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Epigenetic vs. Genetic, a Storyof the Evolution of the GermlineMichael LachmannGuy Sella
SFI WORKING PAPER: 2003-02-012
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SANTA FE INSTITUTE
Epigenetic vs. Genetic, a story of the evolution of
the germline
Michael Lachmann
Max Planck Institute for
mathematics in the sciences
Inselstr 22
D014103 Leipzig, Germany
e-mail: [email protected]
Guy Sella
The Weizmann Institute of Science
POB 26
Rehovot 76100, Israel
e-mail: [email protected]
17th January 2003
Abstract
Differentiation of multicellular organisms is controlled by epigenetic markers transmitted
through cell division. Many of the systems that encode these markers exist also in
unicellulars, but in unicellulars these systems do not control differentiation. Thus during
the evolution of multicellularity, epigenetic inheritance systems were exapted for their
current use in differentiation. During this transition there must have been stages at which
1
epigenetic information passed between generations to an even larger extent than it does
now. We show that this can lead to the evolution of cells that do not contribute to the
progeny of the organism, and thus to a germline-soma distinction. This hints that an
intrinsic instability during a transition from unicellulars to multicellulars may be the
reason wide spread of the evolution of germ line.
1 Introduction
Waddington coined the term epigenetics to refer to “the branch of biology which studies
the causal interactions between genes and their products which bring the phenotype into
being” (Waddington 1942). In the same paper Waddington also coined another term,
“epigenotype”, to describe the sum total of the patterns of development that a particular
genotype manifests during the process that leads from a fertilized egg into an adult
phenotype. It is believed today that part of the information of the epigenotype is carried
within epigenetic inheritance systems, systems that can transmit information stably
across cell-division, but are not encoded as bases on the DNA. Epigenetic inheritance
systems exist also in unicellulars, where they play a different role than the role of
regulating differentiation that they play in multicellulars. In unicellulars these systems
seem to mainly transmit state information, or are simply another inheritance system. In
this paper we study the consequences of taking an inheritance system that transmits state
information across cell-division, and evolving to use it for control of differentiation.
During the transition period, epigenetic information is both modified by gene-regulation,
and selected on at the population level. We will show that this process makes the state in
2
which two or more cell types produce a new generation of organisms unstable. This
eventually leads to the evolution of a germline-soma separation.
Because the full models that this paper examines are somewhat complex, we will
introduce some of the assumptions gradually. Section 2 gives and overview of epigenetic
systems, as they are used in this paper. In section 3 we introduce the first model, with just
two cell types, and equal reproduction for all cells in the adult. This model is then
analyzed in section 4. Section 5 adds another assumption to the model: cells in the adult
do not necessarily reproduce equally. It will be shown that in the model some cells evolve
to give up their reproductive ability. In section 6 it is shown that these results do not
depend on the fact that we chose a system with two cell types. It is shown that a system
with an arbitrary number of cells, and an arbitrary differentiation graph will tend to
evolve towards a more star-like differentiation graph, which corresponds to the evolution
of a germline-soma separation. Section 7 then introduces a model, which is fully
described in Appendix A, that allows for evolution of “generalized differentiation”. We
will discuss a few simulation results from this model, and to what extant they agree with
the preceding sections. Finally, the paper ends with a discussion of the results.
2 Epigenetics
There have recently been several papers that commented on the “hijacking” of the term
epigenetics to be used mainly in describing transmission of information across
generations in addition to the information on the DNA, and less to mean the translation of
genotype to phenotype (Wu and R. 2001; Cavalli 2002). Since this paper will deal with
3
both, we will use the term “epigenetic inheritance systems” (EIS), for the chemical
systems that enable the transmission of information across cell division, in addition to the
information in the DNA. We will not specify whether these transmit information across
generations.
The best understood epigenetic inheritance system is the methylation marking system
where the presence of methyl (CH3) groups on some cytosines (in most vertebrates and
plants these are cytosines that have guanines as neighbors) or other nucleotides, are
transmitted from one cell generation to the next. Inactive genes are often highly
methylated, whereas the same genes may be transcribed if the methylation level is low.
Developmental and environmental cues lead to changes in methylation, so the same gene
may carry distinctly different methylation patterns (’marks’) in different cell types
(Holliday 1990). Other than methylation marks, which are the best understood DNA
associated marks, there exist other types of marks, involving DNA-associated proteins
that affect gene activity and can also be transmitted in cell lineages, and are maintained
and reconstituted following DNA replication (Lyko and Paro. 1999). Differences in cell
states can also be transmitted in other ways, such as through positive regulatory
feedback-loops where a gene that was turned on by a transitory external stimulus,
produces a product that then acts as a positive regulator that maintains transcription of the
gene. Another type of epigenetic inheritance is based on the 3D templating of protein
complexes. (a more review of these and other EISs is reviewed in Jablonka, Lachmann,
and Lamb 1992 and in Jablonka and Lamb 1995).
