Tag Archives: variation

50 whys to look for genes: 17. Evolution = change of gene frequencies in populations

Biology textbooks usually define evolution as a change of gene frequencies in populations over time.  A change in the frequency of some observed trait over time might be related to changes in environmental conditions and reversed if those conditions revert to earlier levels.


Evolution could be defined as a change of trait frequencies in populations over time, leaving for investigation whether the change is reversible, accompanied by a change of gene frequencies, and so on. Continue reading

Depictions of human genetic relationships: Exploration 6

Exploration 6: Superimposing changes in genetic location on an ancestry diagram, a simulation

In the previous post, the depiction of a 2-D ancestry “fan” plus “aprons” allowed us to represent within group variation as well as branching.  Whereas in a branching diagram we sought to minimize the crossing over of branches because “they suggest that the two branches at a fork are further away from each other than to one of the earlier branches, which goes against the information contained in the sequence of branches” (see earlier post), with the inclusion of aprons that overlap we can embrace branches that cross over.  Consider the following simulation, which also allows for evolution along branches to happen at different rates.

In a branching process, each group breaks into two.  Imagine that the new groups are small so that by genetic drift, that is, by chance, all members end up with the same variant a some genetic locus (position on the genome), that is, this locus does not contribute genetic variation.  (See an analogy given in the wikipedia entry on genetic drift.)  The population eventually grows larger and genetic drift ceases to be significant.  Each of the new groups then represents a subset of the variation existing in their common ancestor group.  If we discount new mutations for now, none of the branched-off groups can have more genetic variation than groups from which they are descended.

The following diagram uses a random simulation to generate directions of branching and the distances of each branch from its most recent common ancestor.  The two dimensions stand for the genetic variation of the whole set of populations.  No aprons are drawn around the midpoints of the groups, but it should be noted that the variation of the original population spans a space five times as wide as the area shown in the diagram.

The following slide show builds up the messy web branching from one group (AR) to two (AB and NR), and so on, step by step.

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Of course, this is only a simulation.  The actual genetic data might yield a 2-D web that is quite different.  Nevertheless, in the next post, we add aprons to the simulation to complete a picture of similarity, diversity, and ancestry.

Depictions of human genetic relationships: Exploration 5

Exploration 5: Superimposing genetic variation on the ancestry diagram

The 2-D depiction in the previous post greatly improved (when compared with the original Tishkoff tree of human ancestry) the degree to which the distance between groups was proportional to the time since the groups shared a common ancestor.  (As already noted, we could adjust the depiction if we had a more refined analysis giving us data on different speeds of divergence from the common ancestor down different branches.)  The 2-D depiction cannot, however, eliminate spurious appearances of similarity.  Even if we put that objection aside for a moment, we need to note that the 2-D depiction still omits the genetic variation around the mid-point of any branch.

Two features of the original Tishkoff ancestry diagram gives us a whiff of variation around the mid-point of the branches: 1. the relative thickness of the branches—the thick trunk at the top indicates more genetic variation in the ancestral group than the think tips in the branches at the base; and 2. the density of the color of the branches—the deepest blue indicates more genetic variation than a lighter-shaded branch.  (Tishkoff and collaborators suggest that the migration out of Africa brought with it only a small subset of the genetic variation in the African ancestral branch from which it broke off.  The original population migrating out of Africa was, it seems, quite small.)

Although variation around the group’s midpoint is suggested by the preceding two features, the Tishkoff ancestry diagram does not in any way convey the fact that, on average, for any genetic locus roughly 85 % of the variation is within a population, 7 % is within a region, and only 6 % occurs among regions (using oft-cited figures from Lewontin 1973, subject to later refinement, but not, to my knowledge, qualitative revision).  To convey this, we can add “aprons” around the mid-points of the 2-D depiction.  In the following diagram aprons are added around groups A and H only.

