The evolutionary origin of complex
Richard E. Lenski*, Charles Ofria†, Robert T. Pennock‡ & Christoph Adami§
*Department of Microbiology & Molecular Genetics, †Department of Computer Science & Engineering, and ‡Lyman Briggs School & Department of Philosophy,
Michigan State University, East Lansing, Michigan 48824, USA
§Digital Life Laboratory, California Institute of Technology, Pasadena, California 91125, USA
A long-standing challenge to evolutionary theory has been whether it can explain the origin of complex organismal features. We
examined this issue using digital organisms—computer programs that self-replicate, mutate, compete and evolve. Populations of
digital organisms often evolved the ability to perform complex logic functions requiring the coordinated execution of many
genomic instructions. Complex functions evolved by building on simpler functions that had evolved earlier, provided that these
were also selectively favoured. However, no particular intermediate stage was essential for evolving complex functions. The first
from the ancestor by many mutations that were also crucial to the new functions. In some cases, mutations that were deleterious
when they appeared served as stepping-stones in the evolution of complex features. These findings show how complex functions
can originate by random mutation and natural selection.
Charles Darwin’s theory of evolution1, including its intertwined
hypotheses of descent with modification and adaptation by natural
selection, is widely regarded as one of the greatest scientific
achievements of all time. From the outset, Darwin realized that
“organs of extreme perfection and complication”, such as the eye,
posed a difficulty for his theory. Such features are much too
complex to appear de novo, and he reasoned that they must evolve
times undergoing changes in function. There now exists substantial
evidence concerning the evolution of complex features that sup-
ports Darwin’s general model2–16. Nonetheless, it is difficult to
provide a complete account of the origin of any complex feature
owing to the extinction of intermediate forms, imperfection of
the fossil record, and incomplete knowledge of the genetic and
developmental mechanisms that produce such features.
To examine the evolutionaryorigin of a complexfeature in much
greater detail than has previously been possible, we have performed
experiments with digital organisms—computer programs that self-
replicate,mutate andcompete17–26. As Daniel Dennett27has empha-
sized, “…evolution will occur whenever and wherever three con-
ditions are met: replication, variation (mutation), and differential
fitness (competition)”. By using this tractable system, we aim to
shed light on principles relevant to any evolving system. Digital
organisms are also of interest as computer scientists and engineers
explore ways to apply evolutionary principles to program design,
mental system, including the logic functions that digital organisms
can use to obtain energy. There follows a case study of the genomic
and phenotypic changes in a population that evolved an especially
complex function, and then a functional-genomic analysis of the
first genotype able to perform that function. Next we compare the
trajectories and solutions of many populations that independently
evolved this same function, and we conclude by examining the
influence of different selective environments on the propensity of
digital organisms to evolve the function.
Avida is a software platform for research on digital organisms19. To
convey what digital organisms are, it is helpful to compare them
with computer viruses. Digital organisms are self-replicating com-
puter programs, as are viruses. However, computer viruses require
direct intervention to mutate and evolve, whereas digital organisms
exist in a computational environment where copying is imperfect
such that they mutate randomly and evolve spontaneously. Also,
digital organisms compete for energy and, depending on the
environment, can obtain energy by performing logic functions19,25.
In Avida, a genome is a circular sequence of instructions (Fig. 1)
that are executed sequentially except when the execution of one
instruction causes the instruction pointer to jump to another
position. Jumps are encoded using a template-based system,
which is more robust to mutation than is numerical addressing17,24.
Each item in a sequence is one of 26 possible instructions (Sup-
plementary Information). Reproduction is asexual and occurs by
binary fission. Experiments began with an ancestor that could
replicate but could not perform any logic functions. All organisms
virtual CPU with two stacks and three registers that hold 32-bit strings. Execution of
the genomic program generates a computational metabolism, whereby numerical
substrates can be input from the environment, processed in stacks and registers, and
resulting products output to the environment. See main text for details.