Epigenetic inheritance systems involving all three types of EISs (based on chromatin
marking, on self sustaining regulatory loops, or on 3D templating) are observed in
4
unicellular organisms. For example, bacteria and yeast cells have epigenetic inheritance
systems and can therefore transmit induced and accidental functional and structural states
to their progeny (Grandjean, Hauck, Beloin, Le Hegarat, and Hirschbein 1998; Klar
1998). Unicellular organisms do not, however, undergo epigenesis in the classical sense:
this notion usually refers to processes of development and cell differentiation in
multicellular organisms. Since unicellular EISs were the precursors of cellular heredity in
multicellular organisms, the question is how did this change of function happen during
the evolution of multicellularity? Are there interesting phenomena that happen during
this transition?
In order to answer this question, we must clarify the difference between epigenetic and
genetic heritable variations. One could say that genetic information provides a plan or
program for the cell’s action, whereas epigenetic information codes for the current state
the cell is in, when the state is to be transmitted across cell divisions. In many cases, this
distinction is clear, since epigenetic variations are usually erased during the formation of
gametes. The neo-Darwinian view assumed for some time that in multicellular organisms
this distinction is completely clear-cut. It was assumed that epigenetic inheritance only
codes for the current state, and is never transmitted from generation to generation, while
genomic information is never modified during development. It was assumed that during
sexual reproduction epigenetic marks from the previous generation are always erased
before development gets underway. However, there are cases in multicellular organisms
in which epigenetic marks are transmitted through several generations. For example, it is
now recognized that a well-studied heritable variation in mouse coat color is caused by an
epigenetic modification, not a mutation (Morgan, Sutherland, Martin, and Whitelaw
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1999). Similarly, the peloric form of toadflax, a “mutant” described by Linnaeus over 250
years ago, has turned out to be an “epimutant” - a difference in methylation pattern, not
DNA sequence (Cubas, Vincent, and Coen 1999).
Another property that may distinguish between genetic and epigenetic variations is the
inducability of the variation. Genetic variations are usually random in the sense that their
specificity with respect to the inducing stimulus is rather low, and they are usually not
adaptive responses to the stimulus. Epigenetic variations can be random or induced, and
in the latter case both specificity and adaptedness may be quite high. Since there are
examples of genetic variations that are highly specific and developmentally regulated this
distinction is not always valid.
For the purpose of this paper, we will use the following definition: Information that is
transmitted across cell division, and can be induced to change by the organism is part of
the epigenetic inheritance system. Information that can be transmitted across cell
division, but changes only through random mutation will be called part of the genetic
inheritance system.
Will the grey area in which epigenetic inheritance systems play both the role of
genetic-information carriers, and the role of state-information carriers effect evolution?
We will present an example in which it does. In this example novel evolutionary effects
occur as a result, and we will also see how the effect can also facilitate the evolution of a
germline-soma separation.
6
3 Description of the model
Now let us turn to the main model this paper is based on. The organisms in the model
will be primitive multicellulars, with functional cell differentiation, but no germline-soma
separation. Cell state is determined through an epigenetic inheritance system, and all cell
types can produce spores to make a new adult. The genetic/epigenetic system of the
organism controls differentiation through changes in the epigenetic state of cells. For
clarity we will assume that the epigenetic system is based on DNA methylation, though
the model would apply equally well to other epigenetic inheritance systems. For
simplicity, we assume asexual reproduction. The implications of sexual reproduction, and
in particular of diploid organisms are addressed in the discussion. The epigenetic
inheritance system will exhibit heritable variation of random mutations and induced
changes.
Each organism starts its life as a single cell, a spore. The organism then undergoes
growth through cell division, and differentiation. For simplicity we assume that all adult
organisms express the same organization of cells. The adult contains cells of two types -
A andB. Every adult hasNA cells of typeA, andNB cells of typeB. This assumption
corresponds to a fitness function in which any offspring that does not have exactlyNA
cells of typeA andNB of typeB is not viable. In section 7 we explore such a model.
As stated above, this model describes an organism before the evolution of a germline.
Thus the initial cell of the organism is not necessarily of a certain epigenotype – it may be
of typeA or of typeB. This first cell will then divide and replicate its epigenetic pattern to
create cells of the same type, and also divide and modify its epigenetic pattern to create
cells of the opposite type. The epigenetic pattern of the cell determines gene activity in
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the cell, and thus determines the difference in activity between typeA and typeB. The
type of the first cell is determined by the type of the spore, which in turn is determined by
the type of the cell that produced it.
The number of spores produced by each cell in the adult is under genetic control, but
initially we just assume that each cell in the adult producesk spores. An adult organism
has a fitnessf , which determines how many spores it can produce. Following is a
summary of these assumptions:
• Each multicellular organism consists of cells of two distinct epigenetic types, and
distinct function: cells of typeA and cells of typeB.
• The adult form always contains exactlyNA cells of typeA, andNB cells of typeB.
• A cell of type i in the adult producesk · f spores, wheref is the fitness of the
parent. The spores maintain the epigenetic identity of their parent cells.
• During differentiation, a cell of typeA can replicate its epigenetic patterns to
produce cells of typeA, or change its epigenetic patterns (i.e. differentiate) through
genetically coded mechanisms to produce cells of typeB. Similarly, cells of typeB
replicate to produce typeB and differentiate to produce typeA.
Figure 1 shows the life cycle of these organisms, and the differentiation graph.
