INSIGHTS | PERSPECTIVES
26 6 JANUARY 2017 • VOL 355 ISSUE 6320 sciencemag.org SCIENCE
magnitude ( 4), which is historically called the
Weber fraction ( 3). In the example above, an
increase in bulbs in the second condition that
would be proportional to the first is from 50
to 100 bulbs.
Thus, as a stimulus increases in physical
magnitude, the just-noticeable difference
also gets larger. In other words, using proportions to compare ever larger stimuli makes it
more difficult to perceive stimulus changes;
as a large stimulus increases, perception of
its size or value appears to remain the same.
The use of proportional perception is
not limited to humans. In other animals—
including insects, birds, amphibians, and
nonhuman mammals—perception of visual,
acoustic, chemical, magnetic, tactile, and
electrical stimuli is also proportional ( 5). As
evidence for the universality of proportional
perceptions accumulates, we must determine
how it drives the evolution of observable
traits. This is important because one possible
limit on the evolution of ever more exaggerated traits (such as sexual signals included in
plumage and song) is the diminishing return
on increasing the size of already large traits;
observers will be unable to perceive differences unless the change is proportional to
their large magnitude ( 6). Such a check on
directional selection has been inferred from
data showing proportional perception ( 7).
Furthermore, when a trait is so large that it
becomes too difficult to produce a perceivable change, the observer may evaluate a
different trait that is still within its distinguishable range.
Proportional perception may limit trait
evolution in many ecological contexts. In their
study, Nachev et al. (1) investigate how perception that is based on proportions affects
the evolution of traits in flowers that attract
pollinators. They designed field experiments
to determine how flowers evolve dilute nectar, even though pollinator bats prefer higher
concentrations of sugar. The authors allowed
bats to visit computer-controlled artificial
flowers with virtual genomes that varied in
their nectar production. Thus, although the
bats were real pollinators, they were selecting
for new generations of virtual “seeds” with
different genomic profiles for nectar production. The resulting artificial flowers evolved
intermediate nectar concentrations rather
than an ever more syrupy juice.
There are at least two stimuli that the
bats could be evaluating: the sugar concen-
tration and the overall nectar volume. The
magnitudes of both concentration and vol-
ume can, however, change as a result of con-
sumption by bats. These changes can affect
which stimulus is more easily distinguished.
Nachev et al. used computer simulations
and laboratory experiments to under-
stand how these stimuli and their changes
contribute to the evolution of intermediate
nectar concentrations. They show that the
field results can only be confirmed if bats
judge the stimuli according to proportions.
The reason is that differences in high nec-
tar concentrations and larger volumes are
more difficult to discriminate than are the
same absolute differences in low nectar
concentrations and small volumes.
Decisions based on the two stimuli are not
necessarily coupled, however. The authors
show that when proportional perception
makes it difficult to distinguish one stimu-
lus dimension because its magnitude is too
high, bats may choose flowers according to
the other stimulus dimension. That is, when
distinguishing high concentrations is too dif-
ficult, the bats may choose flowers on the ba-
sis of nectar volume, leading to the evolution
of diluted nectar.
Nachev et al.’s study successfully integrates
psychophysics (measuring the psychological
experience of a physical stimulus) and evo-
lutionary biology. This integration is long
overdue; Darwin wrote in 1872 that inherited
variation in certain traits depends “on the
powers of perception, taste, and will” of ob-
servers ( 8). Models of trait evolution that are
driven by the ability of individuals to choose
or distinguish characters ( 9) would benefit
from definitive measurements of perceptual
systems. Such data would improve our un-
derstanding of how perception influences
In concert, a comparative approach in
psychophysics could determine which perceptual mechanisms are universal and
which have evolved specializations to mediate particular decisions in particular species
( 10). For example, even though proportional
perception has been studied for more than
a hundred years, it is still unknown how
selection alters those proportions in different species and whether the underlying
neural mechanisms are shared. The study
by Nachev et al. should serve as a model for
how such interdisciplinary work can lead to
novel and more complete explanations of
trait evolution. j
1. V. Nachev et al. , Science 355, 75 (2017).
2. J. Skelhorn, C. Ro we, Proc. Biol. Sci. 283, 20152890
3. J.J.Zwislocki, Sensory Neuroscience: Four Laws of
Psychophysics (Springer, 2009).
4. S.S.Stevens, Psychophysics: Introduction to its
Perceptual, Neural, and Social Prospects (Transaction,
5. K.L.Akre, S.Johnsen, Trends Ecol. Evol. 29,291(2014).
6. J. D. Cohen, Z. Tierpsychol. 64, 1 (1984).
7. K.L.Akre et al., Science 333, 751 (2011).
8. C. Dar win, The Descent of Man, and Selection in Relation to
Sex (D. Appleton and Company, ed. 1, 1872).
9. L. S. Mead, S. J. Arnold, Trends Ecol. Evol. 19, 264 (2004).
10. S.J.Shettleworth, Cognition, Evolution and Behavior
(Oxford Univ. Press, 1998).
The discovery of
bismuth is a challenge
to standard theory
By Kamran Behnia
The first superconductor was discov- ered in 1911, when elemental mercury was cooled below the helium liquefac- tion temperature. Suddenly, it ceased to show any resistance to the flow of electricity. Soon after, it became clear
that some metals become superconducting upon cooling, and some do not. Half a
century or so later, a quantum-mechanical
theory of superconductivity was conceived
by Bardeen, Cooper, and Schrieffer (BCS).
On page 52 of this issue, Prakash et al. (1)
report the surprise discovery of superconductivity at extremely low temperatures in
bismuth, a familiar and extensively documented metal (2). The results mark a new
episode in the history of superconductivity.
The central idea in BCS theory is the
pairing up of electrons. The condensation
of these pairs to form a macroscopic wave
function then turns the metal into a superconductor. A phase transition transforms
a liquid of individual electrons (which retain their distinct quantum numbers) into
a superfluid condensate (where individual
electrons cease to exist). The main requirement for pairing to occur is an infinitesimal
attraction between electrons, despite their
intrinsic repulsion. Attesting to the fertility
of this concept is the role it has played in
explaining the superfluidity of 3He ( 3) and
LPEM-CNRS, Ecole Supérieure de Physique et de Chimie
Industrielles, PSL Research University, 75005 Paris, France.
“The lattice structure
[of Bi] has modified the