Bioblog is now on vacation. Thanks to those reading, and check back in mid-August, when I will return.

Is mathematics an emergent property of sociality? I posed this intriguing question to a mathematician colleague, who is also an evolutionary biologist, and he said yes. The question came up because I have argued that rules are actually a social construct; a solitary species needs few or no rules governing its interactions with other individuals of its species, because other than mating or occasional territorial conflict, it has almost none. Individuals in social species, by contrast, are completely dependent on rules to survive and reproduce, because interactions with other members of the species are constant, and determine standing within a social group, and thus generally reproductive success.

Most evolutionary arguments applied to humans are tenuous, because of cultural complexities that overly our basic biology. Complicating the picture further, aberrant behavior (that which does not comply to a given social norm) is also probably more common among humans than among other social animals, because 1) we have chemical treatments that suppress some symptoms of such conditions, 2) we have easy access to addictive products which our brains did not evolve to cope with, such as drugs, junk food, slot machines, etc., and use of these can lead to self-destructive behavior, and 3) many aberrant people are smart enough to overcome or disguise their problems enough to fit in somewhat. So, there are many ways in which humans seem to get away with behaving in socially maladaptive ways, without suffering reproductive consequences, as other social primates probably would.

However, we did evolve as a social species, and much of our behavior is indeed a legacy of that evolutionary history. The playing of games is an example. Games are all about rules. Kids love learning new games, because their brains are wired to learn rules -- particularly rules for navigating in real society, but an artificial society with artificial rules will do. Whether it is sports or war games or pin-the-tail-on-the-donkey, humans love games. Games with complex rules are more fun to learn for many of us, but those with fairly simple rules but complex strategy, such as Go or hearts or chess, usually capture the most active minds. It is our love of rules that make us despise the referee who makes a bad call. In our minds, if a rule is broken, the entire game should be void.

It seems that mathematics is universal, a truth that existed before humans and that they discovered. But to humans at least, mathematics is also all about rules, and perhaps the way that we perceive mathematics is filtered through our obsession with rules. We all learned them at the beginning of every school year for a decade. "Addition and multiplication are commutative. The transitive property says that if a=b and b=c, then a=c. The distributive property says that a * (b + c) = a * b + a * c" and so on. If you take higher level math classes in college, you discover that there are other mathematical systems with different rules; for instance, matrix multiplication is not commutative. So math is indeed a world of many rules that apply one way in one context but another way in a different context, very much like the rules of social interactions -- for example, it is inappropriate to wear a bikini at the opera, but just fine at the beach.

Although many would protest the truth of the statement, humans are wired for math. (If you hate math, it is not that you are "no good" at it; it is because the way it was taught to you made it painful and boring. This is a persistent problem that will likely never be corrected on a large scale, because of the vicious cycle of elementary school teachers who dislike math and barely get through it in college, go on to teach it poorly, cause their students to dislike it, and so on.) The interesting question is, would, or could, an intelligent solitary species have developed math? Some would say the question is completely moot because only a social species would have evolved brains as large as ours, because sociality requires a larger brain to navigate the intricacies of social interactions, in addition to the basic needs of finding food and mates and defending oneself. It is perhaps a chicken-and-egg question. But what is no question is that complex rules govern sociality, human brains are therefore wired to learn and use rules, and mathematics is a system of rules. Mathematics, very much like religion, is likely a byproduct of our success as a social species.

Labels: brain, evolution, humans, mathematics, sociality

Isn't parenthood supposed to be about raising a kid to be a healthy, happy, independently functioning, contributing member of society? These distorted, egocentric days in Yuppieville, it seems instead to be all about the reproductive process, rather than a far-off endpoint, that bolsters the parent's self esteem. All the issues surrounding having kids -- when, how, and not to mention whether -- focus on the parents' wants and needs, as if they were choosing the car which best projects their self-image.

Here's a woman who, after struggling with health problems that threatened her ability to get pregnant, was able to give birth to a healthy boy at age 40. One would think she would feel extremely fortunate. Instead:

"I had my sense of self-worth tied up with having a 'normal' family," Deborah explained. "You know, the family with two children. It was always this destination to be counted upon. It was what made tolerable all the losses along the way, the surgeries, the ostomy bags, everything. So when this path felt threatened, all those other losses suddenly took on more substance."

