We assumed individual plants in our population to have equal rates of photosynthesis
and invest equal amounts of photosynthate, as
sugar, into nectar ( 9). However, the sugar concentration of the nectar was determined by a
flower’s virtual genome, which consisted of a
diploid set of four diallelic genes. The effect
of the eight codominant alleles determined the
water component of the nectar and thus its
final sugar concentration. Some alleles coded
for smaller water components and some alleles
coded for larger water components, making
the sugar concentration of nectar a multilocus
trait ( 12).

Upon leaving a flower, a bat was assumed to
transfer virtual pollen to the next flower and
generate a virtual offspring seed there. Twenty-three such seeds, selected from a night’s production by stochastic universal sampling, formed
the next generation of virtual plants (Fig. 1B).
Flowers that were visited more frequently were
thus more likely to have their alleles represented
in the next generation.

We tracked the evolution of two lineages ofartificial flowers over multiple generations. Theevolutionary outcome differed significantly fromthat expected under genetic drift (Fig. 1C). Batsmade fewer visits to flowers with either verydilute or very concentrated nectar (fig. S1). Asa result, sugar concentration of nectar in bothlineages, which started from 17.8% for dilutenectar or 42.2% for concentrated nectar, evolvedto about 36% [95% confidence interval (CI) 33to 40%] within 10 to 12 generations, where onegeneration was produced per night (Fig. 1, Cand D). This result was consistent with stabilizingselection converging on an equilibrium [Fig. 1D;linear regression: P < 0.001, adjusted coefficientof determination (R2) = 0.48].An optimal forager should choose among avail-able alternatives based on the highest energyreturn. However, studies of the ability of bats todiscriminate nectar volume ( 13) and concentra-tion (2, 10) in binary choice designs have yieldedpsychometric curves consistent with Weber’slaw (Fig. 2, A and B). This law states that theability to perceive a stimulus as different fromanother requires a minimum difference in in-tensity that is proportional to the intensity ofthe initial stimulus (2, 14). The proportional pro-cessing of volume and concentration may resultfrom underlying subjective value (psychophysical)functions, in which value progressively increaseswith stimulus magnitude, but with a decreasingslope ( 10, 13–16).With such concave-down value functions (e.g.,logarithmic or power functions), if nectar qualitychanges by a specific amount, then a reductionin magnitude changes choice probabilities morestrongly than a corresponding increase in mag-nitude. As seen in the psychometric function,the slope decreases with higher magnitudes(Fig. 2, A and B). This is relevant here, wherenectar rewards are evaluated along two dimen-sions (volume and sugar concentration) andwhere there is a trade-off between a decrease invalue along one dimension and an increasealong the other dimension.To explore potential effects of proportionalprocessing on natural selection of nectar concen-trations, we modeled the experimental flowerarray and tested the evolutionary consequencesof virtual nectar-foraging bats. The virtual batsmade choices by integrating information aboutnectar volume and concentration into a singlerepresentation of value (supplementary mate-rials and methods). Our simulations contrastedlogarithmic value functions (Fig. 2) with functionswith a linear relationship between choice prob-ability and caloric value. We also examined howthe supply/demand ratio influences selectiondynamics. At low supply, bats encountered smallervolumes of nectar, which made discriminatingnectar quantity easier because smaller outcomesare represented internally more sharply thanlarger ones ( 14) (Fig. 2B).

Both psychophysics and pollinator density
may thus affect nectar evolution. To elucidate
their influences, we performed four simulations
comparing linear versus nonlinear value functions in conditions of either high or low supply/
demand ratios. Only the simulations that incorporated nonlinear value functions (Fig. 3, A, B,
E, and F) were congruent with the main result
of our field experiments in that evolved concentrations converged to intermediate equilibrium
values. In contrast, simulations incorporating
linear value functions resulted in either directional selection to sugar concentrations greater
than 43% or no selection (Fig. 3, C, D, G, and H).
Because all simulations incorporated the designed dynamics of our flower array and the frequency and consistency of flower visits by bats
in similar foraging situations, concave-down value
functions appear essential to understanding our

76 6 JANUARY 2017 • VOL 355 ISSUE 6320 sciencemag.org SCIENCE
Fig. 2. Psychophysical and population effects
on decision making. (A and B) Probabilities of
choosing an option compared to a reference (black
circles) for nectar sugar concentration (A) or volume (B). The different line types (solid, dashed, or
dotted) represent curves calculated from psychometric functions of intensity perception based on
different references (black circles). Probabilities
change more for decreased than increased values
(2), and this asymmetry is stronger at low magnitude. Symbols with error bars labeled “ 3 bats” or
“ 9 bats” are medians (± interquartile ranges) of
concentration (% w/w) or volume experienced
during laboratory experiments over the complete
runs; distributions differ primarily in volume. (A,
inset) A psychometric function of intensity perception. Such functions were used to calculate choice
probabilities in (A) and (B) for specific reference
values (black circles). (C) An analytical example of
reward value maximization when sugar energy is fixed but water content is variable, assuming logarithmic preference for alternatives. Consider a flower with a fixed rate of sugar production and an independent
rate of water added to this sugar. When harvested by a single forager
at regular time intervals ( 20, 60, and 120 min), the amount of sugar
collected per visit decreases when collection intervals decrease. Iso-caloric lines connect combinations of volume and concentration with
identical quantities of sugar in a portion resulting from the fixed revisit
interval and constant secretion rate. Black dots show the nectar concentration at which perceived value is maximal. As the amount of sugar
in a portion decreases, the optimal concentration also decreases (arrow).