The aprons are the same size because I can make the key point without exploring the available data to calibrate the apron size to match the different degrees of genetic variation within the groups ate the ends of the branches.  That point is that ancestry trees show the genetic mid-points of branches and thus mostly hide the large amount of genetic variation not captured by the branching pattern. Such variation makes it difficult, on the basis of a random selection of genetic loci, to assign an individual to one branch or the other. Difficult but not impossible; merely subject to more errors than to correct assignments. Random selection because clearly there must be some genetic differences that are specific to a branch in order for us to be able to trace ancestry patterns at all. If there are mutations that are very common in some people and rare in others, a tree can be made that captures the most likely branching pattern (i.e., one that assumes the least reversions, i.e, mutation in one direction, mutation back again to the original condition) even if most genes vary in ways that bear no sign of that branching.

Now, the 2-D fan diagram is far from perfect and I used a back of the envelope way of determining the size of the aprons, but the combination of the 2-D fan and aprons holds some promise for allowing simultaneously for similarity, diversity, and ancestry—the original question motivating this series of posts.  The next posts explore 2-D depictions further.


Lewontin, R. D. (1973). “The apportionment of human diversity.” Evolutionary Biology 6: 381-397.

Heritability, a technical term, can be visualized by non-specialists

Heritability is a technical term, which originated in agriculture before World War 2, that has no obvious relationship with the colloquial idea of a parent passing on genes to an offspring.  The technical meaning can be presented in a not-so-mathematical way and thus made accessible for non-specialists.  (That, in turn, makes it easier to speak clearly about the limitations of research on the heritability of human characteristics, but that is not a topic for this post.)

In the picture below, we imagine many genetically defined and reproducible varieties of, say, plants, raised in many locations.   (Genetically defined is easy to visualize if individuals of the variety are clones of each other, as they are when a plant is grown from a cutting of another plant.  It can also be thought of as genealogically defined, e.g., each individual is a grandchild of the same two pairs of grandparents.)

In each location multiple individuals—”replicates”—are raised.  The individuals in all the locations for all the varieties are all measured for, say, height, and there is variation among those measures—thus the different sized curly brackets below.

The average or mean height for each variety can be calculated and there is variation among those variety means.   Heritability is the ratio of variation among the variety means and the total variation across the whole data set.  That’s it.  Notice that heritability is derived from measurements of an observed trait; there has been no mention of genetic or environmental factors involved in producing the trait.

With humans, we can replicate a variety in the form of identical or fraternal twins, so, with only two individuals in each genetically defined variety, there will be many, many points in the diagram below for which there is no measured value.  That means that the estimate of heritability must be more approximate.

Taxonomy of heterogeneities

Contention motivating this taxonomizing: Research as well as the application of knowledge resulting from research are untroubled by heterogeneity to the extent that populations are well controlled. Such control can only be established and maintained with considerable effort or social infrastructure, which invites attention to possibilities for participation instead of control of human subjects.

The taxonomizing is an incomplete work in progress; comments welcome.

Kinds of heterogeneity

Static 1. There is an assortment, each a separate type (“cabinet of curiosities”)
or 2. Mixture of types (e.g., allelic heterogeneity & locus heterogeneity in genetics)
Variational 3. Trait = composite of types (analogy: the 3 components of a triathalon)
4. There is variation, not types
5. Variation in a set of traits involves a composite of variance/covariance structures (statistical heterogeneity)
6. When similar responses of different individual (e.g., genetic) types are observed, it is not necessarily the case that similar conjunctions of risk or protective factors have been involved in producing those responses (=possibility of “underlying heterogeneity”)
Dynamic 7. Variation produces qualitative changes in results from standard theory based on uniform units (e.g., theory about Malthusian population growth, tragedy of the commons, prisoner’s dilemma)
8. “Unruly complexity,” which arises whenever there is ongoing change in the structure of situations that have built up over time from heterogeneous components and are embedded or situated within wider dynamics. (Synonym: “intersecting processes”)
8a. In heterogeneous construction researchers establish knowledge and technological reliability through practices that are developed through diverse and often modest practical choices. This is the same as saying they are involved in contingent and on-going mobilizing of diverse materials, tools, people, and other resources into webs of interconnected resources.
Dynamic-participatory 9. Multiple points of engagement allow for participatory restructuring of unruly complexity or heterogeneous construction
10. Participatory restructuring, which occurs in tension with deployment or withholding of trans-local knowledge and resources.