Now we turn to the main assumptions of the model: We now assume that at some point
the epigenetic pattern of a cell of typeA undergoes an epimutation, to give a cell of type
A′. The change is in the epigenetic information, and not in the genetic code of the cell -
its genes are still identical to the genes of all other cells in the organism (see figure 2 for
possible methylation patterns of cells of typeA, B, andA′).
8
B
BA
A
A B
B B
B
AA
A
BA
adult
k spores
k spores
spore spore
(a) orig. life cycle.eps
A B
(b) orig. differentiation graph
Figure 1: (a) Original life cycle of the organism, as described above. The adult has a
fixed number of cells of two types,A andB. Cells of both types give rise to spores which
maintain their epigenetic identity, and can differentiate into a new adult.
(b) Differentiation graph of the organism. Nodes represent cells of an epigenetic type,
arrows represent the possibility for a cell type in the spore to produce another cell type in
the adult through replication or differentiation.
* *
* *
* **
B
A
’A
Figure 2: Possible methylation pattern for the different cell types. The patterns for types
A and B are different, and transform to one another during epigenesis. The pattern for A’
is different from these two, and the process that transforms A to B will transform A’ to B,
also.
9
B
BB
B
B
B
B A
A
adult
B
B
B
A’
A’
adult
A
AA
A
A
k spores
spore
k spores
spore
Mutated type, high fitness
k spores
spore
A’
A’
A’
A’
A’
(a) mod. life cycle
A B
A’
(b) mod. differentiation graph
Figure 3: (a) Modified life cycle of the system with cells of typeA, B, andA′.
(b) Differentiation graph with the epimutationA′. Notice that cells of typeA′ produce cells
of typeA′ andB, but that cells of typeB can not produce cells of typeA′.
We also assume the following:
• Cells of typeA′ will produce spores of typeA′. Organisms originating from such
spores will containNA cells of typeA′, andNB cells of typeB. During
differentiation, cells of typeA′ will replicate to produce cells of typeA′, and
differentiate to cells of typeB. Thus we assume that the differentiation pathway
which causes cells of typeA to become typeB will cause cells of typeA′ to become
cells of typeB.
• An organism with cells of typeA′ andB has a sufficiently higher fitness than the
original organism with cells of typeA andB. Later it will be shown how much
higher the fitness of such an organism has to be. An adult with cells of typeA andB
has fitnessf , and one with cells of typeA′, andB has fitnessf ′.
10
4 Formal description of the model
Epigenetic types of the cells areA, B, andA′. The frequencies of spores of typei at the
beginning of a generation ispi . The number of cells of typej in an adult that started from
a spore of typei, denoted byGi j is:
G =
GAA GBA GA′A
GAB GBB GA′B
GAA′ GBA′ GA′A′
=
NA NA 0
NB NB NB
0 0 NA
(1)
This matrix represents the differentiation graph of the system, in which an entry at
positioni, j is non-zero if a spore of typei will produce a cell of typej in the adult.
The fitness of an adult that started as a spore of typei is fi . This fitness can be
represented by the following matrix:
F =
f 0 0
0 f 0
0 0 f ′
(2)
Thus the number of cells of the various epigenetic types in the population in the adult
stage isF×G×−→p , and the number of spores of the different types in the next generation
is k ·F×G×−→p . The total number of spores produced is−→1 ×k ·F×G×−→p , where we
denote−→1 ≡ (1,1,1). Thus the distribution of spores in the next generation, is
−→p t+1 =k ·F×G×−→pt
−→1 ×k ·F×G×−→p t
(3)
11
The equilibrium distribution of this system depends on the eigenvalues of the matrix
F×G, which is
F×G =
f NA f NA 0
f NB f NB f ′NB
0 0 f ′NA
(4)
when f ′NA is bigger than the largest eigenvalue of the upper left-hand 2×2 matrix
f NA f NA
f NB f NB
(5)
then the eigenvector with largest eigenvalue of the system cannot be of the form(a,b,0),
and thusA′ is present in the equilibrium population. Thus if
f ′
f> 1+
NB
NA(6)
A′ will successfully invade the population. In that case, The largest eigenvalue isf ′NA
and thus typeA′ acts as a source for the population, and typesA andB as sinks.
5 Reproductive ability of cells
Till now we assumed that every cell in the adult produces exactlyk spores. We will now
add an additional assumption, which will make it possible for a cell to specialize in
reproduction. Assume that the genome can determine allocation of resources in a certain
cell type, either to spore production, or towards aiding in spore production of other cells.
12
We will also assume that in transferring resources from one cell to another, potentially
some of the resources are lost.