...days before the process was to begin, she found herself lying awake nights, frantic over whether she was doing the right thing. "What gets to me is that the three of them would be genetically related," she said, "and I would be the one. . . . It's not about passing on my genes. It's that I don't want to be an outsider in my own family. I don't want to feel less legitimate in my child's eyes."

If not sharing genes somehow makes this woman an "outsider in my own family," than clearly it is about passing on genes. In one sense this woman cannot help but feel this way. She wanted to adopt a second child, but her husband, who claimed he didn't have enough time to spend with the son they already have, insisted that the next child must share his genes. These people are both trapped into their views of what is "normal" reproductively. Do they put as much thought into actually raising these kids?

Before starting our donor cycle, my husband and I met once with a social worker, a standard requirement for couples using donor eggs -- though, again, not for those using donor sperm. Her job wasn't to screen us (she did, after all, work for the clinic and had little incentive to reject anyone) but to help us imagine how the genetic asymmetry might play out.

Do you know why it is not required for sperm donation? Because most men do not freak out about using donors the way that women do (excepting the jerk above who obviously thought his manhood was in jepoardy if the child was not his genetically). Using donated sperm has been common for much longer, so maybe it is just a lag in how used we are to these technologies. But in general, it is women who seem to obsess over these issues, and read deep significance into every possible stage of the reproductive process. One of the most absurd examples I have encountered was a remark made by a woman who had given birth recently by emergency cesarean section. Referring to my own c-section, I was corrected by her: "You should say 'cesarean birth' so that it affirms that you gave birth to the baby." I could only stare open-mouthed. I hauled my kid around in my guts for nine months (most of which time her presence made me miserable), and this woman actually thinks that someone out there thinks I did not really give birth because the baby didn't exit through my vagina? She was in me, and then came out. Even it had been through my nose, I would certainly define that as "birth."

But in a sense perhaps the woman was right. She either said what she did because she is pathetically insecure, or because in her mind a vaginal birth was somehow superior or more valid. My own doctor was needlessly apologetic when he informed me of the necessity of my having a cesarean. I read a parent magazine article that actually discussed making the choice to attempt a vaginal birth of a breech baby as if it were a positive thing.

It is not convincing to suggest that safety due to protection from surgery is an adequate reason for making such a choice. In a western hospital, complications from a cesarean are not much more common than those from vaginal birth. From the baby's perspective, however, it is significantly more dangerous. I am close to someone who was a breech delivery, and became slightly brain-damaged as a result of being choked by her own umbilical cord. Why any mother would put her own desires (this does not include maternal health risks, which are a separate issue) above what is safest for the baby is beyond me. But such desires have fed the growing popularity of giving birth at home (also promoted by articles in the same magazine), and underwater in birthing tubs.

The egg donor article continues:

"People see a child in a supermarket checkout line and almost reflexively make some comment about who he looks like or doesn't look like," said Robert Nachtigall, an adjunct clinical professor of obstetrics, gynecology and reproductive sciences at the University of California, San Francisco and a co-author of the paper. "We interpret it as a kind of shorthand by which people validate the child's position in the family, in society, by basically making comments that refer to the blood relationship that must exist between the child and his or her parents. The problem for people who have conceived with donor gametes is that they know it's not true. And the dilemma for them is how to respond, if at all."...The difference is that there's widespread cultural support for adoption in a way there isn't for donor conception.

So we are supposed to have special sympathy for those who make the choice to spend $40,000 on an ovum rather than a child? Why is it anyone's business in the first place? What happened to smiling and nodding politely? The answer is that they want to make it everyone's business because they have a bizarre need to have their choice "validated" by strangers. If the process of reproduction affects the child's "position in the family, in society" it is a self-fulfilling prophecy caused by constant parental worry. Plenty of adoptive parents have a good laugh when well meaning strangers remark on how their child resembles them. It happens all the time.

Resemblance talk did something else, too: although emphatic that it didn't change their love for their child, mothers said it was a constant reminder of their own infertility.

