the
protein-producer to differentially "expeFor simplicity and purposes of comparison, rience" the benefits of the protein in greatassume Bx = B2= B and r, = r2 = r in equa- er amounts than that given by the square
tions (13). In this case, an equilibrium ex- of its concentration. This is facilitated by
ists at X, = X2 = XT/2, X3 = 0. The Mal- the existence of population structure as will
thusian replicator will increase when rare be discussed in the next section.
if
A
r3 - r
BXn
(14)
Consequently, it is twice as easy for a rare
Malthusian replicator to out-compete a twomembered hypercycle than it is to outcompete a one-membered cycle (cf., eqs.
(14) and (11): see also Eigen, 1971, p. 507).
On hindsight, the reason is obvious. In the
case of the two-membered cycle, the finite
supply of resources must be divided among
both members of the cycle and so each
member is less common (in the previous
example by a factor of Vz) than the singlemembered cycle. As already pointed out,
as hypercycles decrease in frequency, their
competitive advantage vis-a-vis Malthusian
POPULATION STRUCTURE AND
THE PROTO-ORGANISM
Most work dealing with the origin of life
has concentrated on the origin of protocellular structures, such as coacervates
(Oparin, 1965, 1968) or proteinoid microspheres (Fox and Harada, 1960). Instead,
the work described here (see also Eigen
and co-workers, 1971-1981, Bernstein et
ai, 1983 or Dawkins, 1976) concentrates
on those processes, such as replication, which
are absolutely basic to all systems which are
capable of natural selection, whether or
not such systems are cellular or even "living" (Bernstein et «/., 1983). While such
structures as coacervates and microspheres
may be essential for the encapsulation of
THE FIRST REPLICATORS
11
molecular replicators and their proteins,
they are not necessary for the origin of
nonenzymatic, templated-directed replication, nor even for the origin of protein
production as will be shown here.
The primordial "soup" envisioned by
Haldane (1929) and Oparin (1924) was certainly not homogeneous with regard to the Fic. 3. Diagram of population structure of the early
distribution of macromolecules. Rock macromolecules associated with life. See text for furcrevices and suspended clay particles (van ther discussion.
Holde, 1980) would provide local habitats
within which macromolecules would be
distributed. In addition, Woese (1980) and licator 2 has no specificity with regard to
Towe (1981) have suggested an atmo- catalyzing the replication of replicator 1 or
spheric setting for the origin of life in sus- 2. Any differential effect benefiting replipended water droplets within which mac- cator 2 more would, of course, facilitate its
romolecules may be distributed by winds. evolution. Consequently, the general cat"In this atmosphere all stages in evolution alyst scenario is a "worst case" approach.
are basically 'cellular.' The droplet phase It should be pointed out that it is not necserves as a natural definition of the pro- essary to assume, as Barbieri (1981, p. 581)
tocell" (Woese, 1980, p. 68). Let a2 rep- claims, the existence of a complex tranresent the variance in the distribution of scription and translation apparatus for the
macromolecules over these various local replicator to make a protein. Instead, the
habitats. In Figure 3, a continuum of pop- protein may initially have been produced
ulation structure is diagrammed. At one by direct pairing between the nucleotide
extreme is a totally homogeneous distri- base sequence and amino acids (see, e.g.,
bution of macromolecules (a2 = 0). At the Hendry et ai, 1981a, b or Woese, 1967).
other extreme is the encapsulation of the Indeed, Woese (1967) has contended "in
macromolecules necessary for life in some my opinion, it is difficult not to conclude
sort of protocellular phase—perhaps sim- that codon-amino acid pairing played a mailar to coacervates or proteinoid micro- jor role in the shaping of the genetic code.''
spheres. This end of the spectrum repreContinuing with the model, assume that
sents the "organism"—the genotype along
(i) the catalyst is produced at some cost,
with its proteins in a cellular structure.
C, in the template replication rate of
However, in between these two extremes
replicator 2,
lies a region of structure, which, to my
(ii) the catalyst density, e, is directly proknowledge, has not been explored in sceportional to X2, e = kX2, where k is a
narios of the evolution of life. The subsequent calculations, although preliminary,
constant, and
are a step in this direction.
(iii) the macromolecules are distributed
into local habitats each of size N (2
y
V = XT). N is assumed constant for
Model and Results
simplicity
(i.e., all rock crevices or
Let X, and X2 now represent the total
water
droplets
are the same size).
overall abundance of two replicators in some
large population. In the absence of proLet P(y) be the probability density functeins, these replicators are assumed to obey tion of type 2 in the local habitats. P(j) may
the Malthusian dynamic given in equation be interpreted as the frequency of habitats
(4). I assume that one of these replicators, with y type 2 replicators (y = 0, 1, . . . , N).
replicator 2 say, is able to polymerize ami- The local density of type 1 in such a haibtat
no acids into a protein which then serves with y type 2 replicators, is then yV — y and
as a general surface to catalyze the poly- the local density of the protein is ky.
merization of nucleotides. In addition, I
Define P(y\i) as the conditional distriassume that the protein produced by rep- bution of type 2 given type i (i = 1,2). If
12
RICHARD E. MICHOD
you are a replicator of type i (i = 1,2), then
P(y\i) is the probability you will be in a
habitat with y type 2's and hence ky protein
catalysts. Then
fi(l - f.)