In general the genome could specify how much resources a certain cell-type gives up, and
how much it contributes to each of the other cells. For simplicity, we will assume that the
resources simply re-distributed among the cells in proportion to their reproductive ability,
though our results do not rely on this assumption. We will assume that the genome can
specify a single parameter per cell type, the reproductive abilityr. Cells of typeB with
reproductive abilityr, then use a proportionr of their resources to produce spores. A
proportion 1− r of theB’s resources is contributed to a general pool that is divided with a
loss among all cells, in proportion to their reproductive ability. In transferring resources
between different cells, a proportionL is lost.L is called the loss factor. The number of
spores of typei produced in the next generation in an organism with fitnessf is
kNi
(f r i + f
r i
∑ j r jNj(1−L)∑
j(1− r j)Nj
)(7)
wherer i is the reproductive ability of cells of typei. This is a linear model, in which the
reproductive ability given up by some cells is divided among all cells in the organism in
proportion to their reproductive ability. The constantk can be seen as the number of
spores produced by one unit of resources of the cells. Summing overi in equation 7 we
can see that the total number of spores produced by the organism is
(∑ j Nj
∑ j r jNj(1−L)+L
)· f k ·∑
ir iNi (8)
To understand this equation better, we will also writeN for ∑i Ni andn for ∑i r iNi . Then
13
the total number of spores produced by the organism is
f ·k ·(
Nn
(1−L)+L
)n = f ·k ·
(N−L(N−n)
)When the reproductive ability of all cells is 1, the total number of spores produced is
f ·k ·N so that when the reproductive ability of some cells is smaller than 1, the organism
gives up the production off ·k ·L · (N−n) spores. Notice that in models of
specialization, it is assumed that when a cell type gives up its reproductive ability, the
organism gains more than it loses in the overall production of spores - this would
correspond toL < 0 using our formalism.
Now we will make the following claim, for 1> L > 0: before the invasion of the
epimutationA′, any mutation that increasesr will invade, and thus all cell types will
reproduce equally. After the invasion of the epimutationA′, any mutation that decreases
rB will invade, and thus cells of typeB will give up their reproductive ability. These cells
will become soma, and cells of typeA′ will become the germline.
The model as described in the previous section was simulated, for a population size of
1000. Figure 4 shows the results from a representative run. We can see that at first the
reproductive ability ofB stayed at 1. OnceA′ invaded the population, the reproductive
ability of B declined, until it reached almost 0 by generation 1000. The selection pressure
to lower the reproductive ability ofB declines as the reproductive ability ofB declines,
because the cost imposed byB’s production of offspring declines.
One can ask what happens if through genetic changes cells of typeB gain the ability to
produce cells of typeA′ instead ofA. Such a mutation will invade the population. In that
case, the life cycle of the organism will return to the one described in Figure 1. The
14
0
0.2
0.4
0.6
0.8
1
0 100 200 300 400 500 600 700 800 900 1000
Time (generations)
hello
p(A)p(B)p(A’)
B mean reproductive ability
Figure 4: Results of a typical run. The population size is 1000.NA = NB = 2. f = 1, f ′ = 3,
k = 1, L = 0.5. Shown are proportions of spores of the different types over time, and the
average reproductive ability ofB over time. At around generation 130 the epimutation
A′ invaded. At that stageA′ is the source for the population, andA and B are sinks.
Afterwards, a series of mutations caused the reproductive ability ofB to decline to almost
0 - A′ could be considered germline at the end of the run, andB soma.
15
selection pressure for such a mutation to invade declines as the reproductive ability ofB
declines, until whenB lost all reproductive ability and became soma, there is no pressure
for the ability ofB to produce cells of typeA′. OnceB gained the ability to produceA′, it
will regain its reproductive ability. In this case, the bigger the loss factorL, the fasterB
will regain its reproductive ability. When there is no loss, there is no pressure forB to
regain its reproductive ability. So, with a with a big loss factorB with lose its
reproductive ability slowly, and regain it quickly; with a small loss,B will lose its
reproductive ability quickly, and regain it slowly.
6 Other differentiation graphs
Till now we discussed a differentiation graph with two nodes, with the following
properties after an epimutation: One of the cell types was mutated into new cell type -A
into A′. The old differentiation process acts in basically the same way, except that in one
of the differentiation pathways the mutation is lost: whenA′ differentiates intoB it loses
the epi-mutation.
Now we will show that the observations we have made, will hold also for bigger
differentiation graphs, in which the epimutation acts in the same way: Some of the cell
types will become new types, the basic differentiation graph will be preserved, except
that in some differentiation pathways the epimutation will be lost. First we will go
through two examples of a differentiation graph of size 3. In Figure 5 part (a) we see a
differentiation graph with three nodes, and in parts (b) and (c) we see two possible
epimutations that have the properties mentioned above. In part (b),A mutated intoA′, but
16
A B
C
(a)
AB
CA’
(b)
AB
CA’
B’
(c)
Figure 5: Differentiation graph for 3 cell types. Nodes represent cell type, arrows indicate
that the cell type pointed to will be present in an adult that originated in a spore of the
originating cell type. (a) Original differentiation graph.(b) Differentiation graph with
epimutation in whichA mutates toA′, and this epimutation is lost in the differentiation
to B andC. (c) Differentiation graph in whichA is mutated toA′. The epimutation is
retained in differentiation toB, which leads to the creation ofB′. The epimutation is lost
in differentiation ofA′ andB′ into C.
the epimutation is lost whenA′ makesB and whenA′ makesC. In part (c)A mutates into
A′, and in the differentiation process that madeB out ofA the mutation is not lost, so that
A′ becomesB′. In the transition fromB to C the mutation is lost, soB′ becomesC.