Actions corresponding to each kind of heterogeneity

including the control (C) that allows one not to be troubled by the heterogeneity and possibilities for participation (P)

1. Question [P] (or suppress the question [C]) about why this assortment has been collected into one list.
2. In medical sociology Brown & Harris find common meaning despite different types of experience (through coding of sameness despite surface heterogeneity).
3. Disaggregate/decompose into separate phenomena
4. C: Make people fit types (stereotyping, panopticon, screening & surveillance, public health measures, diagnostic manuals, reassignment surgery…) Control/ignore non-conformers.
6. C: Look for subclasses in which underlying factors are uniform. If found, use to probe or extrapolate (perhaps unsuccessfully) back to other subclasses.
8. Diagramming of intersecting processes, which exposes multiple points of engagement->8a
8a. Mapping by researchers of situations and situatedness [P]
9. Well-facilitated participatory processes


Taylor, P. J. (2005). Unruly Complexity: Ecology, Interpretation, Engagement. Chicago, University of Chicago Press.
Taylor, P. J. (2009). “Infrastructure and Scaffolding: Interpretation and Change of Research Involving Human Genetic Information.” Science as Culture, 18(4):435-459.
Taylor, P. J. (2010). “Three puzzles and eight gaps: What heritability studies and critical commentaries have not paid enough attention to.” Biology & Philosophy, 25:1-31. (DOI 10.1007/s10539-009-9174-x).

2. Taylor 2009
6. Taylor 2010
7. Taylor 2005
8. Taylor 2005
9. Taylor 2005
10. Taylor 2009

“Race: A Social Construct or a Scientific Reality?”

Discussion on WUMB Commonwealth Journal  based on new exhibit at the Boston Museum of Science exhibit, Race: Are we so different?

Broadcast on Sunday February 13, 2011.  Speakers: Peter Taylor, Nina Nolan, Chair, RACE Education Team, Boston Museum of Science, and WUMB host, Janis Pryor. Click here to listen to  Podcast.

Afterthoughts on the discussion:

1.  The host did well to launch us into the discussion without precirculation of questions.  The broadcast ended up cutting out only about 5 minutes of the recorded discussion.

2. I was cast as the scientist who would supply the definitive answers about the biological (genetic) basis of race, as if the answer to the rhetorical question in the title given to the broadcast was there’s no scientific reality to race (with the implication that those who say there is are part of the longstanding, historically given problem of racism in the USA).

3. I tried to take the role of someone who was informed by the science, but wanted all listeners to be able to think about the complexities of the issues around race.

4. One of these issues is helping people who think it’s plausible that average differences in, say, IQ test scores, among social/racial groups could be explained by genetic differences see the problems in supporting such an idea with evidence.

5. Another of the issues is the fact that, even if races are defined by (shifting unreliable) social definitions, the experience of living with such definitions can have a significant impact on one’s biology and psychology–that is, it becomes a scientific reality in another sense.

6. I tried to do #4 on the radio and they didn’t edit it out, but visual aids would have helped and even then I need more practice if the take-home point is to come across.  #5 isn’t so hard to convey, but I didn’t get into countering the rejoinders that hypothesize that average differences in susceptibility to illness among social/racial groups could be explained by genetic differences.

7. Re: the passage at the end where I try to speak of the cost of a racially divided society even to those that benefit from it, I need to keep working on how to express this to have impact (and not seem to discount the far greater costs to minorities).

Comments welcome.