NATURE|VOL 423|8 MAY 2003|www.nature.com/nature
were identical and obtained equal energy to execute their genomic
programs, including the copy commands by which a genome
replicates itself one instruction at a time. Copying is subject to
errors, including point mutations, insertions and deletions. Each
mutation alters the genome and may change an organism’s pheno-
success. As in nature, selection in Avida depends on the phenotypic
effects of a mutation in its genetic context and in relation to
the organism’s environment; the researcher does not specify a
distribution of selection coefficients. Most mutations in Avida are
deleterious or neutral, but a small fraction increases fitness20.
Digital organisms compete for the energy needed to execute
tion processing’ units, or SIPs. Each SIP suffices to execute one
instruction. By executing instructions, a digital organism can
express phenotypes that enable it to obtain more energy and copy
its genome. In Avida, organisms can acquire energy by two mech-
anisms. First, each organism receives SIPs in proportion to its
genome length. Second, an organism can obtain further SIPs by
performing one- and two-input logic operations on 32-bit strings
(Supplementary Information). Only one of the 26 instructions in
the genetic code, nand (‘not and’), is itself a logic operator; and
nand must be executed in coordination with IO (‘input–output’)
instructions to perform the NAND function. All other logic func-
tions can be constructed using one or more nand instructions
within an integrated framework of other instructions.
Two logic functions, NAND and EQU (‘equals’), are shown in
Fig. 1. The execution of the highlighted nand instruction, when
immediately followed by the modifying nop-A (‘no operation’)
instruction, causes the bit-strings in the BX and CX registers to be
combined according to the nand operator and the result to be
written to the AX register. The nand operator returns 0 (‘false’)
when both inputs are 1 (‘true’); it returns1 if one or both inputs are
0. The subsequent IO instruction and its modifying nop-A cause
the string in the AX register to be output. If this output matches
perfectly thecorrectanswerfor afunction that isrewarded, then the
organism’s rate of energy acquisition, and hence the execution of its
genomic program, is accelerated by the factor shown in Table 1. For
example, if the organism in Fig. 1 had previously input the strings
labelled X and Y, and if it now output the string in the AX register
(generated by the preceding nand and nop-A instructions), then
the organism would receive the reward for performing EQU. The
reward is obtained because the output string has a 1 at every
position where X and Yare equal (both 0 or both 1), and it has a
0 at each position where X and Ydiffer. The organism would obtain
already been rewarded in its lifetime for performing EQU.
Our study focuses on the origin of the EQU function. EQU
garners the largest reward in our experiments because its perform-
ance is more complex than any other one- or two-input logic
function, given the available genomic instructions. An exhaustive
search shows that the minimum number of nand operations to
perform EQU is five, which is greater than for any other one- or
two-input logic function. Using the 26 available instructions, we
wrote a program of length 19 that performs EQU but does not
replicate (Supplementary Information). This program seems, but
has not been proven, to be the shortest one to perform EQU.
The ancestor could replicate but could not perform any logic
function. However, an organism that evolved one or more of nine
logic functions would obtain further energy. The benefit increased
exponentially with the approximate difficulty of each function
(Table 1). Functions could be performed in any order during an
individual’s life, but no extra energy was obtained by repeatedly
performing the same function. No single mutation in the ancestor
can produce even the simplest of these functions. Instead, several
mutant instructions must appear in the same lineage, and such that
they are coordinately executed, to perform even a simple function.
Nonetheless, this population (and many others) evolved the
capacity to perform EQU, the most complex of these functions.
Figure 2 shows the trajectory of the population’s divergence from
number of generations in which an individual differed from its
parent by one or more mutations. The horizontal axis is time in
computational updates (see Methods). The colour scale shows the
abundance of genotypes at a given depth. The blue line shows the
exact line of descent leading to the genotype that was most
abundant at the end of the experiment. This final dominant type
was 344 steps removed from its ancestor. That is, an offspring
differed genetically from its parent in 344 of the many thousands of
generations leading to this final type. The final dominant has a
genome 83 instructions long (the ancestral length was 50), and it
performs all nine logic functions that provide energy.