As before, we are still concerned with differentiation graphs in which each node is a cell
type, and an arrow between nodesA andB means that a spore of typeA will make a cell
of typeB in the adult. This graph can be represented by a matrix, in which each
row/column corresponds to a cell type, and entryi, j indicates how many cells of typej in
the adult are produced by a spore of typei. Let us consider an organism withn cell types,
and with a differentiation matrixM. An epimutation occurs, and now we have potentially
n+n cell types. At first let us assume that the mutation is preserved through all
17
differentiation processes. In that case the new differentiation graph can be represented by
the following 2n×2n matrix:
M 0̃
0̃ M
in which 0̃ represents ann×n matrix with all entries 0. In this case the epimutation is not
different from a genetic mutation, and if an organism with the new cell types has a higher
fitness, then it will invade the population. The eigenvector with the highest eigenvalue of
the differentiation matrix times the fitness matrix will have either 0 in the firstn entries,
or 0 in the lastn entries.
Now let us assume that in some differentiation process the epimutation is lost. In this
case the new differentiation matrix will take the form: M A
0̃ M−A
The matrixA represents the transitions in which the epimutation was lost. Since the
epimutation cannot be regained in the differentiation process of the original organism, the
lower left corner of the new differentiation matrix remains 0.
Now the eigenvector with the largest eigenvalue can take one of two forms: either the last
n entries are all 0, in which the epimutation did not invade, or there are non-zero entries
among the lastn entries in the eigenvector, in which case the epimutation manages to
remain stable in the population. When the eigenvector is of the form( x 0 ) thenx must
be an eigenvector of the original differentiation matrixM. When the eigenvector is of the
18
form ( x y ) theny must be an eigenvector of the matrix(M−A). For the epimutation
to be stable in the population, it must provide a fitness advantage that is bigger than the
ratio of the largest eigenvalue ofM to the largest eigenvalue ofM−A.
Since the epimutation can not be regained by the unmutated cells, and yet the epimutation
is stable in the population, this means that as in the simple 2-cell case, the population
with the epimutation acts in this case as a source, and the unmutated cells as a sink for
organisms with the epimutation. Therefore as before genetic mutations can invade that
cause those cell types that have lose the epimutation to give up their replication ability if
they can contribute some of their resources to the other cells.
7 General Differentiation
We have shown a scenario in which a germline-soma separation evolves. How likely is
this to happen when differentiation is free to evolve? This question is very hard to answer
solely by theoretical means. On the theoretical side, one can ask whether models in
which differentiation is free to evolve will exhibit the same behavior as the specialized
model described in the paper. To address this question we constructed a model as
described in Appendix A. The model exhibits a phenotype landscape in which
“generalized” differentiation is possible, for organisms living in a fitness landscape that
rewards a certain differentiation pattern. An organism in the model starts as a single cell
which then divides and differentiates repeatedly, until the organism reaches the adult
stage of 16 cells. At this stage the organism is rewarded with fitness benefits for certain
differentiation patterns: a certain proportion of cells need to exhibit a concrete state of
19
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 500 1000 1500 2000
Ave
rage
r
�
Average fitness of adult
Average fitness over time
(a) fitness
0.4
0.5
0.6
0.7
0.8
0.9
1
0 500 1000 1500 2000
Ave
rage
r
�
generations
Average reproductive value of cells in the adult over time
(b) reproductive ability
Figure 6: Evolution of fitness and reproductive value in a representative run of the model
described in detail in appendix A. a. Average fitness of the population vs. time b. Average
reproductive value of the cells in the adult. The population size is 1000, epimutation rate is
5·10−3, mutation rate is 3·10−4 per individual per generation. After 30000 generation, the
reproductive value of the soma still continued to decline. The gradual increase in average
fitness results from less and less production of unfit offsprings.
gene activity. Gene activity is regulated by epigenetic markers, and these markers are
transmitted from the cells in the adult to the spores that will produce a new organism.
Under these conditions, germline-soma differentiation does indeed evolve. Figure 6
shows a representative run with such differentiation. Notice that around generation 200 a
mutant seems to invade the population, which then is followed by a series of further
mutations which eventually lead to reduced reproductivity in some of the cells in the
organism. In Figure 7 we follow this evolution in more detail. At generation 0, the
organism has very low fitness, and a very simple differentiation graph. At generation 68,
after a series of epigenetic mutations, the organism obtained a higher fitness, while still
20
retaining the very simple differentiation graph. At generation 92 a mutant invades, that
obtains a higher fitness through a more elaborate differentiation graph. In this organism,
spores that are produced from some cells of the adult can not reproduce all the cells of the
adult, and thus have a much lower fitness. After a series of mutations, these cells give up
their reproductive ability and become soma.
8 Discussion
The phenomenon observed in this paper is based on a very simple premise: a
multicellular organism reaches an evolutionary impasse in which certain cell-types can
not recreate the whole organism. When these cell types transmit their ineptness to their
offspring, one of two things can happen: the organism can evolve so that all cell types can
recreate the whole organism again, or it can evolve to transfer resources from the cell
types that can’t recreate the whole organism to the cell types that can. When the second
path is taken, a soma-germline differentiation will have happened.
