Multilevel Selection Processes in Economics: Theory and
Methods
Natalia Zinovyeva
FUNDACIÓN DE ESTUDIOS DE ECONOMÌA APLICADA (FEDEA)
Calle Jorge Juan 46, Madrid, 28001, Spain
January 29, 2010
Abstract
The paper reviews the main directions of research in evolutionary economics related to the analysis
of multilevel selection processes, where multilevel selection refers to the operation of the natural
selection at individual and group level. The study reviews the history and the applications of
multilevel selection approach and summarizes the main findings with respect to the role of the
group in evolutionary dynamics. It also describes how the aggregate evolutionary dynamics could
be decomposed into innovation and selection effects using famous George Price's decomposition
developed for the analysis of biological evolution
.
Keywords: Multilevel selection, group selection, Price's decomposition
JEL codes: B25, L20
Acknowledgement:
The paper extends the earlier version of the paper that has appeared in DRUID working paper series
in April 2004. I am grateful to Esben S. Andersen, Mikhail Anufriev, Andre Lorentz, Toke
Reichstein, Sandro Sapio, and participants of VI Trento Summer School in Evolutionary Economic
Dynamics, the DRUID Academy Winter Ph.D. Conference and seminar at the University of Pisa for
their valuable comments and suggestions on earlier drafts of this paper. The comments of the
anonymous referee helped to substantially improve the paper.
ISBN 87-7873-158-5
Multilevel Selection Processes in Economics: Theory and Methods
1
Introduction
In traditional economics modeling heterogeneity of agents is often reduced to the
introduction of at most few types, mainly due to the historically strong emphasis
on analytically solvable models. At the same time, as experimental literature in
economics confirms, often human behavior is different from the one assumed in variety
of theoretical economic models (Fehr and Gachter, 2000; Kagel and Roth, 1995).
An increasing number of economists look for alternative theoretical foundations, like
those existent in evolutionary biology, which would take into consideration the variety
of behavioral patterns and help explain the stylized facts that do not find explanations
in mainstream economic theory (Dosi, 2005).
One of the ideas often borrowed from evolutionary biology is the concept of multilevel selection, which suggests that the evolution of a system of entities might follow
a multilevel selection process, in which the selection forces operate simultaneously on
individual- and group-level populations. In biology the concept of multilevel selection
is sometimes used for the explanation of major novelties in biological organisms, such
as wings, eyes and so on (Mayr, 1999). Recently multilevel population approach has
started to be utilized in economic models of industry- and country-level dynamics
and in the models of pro-social behavior.
Still, given the complexity and the multidisciplinary nature of these studies, the
borrowed concept is often interpreted in different ways, without having a common
view on the role of multilevel selection and the way the evolutionary dynamics should
be analyzed in the presence of multilevel selection forces (Henrich, 2004). This paper
intends to clarify the main idea of the concept by analyzing existent theoretical and
empirical literature on multilevel selection both in biology and economics.
The rest of the paper is organized as follows. Section 2 describes the concept
of multilevel selection in biological evolutionary processes. Section 3 summarizes
2
briefly the logic behind applying evolutionary methodology to the analysis of economic dynamics. Section 4 reviews the economic literature that relies on the concept
of multilevel selection in its analysis. It also argues that the particular difference
between biological and economic multilevel evolution is the fact that in economic
systems decision-making processes take place at various levels of aggregation and
thus selection criteria could be different for individual and group levels of evolution.
Section 5 briefly describes the modern advances in the literature on locally interacting
agents. Finally, Section 5 concludes.
2
Multilevel evolution in biology
The possible influence of group characteristics on the pace of evolutionary dynamics
has been discussed for decades in paleontology, evolutionary and development biology.
The concept of group evolution has been introduced to explain the emergence of major
novelties in biological organisms, such as wings, eyes and so on. It was argued that
for these novelties to emerge selection process operating only on the organismic level
would require the time period longer than it is actually observed in the fossil record
(Mayr, 1999). It was thought that the long periods of stability of evolution followed
by periods of rapid changes could be attributed to group-level evolution. The idea
of group evolution, often referred to as macroevolution, is that groups of organisms,
similar to Darwinian individual organisms, might be systematically confronted with
the selection environment and as a result groups with better fit expand and groups
with lower fit shrink. These higher-level changes might then lead to formation of new
species.
The major dispute in this area is about the arbitrariness of the distinction between microevolution and macroevolution: macroevolution could be argued to be just
a cumulative of microevolutionary processes. This debate has been also fueled by observational difficulties: presumably, macroevolution is relatively more problematic to
observe than microevolution. The role of the bearers of information across genera3
tions in macroevolution is still played by genes as in the single-level Darwinian theory.
Therefore, as in the case of the single-level evolution, the outcomes of multilevel selection are usually observed by looking at the changes in frequencies of particular
genes. Indeed, in biology discussion of higher level selection refers to the operation
of selective pressures on the nested packages, within which genes are contained and
replicate (Field, 2008). The question that remains open, however, is whether selection process on group characteristics occurs due to fitness optimizing behavior at the
individual level, or such kind of reduction in explanation is impossible at least for
some evolutionary processes.
The first important impulse to the work on macroevolution was given by Simpson
in his book Tempo and Mode in Evolution (1944). The author suggested that the
analysis of macro-patterns (or tempos) of the rates of change observed in paleonthological data can provide information on the way selection pressures (or modes)
change over time. At the same time, he believed that if the factors driving evolutionary dynamics are the same at all levels of evolutionary hierarchy, the analysis of
macroevolution could be ultimately reduced to the level of population genetics.
Wynne-Edwards (1962) in his study of spatial dispersion proposed that species
tend to group into more or less isolated populations which depend on isolated food
resources, and thus group selection becomes possible. This idea was not generally
accepted. The fiercest critic was done by Williams (1966) who argued that this
kind of group selection is consistent with individuals maximizing their own long-run
reproductive interests or those of their close relatives and thus no group level selection
mechanism is necessary to explain the dynamics of isolated groups.