Figure 3 shows the trajectories for two fitness components,
replication efficiency and computational merit, for all 344 geno-
Table 1 Rewards for performing nine one- and two-input logic functions
,(A and B)
ANDA and B
OR_N(A or ,B); (,A or B)
ORA or B
AND_N(A and ,B); (,A and B)
,A and ,B
XOR(A and ,B) or (,A and B)
EQU (A and B) or (,A and ,B)
The symbol ‘ , ’ denotes negation. The reward for computational merit increases with 2n, where n
is the minimum number of nand operations needed to perform the listed function. Symmetrical
operations, shown separated by a semi-colon, are treated as the same function. No added
benefit is obtained for performing any function multiple times. These functions include all one-
and two-input logic operations except ECHO, which requires no nand operations and was not
Logic operationComputational merit
Figure 2 Phylogenetic depth versus time in the case-study population. Phylogenetic
depth is the cumulative number of generations in which an organism’s genotype differs
from its parent. The exact line of descent leading to the most abundant final genotype is
shown as the blue line. Colours indicate the relative abundance of genotypes at any
depth, yellow being more abundant than red.
NATURE|VOL 423|8 MAY 2003|www.nature.com/nature
types along the line of descent. Replication efficiency is the ratio of
an organism’s genome length to the SIPs used during its life cycle.
Computational merit is the total reward obtained over an organ-
ism’s lifetime for performing logic functions. Each genotype’s
expected replication rate, or fitness, equals the product of these
quantities. We also identified every mutation that fell along the line
of descent in this population, and characterized the phenotypic
changes associated with each step (Supplementary Information).
The EQUfunction first appeared atstep 111 (update27,450).There
were 103 single mutations, six double mutations, and two triple
mutations among these steps. Forty-five of the steps increased
overall fitness, 48 were neutral and 18 were deleterious relative to
the immediate parent. The large proportion of beneficial mutations
along the line of descent is not surprising, because this lineage
represents the eventual winners that were assembled by natural
selection. Thirteen of the 45 beneficial steps gave rise to the
expression of logic functions not expressed by the immediate
parent, including six steps inwhich there were trade-offs of simpler
for more complex functions.
The presence of deleterious mutations along the line of descent is
more surprising. Fifteen of the 18 deleterious mutations reduced
fitness by ,3% relative to the parent, and might have hitchhiked
with beneficial mutations that arose soon after in the same genetic
background. However, two mutations reduced fitness by .50%.
One was a point mutation that disrupted replication efficiency. Its
harmful effect was eliminated by the next mutation in the line of
descent, which occurred at a distant site in the genome. The other
very deleterious step was a point mutation, at depth 110, that
knocked out NAND, one of the simplest logic functions. Only two
individuals had this maladapted genotype, yet their descendants
emerged as eventual winners. In fact, in the very next step, this
genotype produced the mutation that gave rise to EQU. Was that
deleterious mutation extremely lucky to hitchhike with such a
beneficial mutation? Or was the deleterious mutation a prerequisite
for producing the EQU function within that genome context? To
distinguish between these hypotheses, we reversed this one-step-
prior mutation in the genotype that first expressed EQU. This
reversal eliminated the EQU function. Therefore, a mutation that
was highly deleterious when it appeared was highly beneficial in
combination with a subsequent mutation. The evolution of a
complex feature, such as EQU, is not always an inexorably upward
climb toward a fitness peak, but instead may involve sideways and
even backward steps, some of which are important.
ofdescentleading tothe finaldominant genotype. Ofthese, 62were
beneficial, 132 neutral and 39 deleterious. All nine logic functions
were performed from genotype 306 onwards.