Granted, there certainly is something biological in people's obsession with fertility. After all, if we did not prefer to raise our own genetic child to raising someone else's, our genes would not get very far. Women may be more easily obsessed with reproduction than men because their investment in children is nearly always much larger than men's (the sole exception being a stay-at-home father of an adopted child). But humans have transcended a lot of base biological urges culturally. Killing is illegal among humans because with our rational brains we can project consequences, and we raise ourselves to a moral standard above what we grant to other animals. Humans also have other ways of leaving a legacy than simply by reproduction. As Stephen Sondheim once pointed out, we gain our immortality through both "children and art." Or an invention. Or a business. A strong biological urge to reproduce genetically should be tempered by the rational knowledge that the successful upbringing of a contributing member of society, carrying our heritage, is more important than whether he or she carries our genes. There are millions of adoptive parents out there who know that their kids are their kids, no matter who gave birth to them. How many abandoned mothers refer to their absent children's fathers as "sperm donors"? How many people want to disown their own rotten (but genetically related) kids?

These angst-ridden women who dwell on such superficial issues should get over themselves, but the truth is that most will not. What we should be concerned about is not how complicated genetic relationships will "play out," but rather that such self-absorbed women are raising kids at all, and for what purpose.

Labels: gender, genetics, health, humans

What is a patient to do? The available medical treatments for every condition or disease under the sun appears to be growing exponentially for those of us fortunate enough to live in a prosperous country such as the United States. Paradoxically, one of the causes for our skyrocketing health insurance costs is the continuing appearance of new procedures, tests, and drugs which are supposed to improve our health, but have the side effect of squeezing many Americans out of health insurance altogether.

Those of us who have the dilemma of choice about our health care should indeed be grateful, but the security of health insurance can be quickly overrun with confusion and stress about health care decisions, which are increasingly made by patients rather than doctors. In this age of ever new technologies and drugs, a primary care physician cannot hope to be up to speed on all the remedies available for all diseases and conditions, even those which do not require a specialist. Even doctors that try to keep up must sort through a medical literature that is sloppy and misrepresented.

An example of this is in prenatal care. An OB/GYN provides a dizzying array of tests and procedures for those concerned about the health of their unborn children, while often not having the time to fully understand the implications for your decision-making of the tests that they offer. The blood test known as the "triple test" or "triple screen," seems now to be a prenatal standard. The test detects levels of three maternal blood components whose quantities vary in a way that correlates somewhat with the condition known as Down Syndrome (DS), in which a person has an extra copy of chromosome 21 (which causes many varied mental and physical impairments). The older the mother, the more likely that DS will occur (although a small proportion of cases do come from the father). For example, the risk of DS is roughly 1 in 365 for a 35-year-old mother, versus 1 in 120 for a 40-year-old mother (reports of these proportions vary depending on the data source).

In the best case scenario, the triple test will be offered with the doctor making clear that its variability results in both false positive results (5-10%), in which the test will indicate Down Syndrome when the baby is normal, and false negative results (10-15%), in which the test will indicate a normal baby when it actually does have DS. Unfortunately, most people - especially average patients, and often even the doctors themselves - do not know how to weigh these probabilities, and therefore do not truly understand what the test is telling them. When a patient has the triple screen done simply as a matter of routine, or because the doctor suggested it, but has not yet decided whether or not to undergo amniocentesis (the only definitive prenatal screen for several birth defects including DS), or whether or not to continue a pregnancy with an affected fetus, a false positive result can add a lot of stress to the already stressful condition of pregnancy itself.

Fortunately, one can calculate the various probabilities implied by the different possible test results using a probability tree, and make a truly informed decision about whether to have the test done or not. In the figure below are example calculations for both a 35-year-old and 40-year-old mother. Note that the numbers are probabilities, rather than percentages (.9975 = 99.75%). (Click to enlarge in a new window.)



Because the false positive rate is so high for this test (I used the conservative end of the scale for these calculations), every woman doing this test should decide before getting the results back what she will do if they are positive. If she is unwilling to do amniocentesis under any circumstances, she should not get this test because it could create undue stress if returning positive. If she is willing to do amniocentesis (bearing in mind that the procedure carries its own probabilities of miscarriage, from .5%-2%), she should decide if a negative result would be satisfying enough to her to then choose not to do amniocentesis. If certain knowledge is paramount above all, women would be wise not to waste time and money with the blood test, and simply go ahead with amniocentesis.

It is tempting of course to do the test to reassure oneself that everything is normal, but a negative result does not completely rule out Down Syndrome, although it greatly reduces the probability. Another caveat is to note that all of these probabilities are estimates. False negative and positive rates vary with exact stage of the pregnancy, and different data sources give slightly different probabilities for DS based on age.