Later the discussion about irreducibility of multilevel selection forces was exposed
to the rigorous analysis within evolutionary game theory, where the role of group
evolution has been made explicit. This work has been pushed ahead by Maynard
Smith and Price (1973). It was shown in game-theoretic framework that considering
multiple levels of selection can help answering the questions like ‘how coordination on
4
Pareto optimal NE occurs’ or ‘why some members of a group accept bearing fitness
cost while conferring fitness advantages on other members of a group’.1 The first type
of questions correspond to the literature on the emergence of norms, and the second
– to the literature on understanding the survival of seemingly altruistic and prosocial behavior in animals. Seemingly altruistic behaviour could be often observed in
biological world. For instance, birds often help to feed and to protect unrelated birds
offspring (Emlen and Wrege, 1988). It has been argued that the balance between
within-group and between-group selection effects can result in survival of altruistic
traits if the positive between-group selection effects are sufficiently strong to outweigh
the negative within-group selection effects.
To illustrate the idea of how group selection can result in the survival of altruistic
behavior consider the following example. Suppose that there exist several groups of
individuals and in each group j ∈ J a certain share of individuals, αj , are pro-social.
Each period each individual interacts with another randomly chosen individual of his
group. In these interactions altruists create benefit b for their partners and bare cost
c. Then, if x is an indicator of pro-social behavior, the average group-level fitness of
pro-social behavior is fij (x = 1) = αj b − c, whereas the fitness of non-social behavior
is fij (x = 0) = αj b since it implies receiving benefit at no cost.
Suppose that there is a reproduction process at place, which defines the number
of each individual’s offspring in relation to the ratio between individual’s fitness and
the average group fitness and the ratio of average group fitness to the population
average fitness :
rij =
fij (x)
fij (x) fj (x)
/
=
fj (x) f (x)
f (x)
(1)
where fj (x) is the average fitness of individuals in group j and f (x) is the average
fitness of individuals in the whole population. Using equation (1) one can derive the
rule characterizing the change of the share of each particular type of individuals in
1
For models on cooperation and ‘other-regarding preferences’ see Richerson and Boyd (2005),
Richerson, Boyd and Henrich (2003), Bowles and Gintis (2005).
5
the population:
ṡi = si
fi (x) − f (x)
!
(2)
f (x)
Equation (2) defines the replicator dynamics of the evolutionary system. Under
certain conditions this system might result in the proliferation of the altruistic trait.
Consider the numerical example in Table 1. In this example there are only two
groups each composed of 100 individuals. In the first group 50% of individuals have
pro-social behavior and in the second group only 20% of individuals have pro-social
behavior.
Table 1: Numerical example of the evolution of altruistic behavior
Period
I
II
A
N
Total
A
N
Total
Number of individuals
Group
1
50
50
100
67.67
75.19
142.86
2
20
80
100
9.02
48.12
57.14
Total
70
130
200
76.69
123.31
200
Share of individuals
Group
1
0.50
0.50
1
0.47
0.53
1
2
0.20
0.80
1
0.16
0.84
1
Total
0.38
0.62
1
0.35
0.65
1
Individual fitness if b = 20 and c = 1
Group
1
9
10
9.5
2
3
4
3.8
Total
6.65
Reproduction coefficient
Group
1
1.35
1.50
1.43
2
0.45
0.60
0.57
Total
1
Price decomposition
∆α
0.033
Cov(rj αj )
0.064
E[Cov(rij αij )]
-0.031
Note: ‘A’ stands for an altruist and ‘N’ – for a non-altruist. See Appendix A for calculations.
6
Suppose that the benefit created during the interaction with an altruist, b, is equal
to 20, whereas the cost that the altruist has to bare for generating this benefit, c, is
equal to 1. Then, as it is shown in the Table, the fitness of altruists is lower relatively
to the average fitness of the corresponding group (9 vs. 9.5 in the first group and
3 vs. 3.8 in the second group). However, the average fitness of the first group is
substantially higher than the average fitness of the second group so that the resulting
fitness of an altruist in the first group is higher than the population-average fitness.
Therefore the reproduction coefficient for altruists in the first group turns out to be
greater than one. As a result of the corresponding replicator dynamics, the aggregate
share of altruists in the population, ∆α, increases from period I to period II by 3.3
percentage points.
In order to analyze how much of the overall evolution of certain population characteristics correspond to between-group evolutionary selection forces Price (1970)
developed a way to decompose the change of a given population characteristics into
two covariance terms (see Appendix B for the derivation):
Ȧ =
1
[Cov(rj Aj ) + E(Cov(rij Aij ))]
r
(3)
where A is the population-average characteristics, Aj is the group-level average of this
characteristics, Aij is the individual value of this characteristics and r and rj are, respectively, population-average and group-average of the reproduction coefficient. The
first term in equation (3) reflects the covariance between the group-level reproduction
coefficient and group average of the analyzed characteristics. The second term reflects
the average of within-group covariances between individual reproduction coefficients
and individual contributions to the population characteristics.
Applying Price decomposition to our numerical example of Table 1 we can see
that the change in the share of altruists in the population ∆α = 0.033, represents
the result of within-group selection, which leads to a 0.031 decrease in the share of
altruists, and between-group selection, which raises this share by 0.064. It is easy to
7
see that when within-group selection is absent (c = 0), only between-group selection
affects the change in the proportion of altruists, so ∆α is equal to 0.064. At the same
time, if the negative effect of within-group selection prevails the positive effect of
between-group selection (c ≥ 2), ∆α is negative. Using Price equation it is possible
to derive the formal condition for altruists to proliferate in our model:
V ar(αj )
c
<
b
E(V ar(αij )) + V ar(αj )
(4)
Generally, the important formal finding of the game theoretic literature is that
group selection can favor individually costly behavior only if 1) the underlying game
design is not of Prisoner-Dilemma type or/and 2) the grouping of individuals is not
random but assortative (see e.g. Bergstrom, 2002). The first condition generalizes
those findings that demonstrate how under conditions of small group size, limited
migration, and long period of group life a collaborative behavior might be favored. For
instance, keeping the group untouched for several reproductive periods can transform
a one-stage Prisoner-Dilemma game design into a game with a single Pareto-optimal
NE (See the haystack model in Eshel, 1972; Boorman and Levitt, 1973; Maynard
Smith, 1976; Bergstrom, 2002). The second condition explains the role of the group
for evolution – it is a mechanism of non-random matching between individuals. So in
the world where groups are randomly formed group level evolution cannot play any
additional explanatory role with respect to the individual level of selection.
