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Do Humans Have Continental Populations?
Abstract. In this paper, I show that population geneticists are acknowledging a kind
of biological population that has hitherto been unappreciated by philosophers. The
new population talk occurs when population geneticists call continent-level human
genetic clusters ‘populations’ in population structure research. My theory is that
the kind of population being referred to is the K population, which is, roughly, a
biological population whose members are united by common genomic ancestry and
population membership is graded. After presenting and defending the theory, I
show that the K population is indeed a kind of biological population. Finally, I
address likely objections.
1. Introduction
There is a recent trend among population geneticists to call the continent-level human
genetic clusters inferred from structure-like algorithms ‘populations’.
1
For example, Michael
Bamshad et al. (2003, 584-585) call Africans, East Asians, Europeans, and Indians “continental
populations” when conducting population assignment with Alu insertions and microsatellites.
Brian McEvoy et al. (2010, 297) call Africans, East Asians, Eurasians, Native Americans, and
Oceanians “geographic populations” when using frappe and structure to detect human population
structure. Marcus Feldman and Richard Lewontin (2008, 90) call these same continental groups
“geographical populations” when summarizing two landmark studies on human population
structure. Furthermore, Lev Zhivotovsky, Noah Rosenberg, and Marcus Feldman (2003, 1183)
call both East Asians and Eurasians “a metapopulation” when doing human genetic clustering
research. However, this linguistic pattern raises two philosophically interesting questions.
First, what kind of population are population geneticists referring to when they call
continent-level human genetic clusters ‘populations’?
2
Second, is the kind of population being
referred to a biological population? The second question requires some clarification. Philosophers
who study populations in biology agree that there are many ways that biologists legitimately divide
living things into populations.
3
However, there is a consensus among these experts that the kind
of population that is minimally appropriate for evolutionary biology is the biological population—
where biological populations are groups that evolve (descend with modification).
4
Perhaps
Roberta Millstein (2009, 268) puts it best when she says, “Populations are the entities that evolve,
prior to any evolution of species…” Sometimes the members of biological populations interact in
evolutionarily-significant ways, but sometimes they don’t. For instance, Lisa Gannett (2003, 997)
1
The term ‘structure-like’ is Weiss and Long’s (2009, 704). I will define the term in section 4.
2
Notice that I do not question whether the continental groups called ‘populations’ by population
geneticists are really populations. Like Jacob Stegenga (2014, 2), I agree that a population is
whatever a linguistic group calls a ‘population’.
3
For evidence, see Gannett (2003), Millstein (2009, 269), Barker and Velasco (2013), and
Stegenga (2014).
4
For instance, Gannett (2003, 990), Millstein (2009, 268), Stegenga (2014, 2), Barker and Velasco
(2013, 973), Gildenhuys (2014, 437), and Reydon and Scholz (2014, 7) are all interested in
populations understood as groups that evolve.
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has shown that population geneticists sometimes identify populations as “breeding units” and
sometimes as “genealogical units.” So, the second question can be restated as, ‘Is the kind of
population being referred to one that requires populations to be groups that evolve?’
The two questions above are philosophically interesting for multiple reasons. Not only is
it interesting to figure out whether continental groups like Native Americans cohere in the right
way to form biological populations, but also, the work done here will inform two ongoing debates
in philosophy of biology. One is about whether there is a single, best conception of a biological
population for evolutionary biology.
5
The other is about whether any of the human continental
groups that population geneticists call ‘populations’ can be legitimately understood as races in any
biological or ordinary sense.
6
My answer to the first question is that the kind of population being referred to in this
context is the K population. This answer constitutes K population theory. While a K population
cannot be understood without jargon from fuzzy set theory and perdurantist metaphysics, it’s
roughly a biological population whose members are united by common genomic ancestry and
whose members can have graded membership. My answer to the second question is that the K
population is indeed a biological population. Note that, in this paper, I do not answer whether
continent-level human genetic clusters are biological populations. That would be an enormous
project that would require defending the sampling scheme, study design, and other methodological
assumptions that go into identifying continent-level human genetic clusters. Rather, what I do is
provide the metaphysical framework for legitimately calling continent-level human genetic
clusters ‘populations’.