To determine how many instructions were required to perform
EQU at its origin in the case-study population, we systematically
replaced each existing instruction with a null instruction in the first
genotype able to perform EQU. We scored each null mutant for
which functions were lost and which remained, and the data from
all the mutants were combined to produce an array showing the
relationship between genome sequence and phenotypic properties
(Fig. 4). The genome of the first EQU-performing organism had 60
instructions; eliminating any of 35 of them destroyed that function.
Although the mutation of only one instruction produced this
innovationwhenit originated, theEQUfunction evidentlydepends
on many interacting components.
The many instructions required to perform EQU, the previous
evolution of simpler functions, and the repeated trade-offs between
simpler and more complex functions all suggest functional inter-
connections between the genetic networks encoding them. We used
the same array to ask how many instructions that were required to
perform EQU were also required for other functions. Besides EQU,
this genotype performed five of the eight simpler logic functions;
AND was lost as a side-effect of the EQU-producing mutation, and
NAND had been eliminated by the one-step-prior mutation. Of the
35 instructions required for EQU, 22 were needed for simpler
functions. Three instructions required for EQU were also essential
were five others. However, 27 of the 35 instructions required to
perform EQU were evolutionarily derived, and all but one of them
had appeared in the line of descent before this function was ever
performed. Thus, although more than two dozen mutations were
used to build EQU, undoing any one of them destroyed this
function. This asymmetry might suggest that EQU is fragile and
cannot last. However, the EQU function lasted throughout the
experiment because, once evolved, it was so valuable that defective
mutants were eliminated by selection.
Variations on a theme
The case-study population was one of 50 that evolved under
identical conditions, 23 of which acquired EQU. The phylogenetic
depth at which EQU first appeared ranged from 51 to 721 steps. In
principle, 16 mutations, coupled with three instructions already
present in the ancestor, could have produced an EQU-performing
organism. The actual paths were much longer and highly variable,
indicating the circuitousness and unpredictability of evolution
leading to this complex feature. We identified the pivotal genotypes
that first performed EQU in each population, and the pivotal
mutations that distinguished them from their parents. We use
‘pivotal’ to mark these milestones, not to imply that earlier
genotypes and mutations were unimportant for the origin of
EQU. A single mutation distinguished the pivotal genotype from
its parent in 19 populations, whereas four involved double
mutations. The pivotal mutations included point mutations, inser-
tions, a small duplication and even deletions. Pivotal point
Figure 3 Trajectories for two fitness components, showing each genotype in the line of
descent for the case-study population. a, Replication efficiency, which is the ratio of
genome length to energy used in an organism’s lifetime. b, Computational merit, shown
log2-transformed, which is the product of all the rewards obtained by an organism for
logic functions performed during its lifetime.
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mutations used 10 of the 26 possible instructions; and several
pivotal insertions and deletions were unique. Therefore, many
different mutations produced the EQU function in the right
Before the pivotal mutations, each line of descent had already
experienced 50 or more steps, including beneficial, neutral and
deleterious mutations. Some deleterious mutations had small
effects and hitchhiked with beneficial mutations; others reverted
or were compensated by mutations elsewhere. But in the case study,
we showed that one deleterious mutation had genetically predis-
posed (through an epistatic interaction) the subsequent origin of
EQU. To investigate this possibility further, we examined all of the
mutations onestepbeforethepivotalmutations. Fiveofthe23one-
step-prior mutations were deleterious in the backgrounds in which
they occurred (including the case study). When these five were
reverted in the pivotal genotypes, the EQU function was eliminated
in three cases. Thus, three genotypes that first performed this
complex function depended on a one-step-prior mutation that
was deleterious when it appeared.
The 23 pivotal genomes ranged in length from 49 to 356
instructions; the ancestor had 50 instructions and so there was a
strong tendency for increased length to precede the origin of EQU.
The parents of the pivotal genotypes performed between four and
all eight of the simpler logic functions, with a median of seven.