Modeling the group-level trait as the weighted average of within-group individual traits is not the only theoretical option that could be found in the literature on
evolutionary biology. The scholars of paleontology suggested that the characteristic
causing differential success of species could be the inherent property of species themselves, and not represent an ensemble or aggregate trait (Gould, 2002; Gould and
Eldredge, 1977; Eldredge, 1999; Gould and Lewontin, 1979). The authors claimed
that as long as the trait cannot be regarded as an emergent character of the organismic properties within species, the explanation of the species selection within the
8
clades is formally irreducible to the conventional Darwinian selection upon organisms
within populations. As an example of such characteristic Gould and Lloyd (1999)
considered the variance of traits within species. Moreover, the authors claimed that,
as an aggregate characteristic, variability need not be interpreted as an adaptation
at the species level.
Still, it was shown that group-level variability of behavior could be explained by
organismic selection only. Bergstrom (1997) described how sustainability of variation
of individual trait in a population is possible as a result of natural selection. He
provides an example of rats and squirrels who decide how much to hoard for the
winter when they do not know how long the winter will be. Hoarding incurs fitness
costs, while random occurrence of long winter requires big reserves. The paper argues
that natural selection is likely to result in random differences in the attitudes toward
systemic risk by genetically identical individuals. Thus group selection based on
variation criterion does not necessarily imply irreducibility. Things may change,
however, if, as it is often the case in economics, the decision-making and group
reinforcing occurs at different levels of evolutionary hierarchy.
3
Evolutionary ideas in economics
The idea of using the evolutionary approach for explaining economic phenomena was
conceived in the 18th century. In fact, Darwin himself got the inspiration for his theory from the observation of Thomas Malthus, who suggested that poverty and famine
are the natural outcomes of population growth and the inability of resources to keep
up with the rising human population. Later on, with the rise of evolutionary thought
in biology, Alfred Marshall proposed to use biological method for economic studies.
The theoretical background for evolutionary theory in economics was significantly
extended by the work of Joseph Schumpeter, even though Schumpeter himself never
explicitly spoke of “evolution”. He suggested that the explanation of the aggregate
phenomena should be looked for in the studies of single industries and firms, who
9
according to him introduce major novelties into economic system. He argued that
this innovation from within the system leads to the process of Creative Destruction,
which implies the destruction of old products and technology.
Nevertheless, a straightforward application of biological methods in economics
has been argued to be quite problematic. Nelson (1995) summarized the differences
between biological and economic evolutionary notions on the example of firms.2 He
pointed out that, first, unlike biological organisms, firms do not have a natural life
span, and not all ultimately die. They also do not have any natural size. Unlike
the living organisms, which are stuck with their genes, firms are not stuck with their
routines. Moreover, firms adapt their routines after having observed environmental
response.
At the same time, several authors tried to develop a broad terminology that
would be enough generic to be applicable in other than biology domains and that
would not constrain the application of biological ideas in other disciplines (Campbell,
1974; Knudsen, 2002; Hodgson, 2002; Hull et al., 2001). In all these works, one
can find the discussion about the co-existence of the following components: sources
of continuity (inheritance in biology), sources of variety (destroying continuity, like
mutation, recombination, gene flow and genetic drift in biology), and sources of
differential fitness (in biology - natural selection due to interaction with environment
and differential reproduction). The first two are the competing forces that result in
changing or in preserving a particular trait (characteristic) of each entity, whereas the
latter confronts the entity with the environment and leads to the differential selection
according to its traits. The task of different evolutionary disciplines is to attribute
particular meaning to these three forces and to specify the mechanism of interaction
between them. This literature does not specify the nature of the sources of evolution
and the interaction mechanism between the three processes.
The above broad definition of evolution and selection can accommodate the pres2
One of the most famous and important critiques of biological analogies in economics was made
by Penrose (1952).
10
ence of adaptive behavior in social evolutionary processes. In fact, economic agents
adapt their behavior not only after observing outcomes both of their own and other
agents’ behavior. They can also adapt their behavior before observing others’ behavior, making decisions based on their own expectations of future agent behavior.
Witt (2004) suggests that “the human mind is capable of suppressing meaningless
novelty and of evaluating the significance of others ex ante, whereas each genetic
novelty is physically expressed by biochemical processes and evaluated by natural
selection ex post.” Therefore, we can speak about two types of selection: the one
that is an outcome of actual interaction with environment and the one that is an
outcome of a “constraint variety formation” due to expectations of future interaction
(Ziman, 2000). Hodgson and Knudsen (2006) call these processes generative and
subset selection respectively.
Even though being quite abstract, evolutionary ontology in economic processes
highlights that the outcome of evolutionary processes in complex social system is
at least in part beyond the control of the individual competing agents (Buenstorf,
2006). At the same time, the discussion about the extent to which human behavior
and cultural evolution could be explained with the use of Darwinian principles and
the way it should be done is still ongoing (Cordes, 2006; Buenstorf, 2006).
4
Multilevel selection in economics
In order to apply the generalized concept of evolution to a system, in which not only
individuals can interact with each other, but also groups of these individuals might
act as independent wholes, one should first identify the grouping criteria, which makes
possible defining the upper levels of evolutionary hierarchy. Intuition suggests broad
taxonomic rules for economic entities, such as industries, sectors, firms, although
depending on the investigated phenomenon these rules could be seen as arbitrary,
and giving wrong representation of population.
There exists the growing literature in evolutionary economics that relies on mul11
tilevel selection structures for explanation of economic phenomena. Friedman (1991)
reviewed of the use of evolutionary game-theoretic models of economic behavior. He
suggested that the areas of potential economic application of evolutionary games
include monetary theory, industrial organization, and international economics. He
claims that they can help explaining such questions as ‘how a medium of exchange
might emerge’, ‘which alternative firm’s strategy can survive’, and ‘what a dynamic
impact of trade and capital restrictions is on sectoral investment and output’. However, the answers to these questions provided by evolutionary game theory rely on a
number of stability assumptions with respect to the process of technological change
and in general to the arrival of novelty. At the same time, in some economic problems
the rate of change due to the emergence of novelty or recombination might be much
faster than the rate of change due to selection forces. Then the timescale of change
can be shorter than it would be required for selection forces to produce systematic
effects. In game-theoretic terms it means that the payoff-matrix of the game might
change and expand very quickly. In this case it is improbable that a system reaches
any ‘equilibrium’ state.