What is the difference between the model presented here, and a model in which
everything was only under genetic control, with no epimutations that are transmitted
across generations? Figure 8 shows transmission of genetic and epigenetic mutations
across cell division for the two cases. As can be seen, in the epigenetic case, ’conflict’
between mutated and non-mutated cells is transmitted across generations. In the parent
mutated and unmutated cell types exist. In the offspring, again, both the mutated and the
non-mutated types co-exist, because the differentiation process restores the original
epigenetic state in some cells. This enables the selection process that was outlined in the
21
000000011 0.04001
1
000000001 0.03965
1 1
1
(a) gen. 0
011001011 11.6822
1
011001001 5.50342
1 1
1
(b) gen. 61
011001011 525.83
011001001 623.573
001001110.94874 3.93593
0.617646
001001100.94874 3.94672
0.617646
0.617646
0.617646
(c) gen. 96
011110111 1207.65
011110101 1344.34
000010010.0996392 9.03731
0.258539
000010000.0996392 0.02284
0.258539
(d) gen. 749
Figure 7: Differentiation graphs at various stages of the evolutionary run. Each node rep-
resents a cell type in the adult organism. Arrows indicate differentiation. The top bits in
each rectangle represent the epigenetic state of gene activity. The left bottom number is
reproductive valuer of this cell type in the adult. The bottom right number is the average
fitness of an adult that is produced by a spore of this cell type. (a) Initial differentia-
tion graph. (b) At generation 61 an individual with a mutated epigenotype invades. The
epigenotype is still not changed by the genome, but this epigenotype achieves a higher fit-
ness. (c) At generation 96 a mutant invades that has a much higher fitness, and an elaborate
differentiation graph. The two bottom cell types can not reproduce the top ones, and thus
have a lower fitness as spores. Because of drift in previous generations, these cells already
have a slightly lower reproductive value. (d) At generation 749 the cell types which can
not reproduce the full organism have a much lower reproductive value, after a series of
invasions of mutants.
22
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epigenetic mutationgenetic mutation
Figure 8: Comparison between inheritance of genetic and epigenetic mutations, in an
organism without germline. On the left a genetic mutation occurs, and is transmitted to all
offspring that that are produced by the mutated cell. On the right an epimutation occurs.
It is transmitted only to the offspring of the mutated cell, but in the differentiation process
the epimutation is lost, and thus in the offsprings, again, both mutated and non-mutated
cells exist
23
paper, in which one of the two cell types loses its reproductive ability. In the genetic case,
on the other hand, the offspring have either only non-mutated cells, or only mutated cells.
The mutant and non-mutant cells co-exist in the same organism only for one generation.
Previous work (Michod and Roze 2001; Michod and Roze 1997) pointed out that even
this one-generation coexistence can be an evolutionary force to lessen the chance of
mutations in the organism.
The model presented deals with a scenario for asexual organisms. Multicellularity arose
in sexual organisms. In sexual organisms, recombination presents an additional constraint
on the transmission of epigenetic information. If different cell types produce gametes
with different epigenetic states, and the epigenetic information resides on the DNA, then
recombinations of the different epigenetic markings have to be viable. This process
probably caused a strong pressure for uniformity of epigenetic information in the
gametes. When the gametes are absolutely uniform with respect to epigenetic
information, then the process outlined in the paper will not occur. If there still is some
residential transfer of epigenetic information through the gametes, which is neutral with
respect to recombination, then the process outlined in the paper will occur.
One of the previous explanations for the evolution of germline-soma differentiation is
based on models of specialization. In those models, one cell type specializes in
reproduction, and other(s) in other tasks. It is assumed that by specializing in other tasks,
more fitness is gained than is lost by giving up the cells reproductive ability. In our
model, on the other hand, during the specialization process, a mutation which causes one
cell type to lose its reproductive ability would invade even if it contributes only a very
small fraction of the reproductive ability it gives up to other cells. The difference between
24
our model and models of specialization stems from the fact that the cell types that give up
their reproductive ability are already an evolutionary dead end, so nothing is lost from
giving up their reproductive ability. Thus, the condition for invasion of specialization is
much weaker. A stronger condition had to happen earlier: in order for the epigenetic
mutation to fix in the population, it had to provide a strong fitness benefit. One can say
that the process of invasion of specialization has been broken into two parts: first invasion
of an epimutation through a strong fitness advantage, and then the invasion of
specialization through a much smaller fitness change.
In some organisms, and in particular in plants, the germline-soma distinction is not as
strong as it is in higher animals. In those organisms it might be possible to observe the
processes described in this paper. A possible empirical question could be how fit are
offspring that are produced by one cell type vs. those that are produced by another. Are
there epigenetic mutations that are transmitted through one type, but erased during
differentiation to another cell type?
We discussed a model for the evolution of differentiation in multicellular organisms, and
showed how in this case reproduction through multiple germ-lines is not stable. The same
process could also describe the evolution of a germline in social insects, such as wasps
and termites. Here the control of the state of an individual in the colony could be carried
out by pheromonal interactions. One would need to show that some of the epigenetic
information of individuals in primitive colonies can be transmitted to the next generation
of the colony.
