Leveraging Math Cognition to Combat Health Innumeracy.

Rational numbers (i.e., fractions, percentages, decimals, and whole-number frequencies) are notoriously difficult mathematical constructs. Yet correctly interpreting rational numbers is imperative for understanding health statistics, such as gauging the likelihood of side effects from a medication. Several pernicious biases affect health decision-making involving rational numbers. In our novel developmental framework, the natural-number bias-a tendency to misapply knowledge about natural numbers to all numbers-is the mechanism underlying other biases that shape health decision-making. Natural-number bias occurs when people automatically process natural-number magnitudes and disregard ratio magnitudes. Math-cognition researchers have identified individual differences and environmental factors underlying natural-number bias and devised ways to teach people how to avoid these biases. Although effective interventions from other areas of research can help adults evaluate numerical health information, they circumvent the core issue: people's penchant to automatically process natural-number magnitudes and disregard ratio magnitudes. We describe the origins of natural-number bias and how researchers may harness the bias to improve rational-number understanding and ameliorate innumeracy in real-world contexts, including health. We recommend modifications to formal math education to help children learn the connections among natural and rational numbers. We also call on researchers to consider individual differences people bring to health decision-making contexts and how measures from math cognition might identify those who would benefit most from support when interpreting health statistics. Investigating innumeracy with an interdisciplinary lens could advance understanding of innumeracy in theoretically meaningful and practical ways.

Ecological diversification of Vibrio fischeri serially passaged for 500 generations in novel squid host Euprymna tasmanica.

Vibrio fischeri isolated from Euprymna scolopes (Cephalopoda: Sepiolidae) was used to create 24 lines that were serially passaged through the non-native host Euprymna tasmanica for 500 generations. These derived lines were characterized for biofilm formation, swarming motility, carbon source utilization, and in vitro bioluminescence. Phenotypic assays were compared between "ES" (E. scolopes) and "ET" (E. tasmanica) V. fischeri wild isolates to determine if convergent evolution was apparent between E. tasmanica evolved lines and ET V. fischeri. Ecological diversification was observed in utilization of most carbon sources examined. Convergent evolution was evident in motility, biofilm formation, and select carbon sources displaying hyperpolymorphic usage in V. fischeri. Convergence in bioluminescence (a 2.5-fold increase in brightness) was collectively evident in the derived lines relative to the ancestor. However, dramatic changes in other properties--time points and cell densities of first light emission and maximal light output and emergence of a lag phase in growth curves of derived lines--suggest that increased light intensity per se was not the only important factor. Convergent evolution implies that gnotobiotic squid light organs subject colonizing V. fischeri to similar selection pressures. Adaptation to novel hosts appears to involve flexible microbial metabolism, establishment of biofilm and swarmer V. fischeri ecotypes, and complex changes in bioluminescence. Our data demonstrate that numerous alternate fitness optima or peaks are available to V. fischeri in host adaptive landscapes, where novel host squids serve as habitat islands. Thus, V. fischeri founder flushes occur during the initiation of light organ colonization that ultimately trigger founder effect diversification.