I begin by presenting jargon from fuzzy set theory and perdurantist metaphysics that serve
as background assumptions for K population theory. Second, I define the K population. Third, I
defend the K population as the kind of population being referred to when population geneticists
call continent-level human genetic clusters ‘populations’. Fourth, I defend the K population as a
kind of biological population. Fifth, I address potential objections to K population theory. I end
with concluding remarks.
2. Background Jargon
The mathematical and metaphysical jargon that I will use to define the K population is the
following. Suppose crisp sets are the objects called ‘sets’ in Zermelo-Fraenkel set theory. Let an
object space be a crisp set of objects. Suppose a membership function is a function such that
. Then, a fuzzy set
is a pair
. Unlike crisp sets, ‘’ has no meaning for fuzzy
sets. The analogous relation is belonging. Suppose
is ’s grade of membership (or strength)
in
. Then, belongs to
just in case
.
An important point to note is that all of the objects that belong to a fuzzy set need not have
a partial membership in that set. In fact, it could be the case that all of the objects that belong to a
fuzzy set have a strength of 1. In such a case, we say that the fuzzy set’s membership function is
a characteristic function, which is a such that
. But here are some more useful terms.
5
For contributions to this debate, see Gannett (2003), Millstein (2009; 2015), Barker and Velasco
(2013), and Stegenga (2014), among others.
6
For contributions to this debate, see Glasgow (2003), Kaplan and Winther (2014), Spencer
(2014), and Millstein (2015), among others.
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Suppose the support of
is the crisp set of all objects that belong to
7
Furthermore,
is empty
iff nothing belongs to it.
8
Finally, the cardinality of
is equal to
.
9
Now suppose we have a crisp set of fuzzy sets Then, a fuzzy set
is the union of all
members of just in case, (a) , (b) the object space of
is identical to the object space of
each member of , and (c) each
is identical to the maximum value among all strengths of
in each member of .
10
Next, suppose we have a finite, crisp set . Then, a crisp set is a fuzzy
K partition of just in case (i) each member of is a fuzzy set, (ii) each member of is non-
empty, (iii) , (iv) , (v) the support of the union of all members of equals
, and (vi) for any object that belongs to any member of , the sum of each grade of membership
that has in each member of is 1. Furthermore, let a member of a fuzzy K partition be a part.
11
Thus, an important point to remember is that a fuzzy K partition is itself a crisp set, but it’s called
‘fuzzy’ because its parts are all fuzzy sets.
Now suppose an object persists iff it exists at different times, an object perdures iff it
persists and it is only partially present at any time it exists, an object that perdures is a perduring
object, and a temporal part is any part of a perduring object that constitutes its partial presence
when it exists.
12
Now I am ready to define the K population.
3. The K Population
Let L be a sexually reproducing species that forms a lineage or a lineage of such species,
but not both.
13
For instance, L could be the species Pan troglodytes (the common chimp) or the
Pan genus (the common chimp and the bonobo).
14
Let be a crisp set of organisms that
constitutes all of the members of L at a time t. Now suppose that any member of has a genome
that consists of a sequence of distinct loci, with one or more alleles at each locus.
15
For instance,
if consists of diploid organisms, then each member of will usually have two alleles at each
locus. Now I will articulate how L can be subdivided into K populations. Let’s start with the
notion of a genomic ancestry partition.
Suppose a crisp genomic ancestry partition of is a fuzzy K partition of such that the
object space for each part in the partition is , each part in the partition is the temporal part of an
7
This definition is needed to articulate condition (v) in the definition of a fuzzy K partition.
8
This definition is needed to articulate condition (ii) in the definition of a fuzzy K partition.
9
This is really the sigma-count cardinality. But I’ll use ‘cardinality’ for convenience. Also, while
this definition is not needed to define a fuzzy K partition, it is needed to articulate the definition
of a K population.
10
This definition is needed to articulate condition (v) in the definition of a fuzzy K partition.
11
All fuzzy-set theoretic definitions are from Zadeh (1965) or Zimmermann (2012).
12
These definitions are from Lewis (1986, 202).
13
The point of defining L in this way is twofold. First, it ensures that members of the same K
population are conspecific. Second, it allows an entire species to be a K population.
14
For the phylogenetic evidence that both the common chimp and Pan form lineages, see Gonder
et al. (2011).
15
By an allele I mean any unique nucleic acid sequence at a locus. Furthermore, this is exactly
how population geneticists talk about alleles in the context of structure-like population structure
analysis. For evidence, see Pritchard et al. (2000) and Tang et al. (2005).