In a perfect world, every obstetrician would have a chart in his or her office with the probabilities of a Down baby based on age and the positive or negative results of the triple screen. Based on my own anecdotal evidence, they do not, and are thus unable to fully advise patients on the implications of this test.

It is difficult to navigate the world of medical decisions these days, but a little research on potential tests and procedures is worth the time. Do not expect your doctor to anticipate all the implications of your test results, with any test. A doctor's failure to do so, however, does not make him or her a bad doctor, just a busy person like you who does not have time to grasp the nuances of every medical treatment or test available.

Labels: health, humans, statistics

Biological control of pest species has come under a lot of criticism in recent years. Employed by governments and private businesses since the late 1800's, the practice was largely unregulated until the 1980's, and regulation remains varied and complicated among different countries, and different states within the U.S.

Classical biological control specifically refers to the importation of an alien species to control pests that are usually aliens themselves. Traditionally, it has been employed in agricultural systems, in which the alien pest arrived in its new location accidentally. More recently, classical biocontrol has been undertaken to control pests in natural systems, which in the case of plants, were usually intentionally introduced through horticulture trade of botanical gardens. It is currently viewed by many ecologists as a critical tool in the battle against invasive alien species, which are growing into an ever larger economic and ecological problem.

The recent criticism of biocontrol has focused on the likelihood of "non-target" attacks, which occur when the introduced agent feeds on unintended prey or plant species, including natives. This is an especially important problem in areas with many endemic species - in the U.S., the states most affected are Hawai`i, California, and Florida because of their high native species diversity. The concern about non-target attacks is excessive, in the opinion of most biocontrol practitioners, including Messing and Wright (2006), who describe a scenario in which the peril to Hawai`i's agriculture and ecosystems is being increased by a bureaucracy that will not allow alien biocontrol agents to be imported, even to combat serious economic and ecological pests in Hawai`i that are contributing to the destruction of native ecosystems.

Certainly their concern for the native species of Hawaii is not misplaced. Invasive alien plants such as thorny blackberry crowd out natives and are less likely to be eaten by foraging alien herbivores such as pigs and goats. Generalist insects such as the two-spotted leafhopper consume hundreds of native plant species which have no natural defenses against the aliens feeding on them. So it does seem unreasonable that Hawai`i is so stingy with its species importation permits, when researchers do their best to show that their biological control agents will not feed on any native species. (I know both of the authors personally, and can verify that they are stringent in their criteria for potential non-target interactions.)

The problem with Messing and Wright's paper is the same problem with most discussions debating the use of biological control in the scientific literature, at conferences, and in online discussions. While we are focusing much energy and attention on predicting non-target interactions, which in many biocontrol programs has thus been adequately addressed, there is almost no discussion about doing a better job of predicting whether or not the introduced agent will actually be effective once introduced.

Messing and Wright themselves toss out that only 16% of effective biological control programs have been effective at controlling the target, and yet later in the paper complain about their inability to introduce agents, which is based on the assumption that the introduced agents will actually work. The high probability that (based on current practices) they will not work is never addressed in their paper. Twice the number of effective biocontrol agents, or around 33% actually establish -- probably an underestimate, since follow-up generally does not extend for years, and those that are not actively controlling the target could be missed early in monitoring -- and rarely has any follow-up been done to understand their role in the native ecosystems. If they are not attacking non-targets, and they are not controlling the pest, how are they interacting with native species?

It is true, as Messing and Wright point out, that in the current modern age of regulation, non-target effects have greatly decreased. But it is also true that even in the case where a known specialist was introduced, there can be indirect food web effects discovered when people have taken the trouble to look, which they rarely do. In one case (Willis and Memmott 2005), a native parasitoid attacking an specialist insect herbivore introduced to control an alien weed increased greatly in numbers and thus made native herbivores much more susceptible to attack, upsetting the food web in the system.

Effective biological control programs are indeed cost-effective, but a lot of money is spent for many years on the assessment of a single agent, and are we getting our money's worth if only 1 in 6 actually work? A whole new science may need to be developed to further our ability to predict the effectiveness of biological control agents. Those who are generally against biocontrol find the balance of effective agents vs. the risk of non-target effects, which while getting lower, will never be zero, to be unacceptable. What if biological programs could predict effectiveness 50% of the time? That would alter the equation, and make these programs more palatable to many ecologists such as myself.