Troubled by Heterogeneity? Opportunities for Fresh Views on Long-standing and Recent Issues in Biology and Biomedicine

“Troubled by Heterogeneity? Opportunities for Fresh Views on Long-standing and Recent Issues in Biology and Biomedicine,” was a talk I gave on 13 Oct. ’10 (abstract). I sketched a number of cases to get the audience thinking about my underlying contention that research and application of knowledge resulting from research are untroubled by heterogeneity to the extent that populations are well controlled. Such control can only be established and maintained with considerable effort or social infrastructure, which invites attention to possibilities for participation instead of control of human subjects.

The pdf of the slides and the audio recording are downloadable. (By noticing when my voice rises in volume, which is when I approach the laptop, you can guess when I am clicking from one slide to the next.) Some of the sketches of cases have been addressed in previous posts (see links on the abstract). This blog post consists of some afterthoughts, including questions needing more thought, in response to discussion after the talk.

1. What am I saying researchers should do?

The contention underlying the talk (above) is at first descriptive. But it does assume that heterogeneity (of various types) is ubiquitous and is often not paid attention to. The title suggests that researchers could be troubled by heterogeneity. But what should they do? Given that my framework incorporates a social level of explanation, what should they change first—their thinking and methods, or the social situations that enable the knowledge they arrive at to become significant (including, to be implemented in policy and associated practice)? What would be their motivation for changing?—To get a better view of the world (one that applies in a wider range of circumstances)? Or because there is a cost in controlling populations (maintaining infrastructure, etc.)? Or because that control breaks down, especially in crises?

2. Varieties of heterogeneity

My exploration of heterogeneity in biology and biomedicine took off after I saw the overlooked significance of underlying heterogeneity in heritability studies. Most of the cases in the talk, however, revolved around a simpler form of heterogeneity, namely, variation around a mean. Should I—for expository and/or conceptual reasons—focus separately on the different kinds of heterogeneity. I have an evolving taxonomy of heterogeneities, http://sicw.wikispaces.umb.edu/heterogeneities.

3. Personalized medicine

The figure I used to discuss the issue of misclassification lacked a crucial element—a cut off point between OK and not OK medical outcomes.

Genetic condition
Medical treatment A B
1 (not treated because not sick) OK OK
2 treated (with say drug X) OK result Not OK

4. Isn’t simplification of complexity sometimes/often/always necessary for scientific progress? After researchers get a handle on the simplified situation, they add back variables that they had previous controlled.

Sometimes researchers add back variables; sometimes they continue to engineer the world so the control over those variables is maintained. They may come to see the world the same way as they control it and need ways to be reminded early and often of what has been left out. This is especially so regarding ecological complexity, where variables left out have dynamics of their own that interact with the variables in focus. Chapter 1B of my book, Unruly Complexity (U. Chicago Press, 2005), illustrates the problem of “apparent interactions” that arise. Indeed, I have come to see the “simplification is necessary for science” line as a way to define out of science many situations that deserve systematic study. What do philosophers and theoreticians think about getting to know situations that, from the start, are not amenable to control or are not the same thing if they are carved out from the whole?


Fresh perspectives can be brought to modern understandings of heredity and life-course development by examining the relationship between control and variation, particularity, or, more generally, heterogeneity. Broadly speaking, my contention is that research and application of resulting knowledge are untroubled by heterogeneity to the extent that populations are well controlled. Such control can only be established and maintained with considerable effort or social infrastructure, which invites attention to possibilities for participation instead of control of human subjects. Building on several recent publications of mine on heterogeneity and heritability, I explain why underlying heterogeneity warrants the attention of quantitative geneticists and critical commentators on nature-nurture debates (see post). I elaborate on my contention through brief sketches of cases from biomedicine, involving: genetic testing; gene-environment interaction; personalized medicine; IQ scores; racial-group membership; and life events and difficulties research. My goal is to stimulate wider exploration of heterogeneity and control in relation to biological and social theories and practice.