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isolated breeding group, each member’s degree of membership in each part is equal to the
proportion of its genome inherited from an organism in the breeding group that the part represents,
and each part’s membership function is a characteristic function. Also, it will be useful to call
each organism that belongs to a part in a crisp genomic ancestry partition an unmixed organism.
Now, suppose and are distinct crisp sets that constitute all of the members of at
distinct times and , respectively, and that occurs before . Also, suppose is the last time
before when L has a crisp genomic ancestry partition into K parts due to hybridization after .
Thus, hybridization could have begun at or at some time between and . Let be a crisp
genomic ancestry partition of into K parts. Then, a fuzzy genomic ancestry partition of into
K parts, call it , is a fuzzy K partition of such that the object space for each part in is ,
there is a one-to-one correspondence between and , each member’s degree of membership
in each part is equal to the proportion of its genome inherited from an organism that belongs to the
part in that corresponds to the part in under consideration or else an unmixed organism
descended from such an organism, and not every part’s membership function is a characteristic
function. Also, it will be useful to call any organism that belongs to a part in a fuzzy genomic
ancestry partition and has a grade of membership in that part in (0,1) a mixed organism.
For clarity, the hybridization model I am presupposing is the following:
(1) Isolated breeding groups undergo hybridization in such a way that none of the
groups involved become extinct.
(1) is one of three biological possibilities for hybridization between breeding groups. The second
and third are below:
(2) Isolated breeding groups undergo hybridization in such a way that all of the
groups involved become extinct.
(3) Isolated breeding groups undergo hybridization in such a way that some, but
not all, of the groups involved become extinct.
The fact that I am presupposing (1) as the hybridization model for K population theory will be
relevant to how K population theory avoids certain objections. In any case, let a genomic ancestry
partition be a crisp genomic ancestry partition or a fuzzy genomic ancestry partition. Now, I will
define K population parts, which are the temporal parts of K populations.
Suppose we call a part in a genomic ancestry partition a K population part (or KP part for
short). Thus, while KP parts must be indexed to at least one time, they need not exist at exactly
one time. Rather, KP parts can exist through time. Now I’m going to make some distinctions
among KP parts in order to define K populations as, roughly, sequences of KP parts through time.
Suppose
and
are KP parts. Then,
is an offspring of
and
is a parent of
iff
originated from a change in
’s object space or membership function. For instance, suppose at
time we have a fuzzy set of Hadza people that counts as a KP part of humans, call it ‘
’. Then,
at a later time a human dies but not a Hadza person. Also suppose that the latter event produces
a new KP part of humans, call it ‘
’, that has the same support and membership function as
.
Then, it is safe to say that
originated from changing the object space of
, and thus,
is an
offspring of
and
is a parent of
.
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Now, suppose two or more KP parts merge iff their offspring is their union, two or more
KP parts fuse iff they merge and they’re approximately equal in cardinality, and two or more KP
parts join iff they merge but do not fuse. Furthermore, let a parent with much lower cardinality in
a joining be a minor parent. Then, a KP beginning is any KP part that originated from its parent(s)
through hybridization, budding, splitting, or fusion. In contrast, a KP end is any KP part that has
no offspring after multiple generation times for its species, has offspring that arose from splitting,
has offspring that arose from fusion, or is a minor parent and has offspring that arose from joining.
We are finally in a position to define a K population.
(4) A K population is, essentially, a perduring object such that all of its temporal
parts are unique KP parts, its successive temporal parts are related as parent and
offspring, its first temporal part is a KP beginning, and it perdures until one of
its temporal parts is a KP end.
So, K populations are, roughly, perduring objects whose temporal parts are fuzzy sets of
conspecific organisms that cohere via common genomic ancestry. Here are some final terms that
will be useful for talking about K populations. First, an organism is a member of a K population
at a time iff it belongs to that K population’s temporal part at . Second, an organism’s grade of
membership in a K population at a time is equal to its grade of membership in that K population’s
temporal part at . Now that I have introduced what a K population is, we can turn to answering
whether population geneticists are actually referring to K populations when they call continent-
level human genetic clusters ‘populations’.
