Moving eyes, moving minds

A paper by Hannah Faye Chua and colleagues of the University of Michigan asserts that there are significant differences between Chinese and American graduate students in "perceptual judgment". This basically means what parts of a scene they devote attention to. Here's the background from the paper:

A growing literature suggests that people from different cultures have differing cognitive processing styles (1, 2). Westerners, in particular North Americans, tend to be more analytic than East Asians. That is, North Americans attend to focal objects more than do East Asians, analyzing their attributes and assigning them to categories. In contrast, East Asians have been held to be more holistic than Westerners and are more likely to attend to contextual information and make judgments based on relationships and similarities.
Causal attributions for events reflect these differences in analytic vs. holistic thought. For example, Westerners tend to explain events in terms that refer primarily or entirely to salient objects (including people), whereas East Asians are more inclined to explain events in terms of contextual factors (3-5). There also are differences in performance on perceptual judgment and memory tasks (6-8). For example, Masuda and Nisbett (6) asked participants to report what they saw in underwater scenes. Americans emphasized focal objects, that is, large, brightly colored, rapidly moving objects. Japanese reported 60% more information about the background (e.g., rocks, color of water, small nonmoving objects) than did Americans. After viewing scenes containing a single animal against a realistic background, Japanese and American participants were asked to make old n

What Nee and colleagues demonstrate is that the converse is not true. Although an invariant ratio does lead to a log-log slope near 1.0, a log-log slope near 1.0 may result from many relationships other than an invariant ratio. In particular, a random set of ratios will still generate a log-log slope near 1.0.

A commentary by Gerdien de Jong (subscription required) explains the paper.

But Nee et al. (2) describe the general rationale of how slopes of 1 at high R2 arise in log-log plots, independent of the distributions of the traits. The culprit is a variable on the y axis that is a fraction of the x-variable: The plot is of y = cx, with c < 1. In a log-log plot of cx versus x, a slope of 1 follows automatically. A wide range on the x axis--from rabbit to whale--guarantees a high R2. The evidence for life history invariants vanishes as the method of finding them evaporates (de Jong 2005:1194).

Why does this happen? Simply put, a short-lived species must have a shorter maturation age than its average life span, but not too much shorter. The slope of 1.0 comes from this fact alone: one variable is constrained to be close to the other, owing to the fact that it is some substantial proportion of that other variable.

Why should the correlation be high? The answer to this should be familiar to any paleontologist: it's a mouse to elephant curve. The independent variable ranges across so many orders of magnitude that the variance about the regression essentially disappears.

The essential emptiness of the theory arises here:

The most notable invariants are typically taken to be those that hold over several orders of magnitude of variation in the value of the biological characters; we now see that it is this wide variability of the characters that inevitably makes the invariants notable (Nee et al. 2005: 1238).

When I read through Charnov's book (Life History Invariants: Some Explorations of Symmetry in Evolutionary Ecology), it was with an eye toward the relationship of average life span to maturation age. Personally, I found the log-log plots less than convincing, because there was too much variation hidden in them. A 0.95 correlation on a log-log plot across primates still allows individual values to vary by a lot, just because a log-log plot appears to smash the variation down so much.

This study attacks the basis of the theory much more directly:

From the time of the introduction of invariants, many other studies and discussions have accepted their existence on the basis of these sorts of demonstrations and attempted to explain them theoretically or infer their consequences. For example, in his review of the canonical monograph on life-history invariants (1), Maynard Smith refers to the M/b data we have just discussed and says "M/b is approximately constant (0.2) for species as different as the tree sparrow and wandering albatross"(31). This is in spite of the fact that the data to which he is referring show the ratio varying between 0.1 and 0.5. Maynard Smith was not the only reviewer to accept that this ratio is constant (32), and the status of these life-history invariants is such that they have now found their way into the popular physics literature (33). In fact, in a population of constant size, the ratio M/b is, essentially, the probability of surviving from egg to breeding age and therefore is constrained to be between 0 and 1 (Nee et al. 2005: 1238).

This was certainly my perception for the primates. There was a strong claim that the values of interest were invariants, despite the fact that the data themselves show fairly wide variation in the actual ratios.

What is the solution to this problem for life history theory? Nee et al. suggest comparisons with other dimensionless values; de Jong suggests a direct examination of fitness relations in different species. The latter approach seems the most likely for hominoids, although this essentially amounts to a species-specific examination in each case.

What I wonder is whether other kinds of relations -- ones we may be more familiar with -- may prove to be manifestations of the same error. I'm going to be looking through some papers in the next few days with that in mind.

References:

Charnov E. 1993. Life History Invariants: Some Explorations of Symmetry in Evolutionary Ecology. Oxford University Press, Oxford.

de Jong G. 2005. Is invariance across animal species just an illusion? Science 309:1193-1195. Full text (subscription required)

Nee S, Colegrave N, West SA, Grafen A. 2005. The illusion of invariant quantities in life histories. Science 309:1236-1239. Full text (subscription required)