The existing alternative to equilibrium analysis is a large branch of evolutionary
literature that is devoted to the analysis of economic change. The theoretical models
in this literature do not disregard emergence of novelty and uncertainty related to
it, which they make explicit by the use of stochastic processes.3 In the majority of
these evolutionary models the key actors are firms (Silverberg, Dosi, Orsenigo, 1988;
Dosi, Marsili, Orsenigo, Salvatore, 1995; Melcalfe, 1998). Formalization of dynamics is usually done using replicator equation, which assigns different market shares
according to firms’ fitness. A particular functional form of replicator dynamics is
typically assumed. There is another type of evolutionary models, where the relative market share dynamics is formulated probabilistically (Silverberg, 1997). The
main approaches here involve the use of continuous time Markov processes or master
3
See Dosi and Winter (2000) for the summary of the literature on evolutionary theory of economic
change.
12
equations, and discrete time Polya urns (Arthur, Ermoliev, Kaniovski, 1984).
There are many examples of the use of the multi-level evolutionary framework in
this far-from-equilibrium modeling. In terms of the architectures of analyzed evolutionary systems the models can be divided in horizontal and vertical, i.e. analyzing
co-evolution of populations and hierarchies of selection environments, respectively.
As an example of models with horizontal architecture one can consider a coevolutionary model of Metcalfe (1998), which describes the selection process in a
population composed of two different types of firms. The selection process is based
on the assumption that each group follows its own replicator dynamics. Metcalfe explored different coordination mechanisms between the two groups and concludes that
population change can be explained both by economic variety contained in the system and by the way in which this variety is coordinated, this process of coordination
being influenced by the difference between the selection rules in the groups.
When analyzing co-evolving structures, researchers tend to focus on one particular
population, but to draw the parameterization of selection process from the assumed
inter-population relation. The other tendency is to black-box the intra-population
processes and to constrain attention only to the interaction structure between the
aggregates of co-evolving populations (Lotka-Volterra type of models).
There are also models that try to analyze the evolutionary dynamics of economic
entities along the hierarchy of evolutionary pressures. For instance, the model of
Jacoby (2002) considered the two selection levels in the evolution of R&D projects
based on their productivity. In her model one selection force operates at the level
of firms, which interact in the competitive market, whereas the other selection force
confronts the R&D projects internally to each firm.
Multilevel selection models could be also found in macroeconomic and growth
literature.4 For example, Verspagen (2002) considered the model of Dutch economy
where firms are put under the pressure of several selection forces. The first operates
4
For the review of the literature on the idea of co-evolution of macro-dynamics and technical
change see Llerena and Lorentz (2004).
13
on the populations of firms, bounded by belonging to the same sector in the Netherlands and abroad. The corresponding replicator dynamics guides the evolution of
imports’ share in sector total domestic sales. The selection criterion at this level is
assumed to be aggregate competitiveness of firms within a sector of an economy. The
second selection force operates on the national level and it is directed on sectors that
are assumed to compete for their share in total national spending. At this level the
selection criterion is attractiveness of a sector for domestic consumption or investment. The third type of selection pressures operate on the country’s export share.
One of them affects the total (i.e., aggregated over sectors) export market share and
the other affects the market share in sectoral export markets. Then, the growth rate
of Dutch exports in a particular sector depends on the growth rates of its shares
in national spending, in sectoral export market and on total spending in the export
market.
Not all evolutionary models consider firms as a basic unit of analysis. For example,
Bowles et al. (2003) extended the traditional model of altruistic behavior (see Section
2) to analyze co-evolution of individual behaviors and social institutions. The authors
first analyzed how two institutions – redistributive taxation and segmentation of
society affect survival of altruistic traits in the standard model of altruistic behavior.
It turns out that higher levels of social institutions are associated with lower withingroup fitness differences and thus reduce within-group selection pressures against
altruistic traits. Finally, the authors model variation in the level of taxation and
segmentation by a stochastic process, assuming also that the social cost of both
institutions for society is rising and convex. In this model when the levels of withingroup altruism are high, taxation can play a fitness reducing role. As a result, very
successful altruistic societies, which keep high level of social institutions, could be
rapidly overthrown in evolutionary selection process.
The simple model of Bowles et al. (2003) could be applied in a variety of economic
contexts, not necessarily when the boundaries of the groups of agents are spaciously
14
localized. Consider, for instance, the case of end-user software evolution. The idea
of end-user software is that users can complement and configure it as well as create
their own end-user programs, which use the main application as a platform software.
Statistical packages, like STATA, could be a good example of end-user software.
STATA is composed of the core platform and a number of inbuilt statistical functions.
If a given function is not contained in the core of the program, a user can program
this function and upload it to the dictionary on his local computer. If the user thinks
that this function can be useful for other users, he can choose to make it public.
However, the cost of making the code public in terms of required effort and time is
quite substantial. Before the program is made public, it should be well tested, the
relationship with other functions should be stated and a very detailed help file in
line with STATA guidelines should be written. End-user software need not to be
open-source, even though many open-source software programs could be considered
as end-user software, given that developers can tailor them according to their needs.
Given that users bare substantial cost when preparing submissions of their program,
the question is why such behavior can survive under evolutionary pressures.