4. The Evidence for K Population Theory
There is plenty of evidence that population geneticists are referring to the K population
when they call continent-level human genetic clusters ‘populations’. But first, here’s some
clarification. The linguistic context in which continental population talk is used in population
genetics is population structure analysis that utilizes structure-like clustering algorithms.
Structure-like clustering algorithms (e.g. structure, frappe, admixture, etc.) attempt to infer
population structure in a group of organisms using an algorithm that searches for the fuzzy K
partition that maximizes allele frequency differences among parts using genotype data from the
organisms. Sometimes what’s investigated is the optimal partition into K parts, and other times
the task is to find the optimal partition at each K level. Suppose we call any population structure
analysis that uses a structure-like clustering algorithm ‘structure-like PSA’. Then, two examples
of structure-like PSA are Gonder et al.’s (2011) use of structure to identify the population structure
of chimpanzees, and Li et al.’s (2008) use of frappe to identify the population structure of humans.
If the continent-level human genetic clusters inferred in structure-like PSA are K
populations, then we can explain how population geneticists model, sample, talk, and otherwise
behave in structure-like PSA. With respect to modeling, the representations in the models used in
structure-like algorithms are what we would expect if the populations being inferred are K
populations.
For example, one important model assumption of structure-like algorithms is that
populations leave behind a genetic trail. This is because structure-like algorithms represent
populations as sequences of allele frequencies (Pritchard et al. 2000, 947; Tang et al. 2005, 290).
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However, K population theory predicts this model assumption nicely because the fact that K
populations leave behind a genetic trail in the form of a sequence of allele frequencies can be
derived from what a KP part is.
Second, K population theory explains why population geneticists sample in the way that
they do. For example, the widespread practice in fuzzy PSA of sampling “ancestry informative
markers” for cluster analysis suggests that what is being sought are genealogical groups, which K
populations are by definition (Tishkoff and Kidd 2004, S23, S25). In fact, one population
geneticist, Marcus Feldman (2010, 157), coined the term ‘ancestry group’ to talk about continent-
level human genetic clusters.
Third, K population theory predicts how population geneticists talk in fuzzy PSA. For
example, population geneticists have no problem saying that continent-level human genetic
clusters originated thousands of years ago, which would make little sense unless the clusters were
perduring objects, like K populations.
16
Finally, K population theory explains many other
behaviors of population geneticists in structure-like PSA that would otherwise be peculiar. For
one, K population theory explains why population geneticists check the accuracy of structure-like
algorithms in the way that they do. For example, Shringarpure and Xing (2014) tested the accuracy
of admixture’s population membership grade assignments by judging how well it predicted “the
proportion of YRI ancestry” in individuals of a fabricated admixed population.
17
Nevertheless, one objection is that K population theory is pointless because the actual
population concept being used here is inconsistent. For example, some population geneticists,
such as Feldman and Lewontin (2008, 81, 90), have no problem calling the continental clusters
both “geographical populations” and ‘ancestry groups’, while others, such as Weiss and Long
(2009, 709), are fine calling the clusters “geographic populations,” but find the ‘ancestry group’
label misleading.
While it is true that there is no consensus among population geneticists about how to define
‘population’ when using it to talk about continent-level human genetic clusters in structure-like
PSA, K population theory is not a project in conceptual analysis, it’s a theory about what
‘population’ refers to in a particular context. This project is compatible with there being
inconsistent beliefs about what ‘population’ means as long as we adopt a referential semantics for
‘population’. Yet another concern is that even if K population theory is right, it still remains to be
shown that the K population is a biological population. So to that I now turn.
5. Why K Populations are Biological Populations
Remember that biological populations must be, at the very least, groups that evolve. Thus,
if K populations are not, at least, groups that evolve, then the population geneticists who are
acknowledging continental populations in humans are using the word ‘population’ in a way that is
not helpful for evolutionary research. However, K populations are groups that evolve, and this
fact can be derived from the definition of a K population.
Suppose we have an arbitrary K population p and we want to know how it originated. By
definition, the first temporal part of p is a KP beginning. Furthermore, KP beginnings, by
definition, are offspring from one or more KP parts that are distinct from it. But for a KP part to
16
For an example, see Wang et al. (2007, 2060).
17
‘YRI’ is shorthand for ‘Yoruba Nigerians from Ibadan’.
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be an offspring it must be a modified version of its parent, either in its object space or membership
function. Thus, p will be a modified descendant the moment its first temporal part originates.