Therefore, at least several simpler functions evolved before EQU in
every population. However, no particular function was essential for
at least one of the 23 parent genotypes. All the pivotal mutations
were beneficial owing to the extra energy obtained by the EQU
function. However, net gains also depended on pleiotropic side-
effects on other traits. Twenty of the 23 pivotal mutations caused
losses of one or more logic functions the parent performed, and 13
reduced replication efficiency. Eight yielded another function, and
three improved replication efficiency. On balance, 20 of the 23
rewarded, whereas three would still have been beneficial. Thus,
beneficial mutations that produced this new function usually, but
not always, engendered trade-offs in other aspects of performance.
We ran the functional-genomic analyses on all 23 pivotal geno-
apparently needed only 17 instructions to perform EQU, whereas
our shortest hand-written program used 19 instructions. Further
examination showed that this unexpectedly low value occurred
at-a-time null mutations did not reveal the full extent of its
computational network. These analyses therefore provide a mini-
mum estimate ofthenumberofinstructions that agenotypeuses to
perform a function.
We carried out experiments to examine the effects of different
selective environments on the propensity to evolve the EQU func-
tion, with all other conditions held constant. Ten further popu-
lations evolved under each of 36 possible regimes in which one or
Figure 4 Functional-genomic array for the first organism to perform EQU in the case-
study population. Its genome sequence is shown to the left; the instruction highlighted in
yellow is the pivotal mutation that yielded EQU but simultaneously eliminated AND. Top
organism can (green) or cannot (red) perform the function. The fill in each interior cell
shows the effect on the function of replacing the instruction with a null instruction. Red,
null mutation destroys existing function; blank, null mutation has no qualitative effect;
green, null mutation produces new function. The number of state changes for each
function is shown at the bottom.
NATURE|VOL 423|8 MAY 2003|www.nature.com/nature
two simpler functions were not rewarded. In all environments, at
least one population evolvedEQU. Evidently, neither any particular
simpler function nor any pairwise combination of functions was
required to evolve this complex feature. In these 36 environments,
the overall fraction of populations that evolved EQU was 124 of 360
(34%), only slightly less than in the ‘reward-all’ environment
(P ¼ 0.0764, one-tailed Fisher’s exact test).
At the other extreme, 50 populations evolved in an environment
where only EQU was rewarded, and no simpler function yielded
energy. We expected that EQU would evolve much less often
because selection would not preserve the simpler functions that
provide foundations to build more complex features. Indeed, none
of these populations evolved EQU, a highly significant difference
from the fraction that did so in the reward-all environment
(P < 4.3 £ 1029, Fisher’s exact test). However, these populations
tested more genotypes, on average, than did those in the reward-all
environment (2.15 £ 107versus 1.22 £ 107; P , 0.0001, Mann-
Whitney test), because they tended to have smaller genomes, faster
generations, and thus turn over more quickly. However, all popu-
lations explored only a tiny fraction of the total genotypic space.
Given the ancestral genome of length 50 and 26 possible instruc-
tions at each site, there are ,5.6 £ 1070genotypes; and even this
number underestimates the genotypic space because length evolves.
By using digital organisms, we traced the exact genealogy, without
any ‘missing links’, from an ancestor that could replicate only to
descendants able to perform multiple logic functions requiring the
coordinated execution of many genomic instructions. The most
complex function, EQU, evolved only when several simpler func-
tions were also useful. Some simpler functions were accessible from
the ancestor by relatively few mutations, and these served as a
foundation on which more complex features were built. The
foundational role of simpler functions in the origin of more
complex ones was evident in the overlap of the genetic networks
underlying their expression, and the frequent loss of simpler
functions as side-effects of mutations yielding more complex
functions. Ourexperiments demonstrate the validityofthe hypoth-
esis, first articulated by Darwin1and supported today by compara-
tive and experimental evidence2–16, that complex features generally
acomplex featurethat couldbebuilt onsimpler functions thatwere
also useful. However, that is precisely what evolutionary theory
requires, and indeed, our experiments showed that the complex
feature never evolved when simpler functions were not rewarded.