It is also possible that the model touches on a general phenomenon in nature - a
phenomenon that can occur whenever individuals at a lower level of organization
25
aggregate to form a higher level of individuality, and in the transition use one of the
low-level modes of information transfer to control organization. The separation of a
germline is a universal phenomenon at many levels of organization in nature. One
important example is the transition to DNA as the information carrier. If pre-cellular life
consisted of a collection of self-replicating molecules, or molecules assisting each other
in self-replication (a Hypercycle), then at some point a transition must have occurred that
made the main self-replicating molecule in the organism the DNA, and other molecules
in the cell being produced by the DNA, being in a sense ’somatic’ molecules. An
instability as described in this paper could be one of the causes for this transition.
Acknowledgments
We would like to thank Eva Jablonka for many intersting discussions that lead to this
paper, Lauren Ancel, Susan Ptak and Carl Bergstrom for many comments. The Santa Fe
Institute provided generous support and hospitality.
References
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27
A Appendix - Description of differentiation model
In the paper we described a scenario in which a germline could evolve. The question is
whether this scenario is similar to the scenario that brought about the evolution of a
germline in so many colonial organisms. In this appendix we describe a model for the
evolution of differentiation, to test whether a germline will evolve here through a scenario
similar to the one described in the paper.
In this model organisms are placed in an environment that favors differentiation. We
assume that the organism is already multicellular, developing from a single-celled spore
to an adult with 16 cells. Initially all the cells in the adult are identical. The fitness
function takes into account the distribution of which genes are turned on or off in how
many cells in the adult. Following is an exact description of the model:
A.1 Epigenotype
Each cell has an epigenotype, which is specified by which genes are on or off. This
epigenotype is transmitted to both of the daughter cells when the cell divides. We model
the epigenotype as a string of bitsei , i = 1. . .nG which tells if genei is on or off. In our
model we used 8 genes, i.e.nG = 8. We also assumed that one of the genes distinguishes
between the two daughter cells of a cell-division, so that it is on in one of the daughter
cells, and off in the other.
28
A.2 Genotype
The genome of the organism determines two things: It determines differentiation, and it
determines the reproductive ability of the various cells in the adult.
A.2.1 Genetic determination of differentiation
The genome determines differentiation by specifying a list of classifiers to match the
epigenotype of the cell, probabilities for a subsequent action to be taken, and a list of
which genes should be turned on and off when this action is taken. Thus the genome has
a list of classifiers, chances and actions(cg, pg,ag). The classifiers are a string of length
nG, each element of which is 1, 0, or X. A ’1’ at position i specifies that genei has to be
on for the classifier to match, a ’0’ that the gene has to be off, and a ’X’ that the gene can
be either on or off. If the classifier matches the epigenotype of the cell after division, then
with probability pg an action is taken. The action is simply a list of which genes will be
turned on, and which will be turned off. For example: Let us assume that the epigenotype
specifies the activity of 8 genes. The initial epigenotype of the cell in consideration is
1102031405161718
The genome has two classifiers:
110203X4X5161708 0.5 on: 2,3,4; off: 1
11X2X3X4X5061708 0.5 off: 3Now let us go through cell-division and differentiation. First the cell divides into two
29
daughter cells, which will have the following epigenotype:
1102031405161718
1102031405161708
As was mentioned before, the last gene is on in one of the daughter cells, and off in the
other. Now these two daughter cells differentiate. The first daughter cell doesn’t match
the first classifier, since it specifies that the last gene should be off, whereas in the cell it
is on. It also doesn’t match the second classifier, for the same reason. The second cell
matches the first classifier: the first 3 genes are on, off, off, as specified by the classifier.
The classifier does not specify the state of genes 4 and 5, and then specifies that genes 6,
7, and 8 should be on, on, and off, as they are in the second cell. Thus with probability
0.5 the action specified by this classifier will be taken, which is to turn genes 2, 3, and 4
on, and turn gene 1 off. Thus with probability 0.5 the second cell will switch to the state
0112131405161708
Once the epigenotype of a cell matches a classifier and an action is taken, it is not
matched against other classifiers.
A.2.2 Genetic determination of reproductive ability
The genome also determines the reproductive ability of the various cell types in the
organism. This is done through a list of classifiers andr values:(cg, rg). For each cell
30
type, ther value of all classifiers it matches to will be multiplied to give the reproductive
ability of the cell. Thus if the adult has the following two cell types:
1102031405161718
0112131405161708
and the following list of classifiers specifying reproductive ability:
1102X3X4X5161718 0.7
X1X2X31405X617X8 0.8Then the first cell type matches only the first classifier, and thus its reproductive ability is
0.7. The second cell type matches both classifiers, and thus its reproductive ability is
0.56. Resources are divided among the different cells in the organism to produce spores
as specified in section 5.