How can something as notoriously unpredictable as species interactions be better assessed before release? One method which would give researchers much better data about the role of species in both native and alien habitats is the construction of quantitative food webs. Normally when biocontrol workers go the country of the target pest's origin, they observe only the two-species interactions between the target species an its natural predators or herbivores. This provides no predictive value because plants and animals do not interact in 2- or 3-species bubbles, they interact complexly both directly and indirectly with many species. Why don't we construct food webs of biocontrol agents in their native habitat and figure out why they seem to be effective there? We can also do retrospective studies on established biocontrol agents that are ineffective and use food webs in both the new and native habitats to try and understand why.

Of course, ecological research is conducted at the whim of funding agencies, largely NSF in the U.S. Politics and inertia often determine what is funded more than science does. Perhaps someday, however, people will realize that for both economic and political reasons, research into the prediction of the effectiveness of biocontrol agents makes clear economic, ecological, and political sense. We do need biocontrol as an option for saving some ecosystems. But we particularly need biocontrol that works.


References

Messing, R.H. and Wright, M.G., 2006. Biological control of invasive species: solution or pollution? Frontiers in Ecology and Evolution 4:132-140.

Willis, A.J. and Memmott, J. 2005. The potential for indirect effects between a weed, one of its biocontrol agents and native herbivores: A food web approach. Biological Control 35:299-306.

Labels: ecology, Hawaii, invasive species, USDA

My recent dearth of posts has only to do with a temporary priorities shift. I have roughly two discretionary hours per day (and that assumes that housework counts as "discretionary") and I elected for the past week to spend it finishing up a quilt top I began almost a year ago, which I decided to display here to prove my excuse. (Although the quilt is neither about biology nor music, it is about math and art, which I decided are close enough.)

The quilt (above) was designed to showcase the eleven regular and semi-regular Archimedean tilings of the Euclidean plane known to those who have studied geometry. Tilings are patterns of polygons which fit together on a flat surface, with no gaps. (There are also multiple tilings of polyhedra in three-dimensional space, for example a soccer ball, which consists of hexagons and pentagons. These can be fit together to form a (nearly round) polyhedron, but cannot fit together in a plane - if a soccer ball were flattened out, some gaps would appear between the shapes. ) This website demonstrating each of the tilings in the Euclidean plane provided me with the color coding.

A regular tiling is one in which one type of regular polygon (a polygon with equal sides and angles) can be fit together repeatedly in a plane with no gaps. The three regular tilings are certainly familiar to most people, who see them used in floors all the time: squares (block 2 above), hexagons (8), and triangles (10). The eight semi-regular tilings use regular polygons of mixed shape to cover a flat surface. These are: octagons and squares (block 1 - also often seen on floors); hexagons and triangles (two ways, block 3 above and the entire quilt); squares and triangles (also two ways, blocks 4 and 7); hexagons, squares, and triangles (9); dodecagons and triangles (5); and dodecagons, hexagons and squares (6). These can be easily derived by figuring out which combinations of angles in the polygons add up exactly to 360°, which is necessary for the tiling to be flat. For example, the angles in a regular hexagon are 120°, so three hexagons can meet at a flat vertex. Squares have 90° angles, and you can either fit four of them together, or combine two squares (180°) with three triangles of 60° each to form a flat 360° vertex. And so on.

Of course, several of these are well known to quilters the world over. Blocks 2, 4, and 10 are most often seen in quilts because they involve squares and triangles, which are relatively easy shapes to cut out, and do not involve sewing into corners. The reason the construction of the blocks took me nearly a year is because the majority of them do involve sewing into corners, which means you cannot assemble the block by sewing straight lines only. Sewing into corners is especially hard on a machine, which I used, and when the angles are acute, which they get to be in the blocks with four or five shapes meeting at a vertex. Blocks 3 and 7 were the real killers for this, and each took me months because I didn't have the patience to focus on them for any length of time. Plus I'm not particularly experienced with this in the first place, so I did a lot of seam ripping.

Because I am a hand quilter, it will probably be another year (at best) before the quilt is finished - it is a very large quilt. So, when more gaps appear in the blog, well, that's just one of the other things I'm doing with my time.

Labels: art, mathematics

The 22nd edition of the Circus of the Spineless is now online at Burning Silo. Check it out for some beautiful photos and accounts of our invertebrate friends.

Labels: biodiversity, carnivals, insects