Quantitative discrimination of flightlessness in fossil Anatidae from skeletal proportions

Flight ability has been lost many times in the family Anatidae (ducks, geese, swans, and allies), and this provides unique insights into the morphological and ecological evolution of the family. Although similar to 15 fossil anatids have been reported to be flightless or possibly so, there has not been an established criterion that is widely applicable to assessing flight ability in fossil anatids. In this study, discriminant rules for the presence-absence of flight ability were constructed by linear discriminant analysis (LDA) based on 7 skeletal measurements in 93 modern anatids in order to set a basis for the inference of flight ability in fossil anatids. Model selection for LDA was conducted by a highdimensional modification of Akaike's Information Criterion, and selected models discriminated the volant and flightless groups with only one misclassification (Tachyeres patachonicus). Flight abilities of fossil anatids were assessed by the constructed rules, supplemented by resampling experiments that were designed to assess the uncertainty in estimating skeletal proportions of fossil anatids in the absence of associated skeletons. The flightless condition was strongly supported for Cnemiornis spp., Branta rhuax, Hawaiianmoa-nalos,Chenonetta finschi, Anas chathamica, Chendytes spp., Shiriyanetta hasegawai, Cayaoa bruneti, and the `` Annaka Short-winged Swan,'' whereas the volant condition was supported for Mergus milleneri and Bambolinetta lignitifila. Results were ambiguous for Branta hylobadistes and Anas marecula. The constructed rules can easily be applied to new observations in the future, although limitations in the inference of ecological traits in fossil species from morphological measurements, including the risk of extrapolations, should be appreciated.