Nevertheless, it’s an empirical question whether p originated from another K population since the
KP part that p originated from could be a temporal part of a different kind of biological
population.
18
In any case, it’s easy to see how K populations form evolutionary networks.
6. Objections and Replies
There are a few objections that one could have with K population theory. First, in a recent
paper, Millstein (2015, 9-10) has offered some healthy skepticism about interpreting continent-
level human genetic clusters as biological populations. Millstein rightly points out that another
possible interpretation is that continent-level human genetic clusters are not populations, but are
just ancestry groups (in Feldman’s sense) of organisms descended from members of past
populations.
While Millstein’s suggestion is a plausible interpretation of some inferred clusters in
structure-like PSA, it’s not a plausible interpretation of continent-level human genetic clusters.
This is because the hybridization model that Millstein is using, which is (2), is not the model that
best fits how population geneticists talk about continental clusters. In order for Millstein’s model
to be correct, population geneticists would have to think that continent-level human genetic
clusters represent only past non-random mating structure. However, population geneticists
regularly talk about continent-level human genetic clusters as reflecting current non-random
mating structure. An example is below.
Each of the large population groups (the Sub-Saharan African farmers, Eurasia, and
East Asia) can be considered as a metapopulation consisting of populations with
some genetic exchange between them and with a common ancestry (Zhivotovsky
et al. 2003, 1183).
19
These authors do not sound like they’re just talking about past non-random mating structure. Of
course, this way of talking is easily explained if we accept that population geneticists intend
continental clusters to represent extant breeding groups. Furthermore, if that is true, then the
appropriate hybridization model is (1), not (2), which is the model used in K population theory.
For clarity, I am not saying that population geneticists are correct in using (1) to model
hybridization among continental groups of humans. All I am saying is that the hybridization model
that they are in fact using when they call continent-level human genetic clusters ‘populations’ is
(1). Second, both Millstein (2009, 269) and Peter Gildenhuys (2014, 434-437) have claimed
that a respectable notion of biological population must be able to explain how populations are
modeled in evolutionary dynamics. For instance, Millstein (2009, 269) claims that migration
modeling in population genetics (e.g. the source-sink model, the island model, etc.) requires that
migration amounts to organisms wholly leaving one population and wholly joining another
18
This quirk is intentional since it allows K populations to have evolved from a more primitive
kind of biological population.
19
See Zhivotovsky et al. (2003, 1174) for what they mean by “farmers.”
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population. However, since organisms are born into K populations in virtue of their genomic
ancestry, it’s hard to imagine how the members of K populations can migrate in the sense given
above.
This is a good concern. The members of K populations are indeed born into them. And
barring the extinction of one’s K population or one’s species, it’s impossible for a member of a K
population to leave her population. However, the latter is a concern only if one presupposes
“monism” about classifying individuals into biological populations, as Millstein (2015, 6) does.
20
However, if one does not presuppose monism, but rather, accepts the possibility of “population
pluralism”—which Stegenga (2014, 1) defines as the view that “there are many ways that a
particular grouping of individuals can be related such that the grouping satisfies the conditions
necessary for those individuals to evolve together”—then the fact that the members of K
populations don’t migrate is not a flaw.
21
Rather, it’s just an example of how classifying organisms
into K populations is not going to be useful in all research projects in population genetics.
In fact, Mishler and Brandon (1987, 401) would call K populations “historical entities”
because they’re essentially genealogical groups (e.g. monophyletic groups). Furthermore, because
they’re historical entities, they’re useful in history-oriented population-genetic research, such as
research on “the history of human migrations” and “human evolutionary history” (Rosenberg et
al. 2002, 2384; Rosenberg et al. 2005, 661).
22
7. Conclusion
In this paper, I have attempted to show that there is a legitimate metaphysical basis for
calling continent-level human genetic clusters ‘populations’. Namely, these groups could be
biological populations in virtue of being K populations. I defended my position by, first,
articulating a K population as, roughly, a biological population whose members are united by
genomic ancestry and population membership is graded. However, the precise definition was
given in (4). Next, I provided evidence that population geneticists are referring to the K population
in population structure analyses that use structure-like clustering algorithms. After this, I defended
K populations as authentic biological populations. Finally, I defended K population theory against
two objections.
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It’s worth noting that Millstein (2015, 6) considers her monism a “defeasible monism,” since
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