Suppose that there exist a population of end-user software packages. The users
of each software have to experience substantial switching costs when moving to other
softwares and this in turn allows to define stable user communities. All users encounter problems that are not trivially solvable using the set of functions provided
by their program. So everyone has to write some specific piece of code to solve his
own problem. Individuals can also decide to invest in preparing the public version of
their own function. This incurs cost c for these individuals, but at the same time it
improves the utility of one other user of the same package by b. The software packages
attract new users proportionally to the utility gains offered by the packages. At the
same time, new users behavior is set proportionately to the relative fitness of each
behavior. If selection forces are such that the system follows the standard replicator
dynamics (as defined in equation (2)), the knowledge-sharing behavior is beneficial
15
for evolutionary survival if inequality (4) holds. Now suppose that contributing individuals can be rewarded in reputation terms. Reputation institution could play
a role of distributive taxation in the model of Bowles et al. (2003), varying across
packages and time. In this case the relative cost of contribution goes down, reducing
the negative selection pressures within a given community, and thus allowing software packages relying on end-user contributions to grow. Moreover, the cost of user
contribution can also change over time and packages.5 Assuming that the cost of
contribution to the end-user software co-evolves with software packages, being higher
for bigger packages and smaller for modular packages, we can explore how the evolution of users’ and developers’ community co-evolves with corresponding software
architectures.6
In the example of Bowles et al. (2003) as well as in the example of end-user
software evolution proposed above the selection criteria affecting the survival of individual behaviors differ across the levels of evolutionary system. In fact, the need
of looking for different selection criteria across the levels of hierarchical population
structures, especially when explaining the evolution of technology, is often mentioned
in economic literature. For instance, Astley (1985) proposed the idea of coexistence
of different hierarchical ecologies. He said that population ecology alone fails to
explain how populations originate in the first place or how evolutionary change occurs through the proliferation of heterogeneous organizational types. He suggested
that looking at community ecology can help to overcome these limitations. Community ecology focuses on the rise and fail of populations as basic units of evolutionary change, simultaneously explaining forces that produce homogeneity and stability
5
The effort and skills that are needed to understand the existing code and to test the added
piece of code may become higher when project grows. In fact, in software engineering the problem
of high cost of development and thus the evolvability of software code is an important concern.
Many studies explore how sizes, the growth rates, and complexity (measured in very different ways,
including estimating the degree of modularity, degree of hierarchical dependences, asymmetry, parameterization, etc.) of particular parts of software source code might lead to evolvability problems
in the future (see Lehman and Belady, 1985; Myers, 2003).
6
The literature analyzing the phenomenon of open-source software has also considered how software architecture is affected by developers’ reputation motivation (Dalle et al., 2004).
16
within populations and heterogeneity between them. The evolutionary development
of organizational communities depends crucially on the nature of technologies, on
which those populations are based. Interdependences between technologies of different populations fuse those populations together into functionally integrated systems,
or organizational communities.7 The model of Astley gives a very rough idea of evolutionary system under consideration. However, it clearly assumes that the drivers
of population dynamics and those of communities’ evolution could be very different.
Mokyr (2000) developed an example of technology and information diffusion
model departing from the standpoint of multilevel population approach. He suggested that, unlike the biological case, in his example extinction is not irreversible.
Complete extinction of technology may happen only if the corresponding to it knowledge is lost and cannot be rediscovered. However, such cases are rare in the history
of technology. In biology, genetic information cannot exist without a living vehicle.
Information, however, can survive outside the technique and evolve quite separately.
Moreover, whereas techniques are vehicles’ for the information they use, they cannot
exist without vehicles such as firms or households. These vehicles are themselves
often the subject of selection. Finally, Mokyr suggests that the result of technology
diffusion should be considered as a result of co-evolution of selection hierarchies.
5
Localized interactions and endogenous group formation
It turns out that in economics groups play a much more important role than in biology, where the source of group formation is usually the spatial distance between
organisms of the same species. Economic processes involve endogenous group formation, for instance based on human cognitive and linguistic capabilities, which result
7
On co-evolution between technology and institutions see also Nelson (2001). According to Nelson’s model, institutions shape ‘social technologies’, which in turn shape the way of implementation
or development of ‘physical technologies’.
17
in capacity to maintain group boundaries and to formulate general rules of behavior
in large groups (Cavalli-Sforza and Feldman, 1973; Sober and Wilson, 1994; Gintis,
2000). Each individual can belong to many groups simultaneously, can ‘migrate’
between groups quite fast and can initiate new groups. Think about individuals
changing their jobs and opening the start-ups, researchers initiating new collaboration networks, plants changing their owners, firms changing technologies and sectors
of specialization.
Agents can have localized pattern of interaction with other agents, even if group
boundaries are not clearly defined. Many studies now analyze the behavior of evolutionary systems where agents are located on a lattice of certain (fixed, stochastic or
endogenous) topology, which constrains the scope of agents with whom a given agent
is likely to interact (Kirman, 1994; Kirman, 1997; Fagiolo and Dosi, 2003; Fagiolo,
2005). The type of interaction usually includes exploration or imitation of neighbors’
strategies. Studies in physics now analyze the Prisoner’s Dilemma models, in which
agents located on a lattice might not only imitate the strategies of their neighbors,
but also learn about the way other agents tend to imitate (Szabo, Szolnoki, Vukov,
2009). Their results suggest that the imitation rule that survives the selection process
provides the highest level of cooperation.
Given the presence of complex evolutionary systems with adaptive behavior and
conscious subset selection coupled with stochastic innovations, the need for an accounting tool such as Price decomposition, mentioned is Section 2 and derived in
Appendix, is especially strong for economic modeling. In his recent article Metcalfe
claims that development of the method of population accounting is “essential to
the further development of an evolutionary economics of growth and development”
(Metcalfe, 2008; p.24). According to him, such method should help giving “en explanation of economic evolution in terms of cause and effect” (p.37). In fact, there exists
a broad literature that advocates the generality of Price’s approach for applications
in economics (Frank, 1995; Metcalfe, 1998; Knudsen, 2002; Andersen, 2003a, b).8
8
It has been also argued that in the analysis of real data Price’s equation can help finding true
18
Still, Price equation is mostly suitable for the analysis of hierarchical evolutionary
structures and is less informative when the topology of selection forces is more complicated. Moreover, any effect associated to endogenous group formation, entry and
exit remains out of Price evolutionary accounting exercise (see Bartelsman and Doms,
2000 and Metcalfe, 2008). So Price’s decomposition may only account for short-term
dynamics without major changes in institutional membership. Still, analyzing how
the patterns of selection pressures identified by Price decomposition change when the
hierarchical system is affected by other co-evolutionary processes can substantially
clarify the role of evolutionary mechanisms inbuilt into a given model.
6
Conclusions
The role of a group in evolutionary selection process has been now long discussed
in biological and game-theoretic literature. Many scholars suggested that group selection can be always explained by the forces of natural selection operating at the
organismic-level, even when the group-level trait that is associated with higher success rates is different from the simple average of organismic traits. At the same time,
it was demonstrated that under certain conditions group-level selection pressures can
help explaining the emergence of norms and seemingly altruistic behavior.