A.3 Fitness
Fitness is determined through a list of fitness components. Each of these fitness
components consists of a list of classifiers, the minimal number of cells that need to
match that classifier, and the fitness benefit that the organism gets if the adult organism
contains the minimal number of cells matching each of the classifiers. For example,
assume that the adult organism contains the following cells:
31
i epigenotype no. of cells of this type
1 1102031405161718 6
2 1112130405161708 5
3 0112130405161718 5And assume that the fitness function has the following fitness benefits:
i min n pattern min n pattern fitness benefit
1 8 XX1001XX 5 XXXX0XXX 1
2 3 XXX1101X 8 XX0X11XX 2
3 7 111XXXXX 6 XX00XXXX 8
4 4 01XXXXXX 11 X11X0XXX 512
1. The first classifier of fitness component 1 matches cell types 2 and 3, and the
second classifier matches all cells. So, the organism has 10 cells matching the first
classifier, which is more than the minimum needed, 8. It also has 16 matching the
second, which is more than the needed 5. So the organism gains a fitness benefit of
1.
2. No cell matches the first classifier of fitness component 2, and a minimum of 3 are
needed, so the organism doesn’t gain any fitness benefit.
3. Cells of type 2 match the first classifier of fitness component 3, so 5 cells match,
but 7 are needed, so no fitness benefit.
4. Cells of type 3 match the first classifier of fitness component 4, so 5 cells match
and a minimum of 4 are needed. Cells of type 2 and 3 match the second classifier,
but 11 are needed, so again no fitness benefit.
32
Overall only fitness component 1 matches, so the total relative fitness of the organism is 1.
A.4 Dynamics
1. Each generation starts with a population of spores. Each spore has the epigenotype
and genotype of the cell that produced it.
2. Each spore goes through differentiation and growth. Differentiation and growth
consist of 4 rounds of cell division and differentiation. During differentiation both
genotype and epigenotype can mutate. Each cell division is followed by a round of
differentiation of both daughter cells. The adult then consists of 16 cells.
3. The fitness of the adult organism is calculated. This is the relative fitness of the
organism, if all cells had a reproductive value of 1. When cells have a reproductive
value less than 1, than the total number of spores that will be produced will be
smaller. The transfer of resources between cell types is as described in section 5.
A.5 Simulation results
A deeper analysis of the results of this model are beyond the scope of this paper. A
simulation as described here was run with a population size of 1000, epigenetic mutation
rate of 0.005 and mutation rate of 0.0003. The loss factor was set to 0.5, which means
that half of the resources transfered from one cell to others are lost. Fitness components
with exponential fitness benefits where chosen at random. In approximately half of the
runs soma evolved, and this depended mainly on the fitness function, i.e. with certain
fitness functions most runs produced a soma. Figure 6 shows the average fitness and
33
average reproductive ability of a representative run in which soma evolved. Figure 7
shows representatives of the surviving lineage in this run. As one can see, a
soma-germline distinction evolved in this run. In the organism that appeared at
generation 749, some of the cells contribute 90% of their reproductive ability to other
cells. In figure 9 we show a possible differentiation path of this organism from single
spore to adult. The fitness function of this run is represented in table 1.
34
01111011
01111011
01111010
01111010
01111011
01111011
01111010
01111011
01111010
00001000
01111011
01111010
01111011
01111011
01111010
00001001
00001000
01111011
01111010
01111011
01111010
01111010
01111011
01111010
01111011
00001000
00001001
00001000
01111011
00001001
00001000
00001001
00001000
01111011
01111010
01111011
01111010
01111011
01111010
01111011
01111010
00001001
00001000
01111011
01111010
011110101
011110111
000010000.0996392
000010010.0996392
011110101
011110111
000010000.0996392
011110111
011110101
011110111
000010000.0996392
011110111
000010000.0996392
000010010.0996392
000010000.0996392
000010010.0996392
spore adulttime
Figure 9: Sample development of an organism from generation 749. Time goes from left
to right. The organism starts as a spore, and then goes through 4 cycles of cell-division
and differentiation. Dashed arrows point to the products of cell division, solid arrows to
the products of differentiation.
35
min n pattern min n pattern fitness benefit
8 XX1001XX 5 XXXX0XXX 13 XXX1101X 8 XX0X11XX 28 XX011XXX 4 X11XXXXX 47 111XXXXX 6 XX00XXXX 84 X11XXXXX 3 X0001XXX 164 XXX1110X 7 XXX0X01X 323 X000XXXX 5 1X10XXXX 643 XXXX01XX 3 X1101XXX 1286 X010XXXX 7 XXX1000X 2564 00XXXXXX 4 X11X0XXX 5125 XXX010XX 6 XXX110XX 1024
min n classifier min n classifier min n classifier fitness benefit
3 XXX1001X 3 XXX101XX 5 XXXX111X 44 XXXX101X 3 XX1X0XXX 6 11X1XXXX 86 X110XXXX 3 0111XXXX 5 XX01X1XX 163 XX101XXX 5 10X1XXXX 5 XX10XXXX 325 X1100XXX 5 XX1001XX 6 XX111XXX 644 XX110XXX 3 X0101XXX 6 XX0111XX 1284 X0110XXX 3 XX0110XX 6 XXX111XX 2565 XX00X1XX 6 XX1XX0XX 6 XXX000XX 5123 XXXXXXXX 5 XXX010XX 6 XXX110XX 10244 XXX01X1X 4 XX1101XX 6 XX101XXX 2048
Table 1: Table of fitness components for the fitness function of the run that is described in
this paper.
36