Monthly Archives: October 2008

Social Network Analysis

Halloween and Social Capital

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Once again, I am simply blown away by the participation rate in my kids' school Halloween parade this year.  In a school of around 500 students, I'd say 98%+ wore a costume today for the Halloween parade.  A substantial fraction of the parents wear something, even if just a silly hat, as well.  Based on my experience growing up on the North Shore of Boston, each year I find this phenomenon hard to fathom.  When I was in school, maybe 10% of kids would come to school in costume.  I suppose that this could just be revealing period differences and (yet again) the fact that I'm not as young as I once was.  However, I think it's something different. 

Palo Alto is a very affluent, highly educated, community.  Parents are amazingly involved in school.  In fact, coming to Palo Alto has given me tremendous insight into the travesty that is American educational disparity.  Why is it that Palo Alto has such a great school system?  I'm sure that dedicated teachers and competent administration plays a major role.  But there is also the fact that so many parents give a lot of time and money to the school.  When our son was in kindergarten, at least two parents volunteered in the classroom each day.  They did all the busy work that goes along with teaching kids to read -- getting appropriate level send-home books into kids' backpacks every day, checking back in the read books, etc. -- allowing the professional teacher to, well, teach.  When a class is having a party and the teacher sends around an email to the parents asking for help, all the needs are taken care of within a day.  "I'll bring cupcakes." "Oh, I can bring mini sandwiches." "Can anyone come and help ladle punch?" "Oh sure, I can do that!" You get the idea.  It's also not hard to imagine when this is lacking (because parents don't have the luxury of participating because they are working multiple jobs to stay afloat or a large fraction of kids only have one parent or kids don't have a neighborhood connection to their school or because violence and apathy make school a frightening place or because parents collectively put their material desires above the needs of their children or communities), teachers have to spend much more time doing drudgery.  Probably all but the most energetic and dedicated scrimp.  Kids and school districts suffer.  

We are very lucky here.

My hypothesis is that participation rates in Halloween parades is a marker of social capital.  This is the concept popularized by Robert Putnam's terrific book, Bowling Alone , in which social relationships are strengthened by shared civic or other community experience. Such ideas go back to Merton and functionalist social analysis. Bowling has the manifest function of being an enjoyable way to pass the time.  It's latent function though is building community by strengthening social capital. Social capital takes on a more explicity instrumental form in Bourdieu's (and others') notion that it is the sum of social resources that an individual can call upon to accomplish social ends.

Coming to school in a costume takes effort.  It takes parental cooperation.  It means buying or making a costume.  It means, if you're a kid, taking the risk that other kids might make fun of you (of course, if enough kids do dress up, then you might get made fun of if you don't dress up, but that's another story).  It typically means that parents (at least one, though I'm always blown away by the number of couples there) have to commit to come watch the whole spectacle.  My Stanford colleagues Rebecca and Doug Bird have done a bunch of terrific work on the role of costly signaling in mediating social roles, particularly where fluid status hierarchies are involved. Costly signals are honest signals because they are harder to fake.  When men do difficult and dangerous things (like hunt large game), they send a signal of their quality.  This aids them in securing political allies among other men and mates among women.  When men or women share food widely, they signal their good citizenship and probably make it more likely that others will share with them at some later date. For a nice discussion of these and other aspects of signaling theory in Anthropology, see Rebecca's (2005) paper with Eric Smith on the topic.

So, here we are in affluent Palo Alto, where 98% of kids, nearly all the teachers and administrators, and a large fraction of their parents participate in an annual (costly) ritual that strengthens community bonds and signals the health of civic engagement and our collective investment in the future.  One can only imagine the types of returns our kids will receive on the social capital thus accrued. This raises major questions about society, democracy, the future.  Is strong social capital really necessary for a functioning democracy, as Putnam argues?  What are the effects of such collective social expressions on the world views of  developing minds?  What are the consequences for developing minds of not experiencing such expressions of community?  How can we enable the formation of social capital in communities for whom the deck is less positively stacked? 

Statistics

Truly Excellent Statistical Graphic

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The figure that appeared on MediaCurves.com (the link to which I found here) following the second presidential debate last night was a truly outstanding example of communicating complex information using simple, effective graphical presentation.

The figure shows the responses of 1004 respondents to the question of who won the debate.  The graphic summarizes quite a bit of information in a readily understandable manner.  What I find particularly striking is (1) 20% of self-reported Republicans think that Barack Obama won and (2) only 68% of self-reported Republicans think that John McCain won.

Not necessarily related to statistical graphics, it will be interesting to see if Nate Silver is as good at predicting presidential elections as he is at predicting baseball outcomes.