One of the key differences of economic evolutionary systems from biological ones
is that in economics the decisions at higher levels of selection hierarchy could be
explicitly undertaken by economic agents. Quite differently from biological envicriteria for defining selection levels (Andersen, 2004). In fact, Price’s equation accounts’ the real
selection process by projecting its outcomes on some particular partition of population. Moving
along the different possibilities of defining the subpopulation it is possible to search for the cases
where the covariance terms are significantly different from zero. However, as Heisler and Damuth
(1987) and Okasha (2003) underline, some groups may be fitter than others simply because they
contain a higher proportion of fitter organisms. Then the group-level covariance term would appear
positive even without group-specific selection at place. The authors propose a so-called ‘contextual
analysis’ as an alternative to the covariance approach. According to this approach, one need to
determine whether there is a correlation between fitness and group characteristic that is not due
to the correlation between fitness and individual characteristic. In other words, it is necessary
to estimate the partial regression coefficient of group characteristic controlling for the effect of
individual characteristics. This problem is typical for the empirical identification of institutional
effects.
19
ronment, economic agents can learn from their neighbors, adapt their behavior and
modify their group belonging very fast. They can also develop institutions, which
substantially increase the success rate of their groups. This feature creates selection
environments, which are rare in biological setting. Thus the role of a group becomes
far more important in economics than in biology. This is reflected in the large number
of studies that analyze group selection processes in economics. The brief summary
of evolutionary models, which rely on multi-level selection approach, reveals a great
variety of problems, where the approach turns out to be insightful. The areas of research, where the use of the approach could be found, include industrial organization,
international economics, behavioral economic, technology diffusion and others.
References
Andersen, E. S. (2003a), “A note on Price’s equation for evolutionary economics: derivation, interpretations, and simple applications”, working paper
at DRUID/IKE, Dept. of Business Studies, Aalborg University.
Andersen, E. S. (2003b), “Population thinking and evolutionary economic analysis”, Draft of Postscript for the Japanese edition of Andersen’s Evolutionary
Economics: Post-Schumpeterian Contributions.
Andersen, E. S. (2004), “Population thinking, Price’s equation and the analysis of
economic evolution”, Evolutionary and Institutional Economics Review.
Arthur, W.B., Ermoliev, Y.M., and Kaniovski, Y.M. (1984), “Strong Laws for a
Class of Path-dependent Stochastic Processes with Applications, Proceedings
of the International Conference on Stochastic Optimization, Berlin: Springer,
287-300.
Astley, W. G. (1985), “The Two Ecologies: Population and Community Perspectives on Organizational Evolution”, Administrative Science Quartely, Vol. 30,
Issue 2: 224-241.
Bartelsman, E. J. and M. Doms (2000), “Understanding productivity: Lessons
from longitudinal microdata”, Journal of Economic Literature, 38: 569–594.
Bergstrom, T. C. (2002), “Evolution of Social Behavior: Individual and Group
Selection”, Journal of Economic Perspectives, Vol. 16, 2, 67–88.
20
Boorman, S. A. and P. R. Levitt (1973), “Group Selection on the Boundary of a
Stable Population”, Theoretical Population Biology, 4, 85-128.
Bowles, S., J. K. Choi, and A. Hopfensitz (2003), ”The Co-evolution of Individual
Behaviors and Social Institutions”, Journal of Theoretical Biology, 223 (2):
135-147.
Bowles, S. and H. Gintis (2005), “Can Self-interest Explain Cooperation?”, Evolutionary and Institutional Economic Review 2(1): 21–41.
Buenstorf, G. (2006), “How Useful Is Universal Darwinism as a Framework to
Study Competition and Industrial Evolution?”, Journal of Evolutionary Economics, Vol. 16(5), pages 511-527.
Campbell, D. (1974), Evolutionary epistemology. In Schilpp (ed.), The Philosophy
of Karl R. Popper, vol. 1. LaSalle, IL: Open Court: 412-463.
Cavalli-Sforza, L.L. and M. W. Feldman (1973), “Models for Cultural Inheritance:
Group Mean and Within Group Variation”, Theoretical Population Biology,
4:42, 42-55.
Cordes, C. (2006), “Darwinism in Economics: From Analogy to Continuity”, Journal of Evolutionary Economics, Vol. 16(5), pages 529-541.
Dalle, J.-M., P.A. David, R.A. Ghosh, and F.A. Wolak (2004), “Free and Open
Source Software Creation and ‘the Economy of Regard: Participation and CodeSigning in the Modules of the Linux Kernel”, A Presentation at OWLS: The
Oxford Workshop on Libre Source Convened at the Oxford Internet Institute,
25-26th June 2004.
Dosi, G. (2005), “Statistical Regularities in the Evolution of Industries. A Guide
through some Evidence and Challenges for the Theory”, LEM working paper
No.2005/17, Sant’Anna School of Advanced Studies.
Dosi, G. and O. Marsili, L. Orsenigo, R. Salvatore (1995) “Learning, Market Selection and the Evolution of Industrial Structures”, Small Business Economics
7: 411-436.
Dosi, G. and S. G. Winter (2000), “Interpreting Economic Change: Evolution,
Structures and Games”, LEM working paper No. 2000/08, Sant’Anna School
of Advanced Studies.
Eldredge, N. (1999), The Pattern of Evolution. New York: W. H. Freeman & Co.
Emlen, S.T. and P.H. Wrege (1988), “The role of kinship in helping decisions among
white-fronted bee-eaters”, Behavioral Ecology Sociobiology 23:305-316.
21
Eshel, I. (1972), “Neighbor Effect and the Evolution of Altruistic Traits”, Theoretical Population Biology, 3:3, 258-277.
Fagiolo, G. (2005), “Endogenous neighborhood formation in a local coordination
model with negative network externalities,” Journal of Economic Dynamics and
Control, Elsevier, vol. 29(1-2), pages 297-319.
Fagiolo, G. and Dosi, G. (2003), “Exploitation, exploration and innovation in a
model of endogenous growth with locally interacting agents,” Structural Change
and Economic Dynamics, Elsevier, vol. 14(3), pages 237-273.
Fehr, E. and Gachter, S. (2000), “Cooperation and punishment in public goods
experiments”. American Economic Review 90 (4), 980–995.
Field, A. J. (2008), “Why Multilevel Selection Matters”, Journal of Bioeconomics,
10, p. 203-238.