Our experiments also show that many different genomic solutions
produce the same complex function. Following any particular path
is extremely unlikely, but the complex function evolved with a high
probability, implying a very large number of potential paths32.
of only one or two mutations, its function invariably depended on
many instructions that had previously evolved to perform other
functions, such that their removal would eliminate the new feature.
Of course, digital organisms differ from organic life in their
genetic constitution, metabolic activities and physical environ-
ments. However, digital organisms undergo the same processes of
reproduction, mutation, inheritance and competition that allow
evolution and adaptation by natural selection in organic forms.
Other similarities are pleiotropy (one mutation affects multiple
traits) and epistasis (multiple mutations interact to determine the
same trait), which emerge in both organic and digital life from the
nonlinear processes by which genomes encode and produce phe-
notypic features. As a consequence, selection acts on organisms
rather thandirectlyontheirgenes. Theorganisms inour studywere
asexual. Sex might accelerate the evolution of complex features by
combining functions that independently evolved in different
lineages. On the other hand, asexuality permits beneficial combi-
nations of mutations to spread even when they are individually
deleterious, as sometimes occurred in our experiments. The con-
sequences of asexual and sexual reproduction for the evolution of
complex features deserve further research. In closing, digital organ-
isms provide opportunities to address important issues in evolu-
tionary biology. They are particularly well suited to problems
that are difficult to study with organic forms owing to incomplete
information, insufficient time and the impracticality of
Avida uses a time-slicing algorithm19to ensure that all organisms execute instructions in
an effectively parallel manner. Experiments ran using Avida version 1.6 on the Linux
operating system on a Beowulf cluster of 64 Pentium III processors. The software and
configuration files for our experiments can be obtained free from our website (http://
myxo.css.msu.edu/papers/nature2003). More information about Avida, and further data
from our experiments, can also be found there.
Every population started with 3,600 identical copies of an ancestral genotype that could
replicate but could not perform any logic functions. Each replicate population that
evolved in the same environment was seeded with a different random number. The hand-
written ancestral genome was 50 instructions long, of which 15 were required for efficient
self-replication; the other 35 were tandem copies of a single no-operation instruction
(nop-C) that performed no function when executed. Copy errors caused point
mutations, in which an existing instruction was replaced by any other (all with equal
probability), at a rate of 0.0025 errors per instruction copied. Single-instruction deletions
andinsertionsalso occurred, eachwithaprobability of0.05 per genome copied.Hence, in
the ancestral genome of length 50, 0.225 mutations are expected, on average, per
replication. Various organisms from nature have genomic mutation rates higher or lower
copied genome, leading to the deletion or duplication of multiple instructions. Each
and computational merit, where the latter is the product of rewards for logic functions
performed. The exponential reward structure shown in Table 1 was used in the reward-all
environment, whereas some functions obtained no reward under other regimes. An
organism’s expected reproductive rate, or fitness, equals its rate of energy acquisition
divided by the amount of energy needed to reproduce. Fitness can also be decomposed
into replication efficiency (ratio of genome length to energy required for replication) and
equal to the execution of30 instructions, onaverage, perorganism. The ancestor used 189
SIPs to produce an offspring, so each run lasted for 15,873 ancestral generations.
Populations existed on a lattice with a capacity of 3,600 individuals. When an organism
copied its genome and divided, the resulting offspring was randomly placed in one of the
was replaced, thus maintaining a constant population size.
Received 19 September 2002; accepted 13 March 2003; doi:10.1038/nature01568.
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Acknowledgements We thank A. Bennett, J. Bull, J. Coyne, D. Lenski, M. Lenski and
E. Zuckerkandl for comments. The authors’ work is supported by the US National Science
Foundation Biocomplexity Program and by the MSU Foundation. Part of this work was carried
out at the Jet Propulsion Laboratory undercontract with the US National Aeronautics and Space
Competing interests statement The authors declare that they have no competing financial
Correspondence and requests for materials should be addressed to R.E.L. (firstname.lastname@example.org).
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