Biofuels, Diet & Nutrition

Biofuels and Water Use

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An opinion piece in the IHT this morning raises the important point that stepped up biofuel production may tax already strained world fresh water supplies.  Peter Brabeck-Letmathe, chairman and former chief executive of Nestlé, suggests that if world biofuel production targets are met, water withdrawals for agriculture can increase by as much as one-third.  Brabeck-Letmathe writes,

Seventy percent of all water withdrawal is already used in agriculture, and while all such activity requires water, growing enough soy or corn to create biofuels is especially water-intensive. For example, to produce just one gallon of diesel fuel up to 9,000 gallons of water are required. Up to 4,000 gallons are needed to produce enough corn for the same amount of ethanol. By way of contrast, producing enough food to meet the caloric needs of one person for one day in, for example, Tunisia or Egypt requires about 666 gallons of water, and twice as much in California (caloric needs and intakes vary widely from region to region due to dietary customs).

This is bad news considering that it is projected that by 2035, one third of the world (over three billion people) will be facing severe water stress.  Even without the increased water pressure of extensive biofuel production, water usage will need to increase substantially in order to feed the world by the middle of the century.

These are the sort of issues that we need to take seriously before plunging headlong into a world where we grow the fuel that drives American (and, increasingly, Chinese) SUVs.

Demography, Evolution

Gadgil & Bossert (1970)

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I am currently teaching a class entitled "Demography and Life History Theory."  For this class, we read the classic paper by Madhav Gadgil and Bill Bossert, "Life Historical Consequences of Natural Selection." In preparing for class, I re-read this paper for about the twelfth time.  Something happened this time.  It really dawned on me what a spectacularly important paper this is.  Just about every important theme in life history theory is addressed in this paper and the analyses remain remarkably relevant.

One of the fundamental ideas this paper brought to life history theory is thinking about the convexity of the functions that describe both the fitness benefits and costs associated with the degree of reproductive effort.  In particular, Gadgil & Bossert show that iteroparity (i.e., repeated breeding) can only evolve if the function relating benefit to effort is concave or the function relating cost to effort is convex.  The figure shows a concave profit function and a linear cost.  Clearly, the maximal value of the difference between the profit and cost happens at some intermediate level of effort \theta_j.

Profit (solid line) and cost (dashed line) as a function of reproductive effort at at age j.

Maddeningly, Gadgil & Bossert invert the terms "convex" and "concave."  I'm sure there is a good historical explanation for this, but contemporary usage indicates that a continuous, twice differentiable function f(\theta) is convex if f''(\theta)>0.  That is a convex function shows increasing marginal returns to effort, whereas a concave function shows diminishing marginal returns to effort.

Their analysis focuses on a discrete-time form of Lotka's characterisitc equation:

1 = \sum_0^n e^{-mx} l_x b_x

where m is the Maulthusian parameter (the intrinsic rate of increase, r, in a density-independent population), l_x is the fraction surviving to age x, b_x is the birth rate (in daughters) to females age x.

What makes this approach so interesting and important is that the vital rates are functions of reproductive effort \theta_x at each age.  In addition to l_x and b_x being  functions of effort, they are also functions of "satisfaction" \psi_x, a measure of environmental quality.  Fertility at age x increases with effort and satisfaction.  Survivorship and growth decrease with effort and increase with satisfaction.  Fertility also increases with body size.

Gadgil and Bossert then maximize m subject to the biological constraints on intrinsic mortality, growth rate, and initial size, and the environmental constraints of satisfaction and mortality due to predation. They used an automatic computer to numerically solve their optimization problem.  They derive a number of quite general results for age-structured populations.

  1. Only when the profit function is concave or the cost function is convex can repeated breeding be optimal.
  2. Reproductive effort increases with age in repeated breeders.  George Williams arrived at a similar conclusion in 1966, but failed to consider the possibility that the fitness profit could decline with age.  Gadgil & Bossert arrive at this result with a much more general approach than that used by Williams.
  3. When mortality increases following some age j, reproductive effort increases for ages less than j.
  4. When reproductive potential increases slowly with size, reproductive effort will be lower at maturity, rise with age, and growth will continue beyond maturity.
  5. A uniform change in mortality -- affecting all ages equally -- will have no direct impact on reproductive effort.
  6. If the population is resource-limited, such a uniform change in mortality will increase satisfaction \psi_j with its consequent effects, including a lowering of age at first breeding and increase in reproductive effort.

I would have to say that this is the desert island paper for life history theory.  If you only ever read one paper (conditional on having the mathematics background to make it worthwhile), this is the one to read, even after 38 years.