Frank, S. A. (1995), “George Price’s contributions to evolutionary genetics”, Journal of Theoretical Biology, 175: 373–388.
Friedman, D. (1991), “Evolutionary Games in Economics”, Econometrica, Vol. 59,
3, 637-666.
Gintis, H. (2000), “Strong Reciprocity and Human Sociality”, Journal of Theoretical Biology, 206:2, 169-179.
Gould, S.J. (2002), The Structure of Evolutionary Theory, The Belknap press of
Harvard University Press, Cambridge, MA, USA.
Gould, S.J. and E. A. Lloyd (1999), “Individuality and adaptation across levels of
selection: How shall we name and generalize the unit of Darwinism?”, Proceedings of National Academy of Science, USA 96 (21): 11904–11909.
Gould, S.J. and N. Eldredge (1977), Punctuated equilibria: The tempo and mode
of evolution reconsidered. Paleobiology 3: 115-151.
Gould, S.J. and R. C. Lewontin (1979), The spandrels of San Marco and the
Panglossian paradigm: A critique of the adaptationist programme . Proceedings
of the Royal Society London B. 205: 581-598.
Heisler, I. L. and J. Damuth, (1987), “A method for analysing selection in hierarchically structured populations”, American Naturalist, 130, 582-602.
Henrich, J. (2004), ”Cultural Group Selection, Coevolutionary Processes and
Large-scale Cooperation”, Journal of Economic Behavior and Organization,
Vol. 53, pp. 3-35.
22
Hodgson, G. M. (2002), “Darwinism in Economics: From Analogy to Ontology”,
Journal of Evolutionary Economics, Vol. 12, pp. 259-281.
Hodgson G M. and T. Knudsen (2006), “The Nature and the Units of Social
Selection”, Journal of Evolutionary Economics, Vol. 16(5): 477-489.
Hull, D., Langman, R., and Glenn, S. (2001), “A General Account of Selection:
Biology, Immunology and Behavior”, Behavioral and Brain Sciences 24 (2).
Jacoby, N. (2002), ”Internal Selection of R&D projects: An Evolutionary Simulation Model”, 8th International Conference of the Society for Computational
Economics, 27-29 June, Aix-en-Provence.
Kagel, J.H., Roth, A.E. (1995) The Handbook of Experimental Economics. Princeton University Press, Princeton, NJ.
Kirman, A. (1994), “Economies with Interacting Agents,” Working Papers 94-05030, Santa Fe Institute.
Kirman, A. (1997), “The economy as an evolving network,” Journal of Evolutionary
Economics, Springer, vol. 7(4), pages 339-353.
Knudsen, T. (2002), “Economic selection theory”, Journal of Evolutionary Economics, 12: 443-470.
Lehman M and Belady L (1985), Program Evolution - Processes of Software
Change, Academic Press, London, 538 p.
Llerena, P. and A. Lorentz (2004), “Co-evolution of Macro-Dynamics and Technological Change: An Alternative View on Growth”, Revue d’Economie Industrielle, Issue 105, pp 47-70.
Maynard Smith, J. (1976), “Group Selection”, Quarterly Review of Biology, 51,
277-83.
Maynard Smith, J. and G. R. Price (1973), “The logic of animal conflict”, Nature
246, 15-18.
Mayr, E. (1999), “Understanding Evolution”, Trends in Ecology and Evolution,
Vol: 14, Issue 9: 372-373.
Metcalfe, J. S. (1998), Evolutionary Economics and Creative Destruction, Routledge, London.
Metcalfe, J.S. (2008), “Accounting for economic evolution: Fitness and the population method”, Journal of Bioeconomics 10, p. 23-49.
23
Mokyr, J. (2000), “Evolutionary phenomena in technological change”, in Technological innovation as an evolutionary process/ ed. by J.M. Ziman, Cambridge
University Press.
Myers, C. (2003), “Software Systems as complex networks: structure, function, and
evolvability of software collaboration graphs”, Physical Review, E 68, 046116.
Nelson, R. R. (1995), “Recent Evolutionary Theorizing about Economic Change”,
Journal of Economic Literature Vol. 33 Issue 1: 48-90.
Nelson, R. R. (2001), “The coevolution of technology and institutions as the driver
of economic growth”, in Frontiers of Evolutionary Economics: Competition,
Self-Organization and Innovation Policy ed. by J. Foster and J. S. Metcalfe,
Edward Elgar Publishing.
Okasha, S. (2003), “Multi-Level Selection, Prices Equation and Causality”, Centre
for Philosophy of Natural and Social Science, LSE, Technical Report 13/03
Penrose, E. T. (1952), “Biological Analogies in the Theory of the Firm”, American
Economic Review 42: 804-819.
Price, G. R. (1970), “Selection and covariance”, Nature 227: 520-521.
Price, G. R. (1972), “Fisher’s ’fundamental theorem’ made clear”, Annals of Human Genetics 36 (2), 129-140.
Richerson, P. J. and R. Boyd (2005), Not by Genes Alone: How Culture Transformed Human Evolution, Chicago: The University of Chicago Press.
Richerson, P. J., Boyd, R. and J. Henrich (2003), “The Cultural Evolution of
Human Cooperation”, in: Hammerstein, P. (ed.), The Genetic and Cultural
Evolution of Cooperation, Cambridge, Mass.: MIT Press, pp. 357-388.
Szabo, G., A. Szolnoki, J. Vukov (2009), “Selection of dynamical rules in spatial Prisoner’s Dilemma games”, A Letters Journal Exploring the Frontiers of
Physics, 87, 18007.
Silverberg, G., G. Dosi, and L. Orsenigo (1988) ”Innovation, Diversity and Diffusion: A Self-Organisation Model”, The Economic Journal, Vol. 98,
Silverberg, G. (1997) “Evolutionary Modeling in Economics: Recent History and
Immediate Prospects”, paper for the workshop on “Evolutionary Economics as
a Scientific Research Programme”, Stockholm, May 26-27.
Simpson, G.G. (1944), Tempo and Mode in Evolution, Columbia University Press,
New York.
24
Sober, E. and D. S. Wilson (1994), “Reintroducing Group Selection to the Human
Behavioral Sciences”, Behavior and Brain Sciences, 17, 585-654.