•[r, + Be, - ( r 2 - C)
- BeJ.
(21)
Some qualitative results can be obtained
without specifying P(y):
P(y|D=
I (N - y)P(y)
(15)
yP(y)
Following Wilson (1980), define et as the
average density of enzyme which replicator i "experiences." Then
e( = k 2 y P ( y | i )
(16)
Recall that the variance of}' is defined as
Using equations (15) and (17), equation (16)
can be expressed as
e, =
(18)
(i) if the "soup" is homogeneous then
e, = e2 and equations (20) and (21)
result in
(22)
r9 — C > r.
as the condition for evoluton of type
2. In other words the "cost," C, must
not be a cost, if r, and r2 are very
similar.
(ii) if the total population is structured
then/, < 0 implies (using eq. (21))
r2 - C - r, + B(e2 - e,) > 0 (23)
Using equation (18) in equation (23), we
have
r2 - C - r,
+ BKov2[i + —!—I > 0.
Ly
N - yj
(24)
e2 =
Comparing equation (24) to equation (22)
where y is the average number of type 2's indicates that any variation in the distriand N — y is the average number of type bution of molecules serves to facilitate evo1 's in a local population. If the distribution lution of the protein-producer.
Assume further that replicator 1 and 2
of molecules into the pockets is "fair" (e.g.,
had
identical growth rates (r, = r2) prebinomial) then
vious to the mutation which allowed 2 to
produce a protein. Using the following def(19) i
y = - l
initions.
Finally, assume that template replication
and enzyme catalyzed replication are two
separate processes and that the benefit in
replication rate caused by the protein is
directly proportional to the expected number of proteins a replicator "experiences."
The growth equations then become, using
Eigen's form of density regulation (eqs. (2)
and (3)),
X, = r ,X, + Be,X 1
X,i//
X 2 = (ir2 - C)X 2 + Be 2 X 2 —
+ Be,X
+
0 = 1•,X,
(r2-
X20
(20)
C)X2 + Be2X2
}\.f
Let J\ _ X ,
X*'
(20) becomes
y _
XT
' "
-x,.
then equation
= kBN
FST
(Wright, 1951),
—
-y)
equation (24) may be represented as
(*"! = r2)
^B- < FSTT
(25)
Equation (25) is analogous to "Hamilton's
rule" in the theory of kin selection (see,
e.g., Michod, 1982), where BT represents
the total "benefit" given out by replicator
2 and FST is a measure of the degree to
which the community of primordial replicators is structured. The variable FST is
the correlation between two replicators
picked at random from a subpopulation
13
THE FIRST REPLICATORS
relative to those picked at random from
the total population (Wright, 1951). If P(y)
is binomial then equation (25) becomes
(26)
ing. Indeed, in his classic paper, Eigen
(1971, p. 505) noted
"It is beyond the scope of this paper to
discuss the details of the reaction mechanisms . . . the properties of which resemble, in many ways, social behavior."
N'
B
which also holds as X2 -* 0 and the protein
producer becomes rare (cf, Charlesworth,
ACKNOWLEDGEMENTS
1978). Equation (26) obtains because the
I would like to thank Harris Bernstein,
protein-producer can "experience" the efHenry
Byerly, Fred Hopf, Dave Jablonski,
fects of its own protein. Consequently, C
Bill
Schaffer
and Krishna Vemulapalli for
is not the total effect of the protein-prodiscussing
these
issues with me. This work
ducer on its own fitness as is usually the
was
supported,
in
part, by NSF grant DEB
case in sociobiological theory (see, e.g.,
81-18248.
Michod, 1982).
DISCUSSION
In this section, I have viewed the organism as one extreme of the population structure of the macromolecules associated with
life. Consequently, the selective pressures
created by population structure per se were
initially equivalent to those fostered by
protocellular structures. Of course, present organisms are much more than a "bag"
of macromolecules, involving highly organized collections of different structures,
each adapted to particular functions. However, the initial advantage of organisms
postulated here was encapsulation. The advantage of encapsulation was localization
of the products of genome directed synthesis, particularly proteins which aided in
replication. According to the above scenario, encapsulation proceeded in a consistent and continuous manner with intermediate stages provided by "passive"
structures in the environment, such as rock
crevices, suspended clay particles or water
droplets. The initial problem "solved" by
this passive encapsulation was to allow the
first protein-producing replicator to overcome the costs associated with a decreased
template replication rate. This was accomplished by directing the benefits of proteinmediated replication to the replicators who
made the protein (or to their derived "relatives"—i.e., copies). Consequently, the
enzyme would be "experienced" by its producer in amounts greater than that given
by considering random interactions in the
population at large. The parallels of this
logic and inequality (25) with current sociobiological theory are, of course, strik-
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