Verspagen, B. (2002), “Evolutionary Macroeconomics: A synthesis between neoSchumpeterian and post-Keynesian lines of thought”, The Electronic Journal of Evolutionary Modeling and Economic Dynamics, 1007, http://www.ejemed.org/1007/index.php.
Williams, G. C. (1966), Adaptation and Natural Selection. Princeton University
Press, Princeton, N.J.
Witt, U. (2004), “On Novelty and Heterogeneity”, working paper No.0405, Max
Planck Institute for Research into Economic Systems, Evolutionary Economics
Group.
Wynne-Edwards, V.C. (1962), Animal Dispersion in Relation to Social Behaviour.
Hafner Publishing Company. New York, NY.
Ziman, J. (2000), “Evolutionary Models for Technological Change”, in: Ziman, J.
(ed.), Technological Innovation as an Evolutionary Process, Cambridge: Cambridge University Press, 3-12.
25
Appendix A: Calculations for the numerical example in Table 1
In the numerical example of Table 1 there are two groups of 100 individuals, one with
50% of altruists and another with 20% of altruists. The benefit of altruistic behavior,
b, is equal to 20 and the cost of it, c, is equal to 1. Using this information, one can
calculate the fitness of altruists in group 1: f1 (x = 1) = 0.5∗20−1 = 9. The fitness of
non-altruists in group 1 is equal to f1 (x = 0) = 0.5 ∗ 20 = 10. The fitness of altruists
and non-altruists in group 2 is equal, respectively, to f2 (x = 1) = 0.2 ∗ 20 − 1 = 3
and to f2 (x = 0) = 0.2 ∗ 20 = 4.
The mean fitness is equal to f1 (x) = 0.5f1 (x = 1) + 0.5f1 (x = 0) = 9.5 for
individuals in group 1 and to f2 (x) = 0.2f2 (x = 1)+0.8f2 (x = 0) = 3.8 for individuals
in group 2. The population average fitness is equal to f (x) = 6.65.
Given the fitness of individuals, one can derive the corresponding reproduction
coefficients. For instance, the reproduction coefficient for altruists in group 1 is equal
to r1 (x = 1) = f1 (x = 1)/(0.5f1 (x) + 0.5f2 (x)) = 9/6.65 ≈ 1.353 and for altruists in
group 2 it is equal to r2 (x = 1) = f2 (x = 1)/(0.5f1 (x) + 0.5f2 (x)) = 3/6.65 ≈ 0.451.
Using reproduction coefficients, one can compute the number of altruists in period
II: r1 (x = 1) ∗ 50 + r2 (x = 1) ∗ 20 ≈ 76.69. Thus the increase in the population share
of altruists is equal to ∆α = αt+1 − αt = 76.69/200 − 70/200 ≈ 0.033.
In order to perform Price decomposition first we need to calculate the group-level
covariance between the reproduction coefficient and the share of altruists: Cov(rj αj ) =
s1 (r1 (x) − r(x))(α1 − α) + s2 (r2 (x) − r(x))(α2 − α) = 0.5(1.43 − 1)(50/100 − 70/200) +
0.5(0.57 − 1)(20/100 − 70/200) ≈ 0.064. Then we need to calculate within-group
covariances according to the following formula:
Cov(rij αij ) = αj (rj (x = 1) − rj )(1 − αj ) + (1 − αj )(rj (x = 0) − rj )(0 − αj ),
where j ∈ {1, 2}. The mean of these covariances is equal to E[Cov(rij αij )] =
s1 Cov(ri1 αi1 ) + s2 Cov(ri1 αi1 ) = 0.5 ∗ (−0.038) + 0.5 ∗ (−0.024) = −0.031.
26
Appendix B: Derivation of Price decomposition
Price (1970, 1972) decomposition describes the change of some average population
trait over time using two terms, which could be interpreted as selection and innovation
effects respectively.
Denote the number of individuals of type j at the first and the second instances
of time by nj and n0j respectively, the population share of these individuals by sj =
nj /n, and some of individual characteristics by Aj . (Aj does not need to be the
characteristics that is directly affected by the selection force, but it should be expected
to be unevenly distributed across evolving entities.) If the reproduction coefficient is
defined by rj = n0j /nj and the population-average of reproduction coefficients is r,
according to Price the over-time change in the population-average of characteristics
Aj could be decomposed in the following way:
∆A =
1
[Cov(rj Aj ) + E(rj ∆Aj )]
r
(5)
The derivation of formula (5) is the following:
∆A =
X
s0j A0j −
j
X
j
sj Aj =
X rj sj
j
r
(Aj + ∆Aj ) −
X
sj Aj
j
"
#
X
1 X
=
(sj (rj − r)Aj ) +
(sj rj ∆Aj )
r j
j
"
#
X
1 X
=
(sj (rj − r)(Aj − A)) +
(sj rj ∆Aj )
r j
j
=
1
[Cov(rj Aj ) + E(rj ∆Aj )]
r
The key in the above derivation is the observation that
X
X
X
X
(sj (rj − r)A) = A
(sj rj − sj r) = A( (sj rj − r
sj )) = A(r − r) = 0
j
j
j
j
Formula (5) can be applied recursively to the second term on the right-hand side.
27
In this case Price decomposition takes the following form:
∆A =
1
[Cov(rj Aj ) + E[Cov g (rij Aij ) + E g (rij ∆Aij )]]
r
(6)
where now rij and Aij stand for individual-level reproduction coefficient and characteristic of interest and rj and Aj denote group j average reproduction coefficient and
characteristics of interest, respectively. Upper index g indicates that covariance and
expected value are calculated separately for the units of each group.
In Price decomposition of equation (6) the first covariance term captures the
evolution of the characteristics of interest that occurs due to group-level selection
pressures, whereas the mean value of covariance terms calculated independently for
each group captures the part of characteristics evolution which is due to within-group
selection pressures. Thus the sum of all covariance terms captures the aggregate
effect of selection. The remaining term represents innovation or mutation, which is
orthogonal to the effect of selection. If in the analyzed system innovation or mutation
never occurs than this remaining term is equal to zero. Then equation (6) could be
re-written in the form, which is used in Section example:
Ȧ =
1
[Cov(rj Aj ) + E(Cov(rij Aij ))]
r
28