Backward error analysis and the substitution law for Lie group integrators

Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio

Roaring high and low: composition and possible functions of the Iberian stag's vocal repertoire

We provide a detailed description of the rutting vocalisations of free-ranging male Iberian deer (Cervus elaphus hispanicus, Hilzheimer 1909), a geographically isolated and morphologically differentiated subspecies of red deer Cervus elaphus. We combine spectrographic examinations, spectral analyses and automated classifications to identify different call types, and compare the composition of the vocal repertoire with that of other red deer subspecies. Iberian stags give bouts of roars (and more rarely, short series of barks) that are typically composed of two different types of calls. Long Common Roars are mostly given at the beginning or at the end of the bout, and are characterised by a high fundamental frequency (F0) resulting in poorly defined formant frequencies but a relatively high amplitude. In contrast, Short Common Roars are typically given in the middle or at the end of the bout, and are characterised by a lower F0 resulting in relatively well defined vocal tract resonances, but low amplitude. While we did not identify entirely Harsh Roars (as described in the Scottish red deer subspecies (Cervus elaphus scoticus), a small percentage of Long Common Roars contained segments of deterministic chaos. We suggest that the evolution of two clearly distinct types of Common Roars may reflect divergent selection pressures favouring either vocal efficiency in high pitched roars or the communication of body size in low-pitched, high spectral density roars highlighting vocal tract resonances. The clear divergence of the Iberian red deer vocal repertoire from those of other documented European red deer populations reinforces the status of this geographical variant as a distinct subspecies

Statistical Computing on Non-Linear Spaces for Computational Anatomy

International audienceComputational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. However, understanding and modeling the shape of organs is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. We explain in this chapter how the Riemannian structure can provide a powerful framework to build generic statistical computing tools. We show that few computational tools derive for each Riemannian metric can be used in practice as the basic atoms to build more complex generic algorithms such as interpolation, filtering and anisotropic diffusion on fields of geometric features. This computational framework is illustrated with the analysis of the shape of the scoliotic spine and the modeling of the brain variability from sulcal lines where the results suggest new anatomical findings

Sexual selection on male vocal fundamental frequency in humans and other anthropoids

D.A.P. was supported by a National Institutes of Mental Health T32 MH70343-05 fellowship. J.R.W. was supported by a National Science Foundation predoctoral fellowship.In many primates, including humans, the vocalizations of males and females differ dramatically, with male vocalizations and vocal anatomy often seeming to exaggerate apparent body size. These traits may be favoured by sexual selection because low-frequency male vocalizations intimidate rivals and/or attract females, but this hypothesis has not been systematically tested across primates, nor is it clear why competitors and potential mates should attend to vocalization frequencies. Here we show across anthropoids that sexual dimorphism in fundamental frequency (F0) increased during evolutionary transitions towards polygyny, and decreased during transitions towards monogamy. Surprisingly, humans exhibit greater F0 sexual dimorphism than any other ape. We also show that low-F0 vocalizations predict perceptions of men’s dominance and attractiveness, and predict hormone profiles (low cortisol and high testosterone) related to immune function. These results suggest that low male F0 signals condition to competitors and mates, and evolved in male anthropoids in response to the intensity of mating competition.PostprintPeer reviewe

Perception of Male Caller Identity in Koalas (Phascolarctos cinereus): Acoustic Analysis and Playback Experiments

The ability to signal individual identity using vocal signals and distinguish between conspecifics based on vocal cues is important in several mammal species. Furthermore, it can be important for receivers to differentiate between callers in reproductive contexts. In this study, we used acoustic analyses to determine whether male koala bellows are individually distinctive and to investigate the relative importance of different acoustic features for coding individuality. We then used a habituation-discrimination paradigm to investigate whether koalas discriminate between the bellow vocalisations of different male callers. Our results show that male koala bellows are highly individualized, and indicate that cues related to vocal tract filtering contribute the most to vocal identity. In addition, we found that male and female koalas habituated to the bellows of a specific male showed a significant dishabituation when they were presented with bellows from a novel male. The significant reduction in behavioural response to a final rehabituation playback shows this was not a chance rebound in response levels. Our findings indicate that male koala bellows are highly individually distinctive and that the identity of male callers is functionally relevant to male and female koalas during the breeding season. We go on to discuss the biological relevance of signalling identity in this species' sexual communication and the potential practical implications of our findings for acoustic monitoring of male population levels

Estrogen and Progestogen Correlates of the Structure of Female Copulation Calls in Semi-Free-Ranging Barbary Macaques (Macaca sylvanus)

Females of many Old World primates produce conspicuous vocalizations in combination with copulations. Indirect evidence exists that in Barbary macaques (Macaca sylvanus), the structure of these copulation calls is related to changes in reproductive hormone levels. However, the structure of these calls does not vary significantly around the timing of ovulation when estrogen and progestogen levels show marked changes. We here aimed to clarify this paradox by investigating how the steroid hormones estrogen and progesterone are related to changes in the acoustic structure of copulation calls. We collected data on semi-free-ranging Barbary macaques in Gibraltar and at La Forêt des Singes in Rocamadour, France. We determined estrogen and progestogen concentrations from fecal samples and combined them with a fine-grained structural analysis of female copulation calls (N = 775 calls of 11 females). Our analysis indicates a time lag of 3 d between changes in fecal hormone levels, adjusted for the excretion lag time, and in the acoustic structure of copulation calls. Specifically, we found that estrogen increased the duration and frequency of the calls, whereas progestogen had an antagonistic effect. Importantly, however, variation in acoustic variables did not track short-term changes such as the peak in estrogen occurring around the timing of ovulation. Taken together, our results help to explain why female Barbary macaque copulation calls are related to changes in hormone levels but fail to indicate the fertile phase

The evolution of language: a comparative review

For many years the evolution of language has been seen as a disreputable topic, mired in fanciful "just so stories" about language origins. However, in the last decade a new synthesis of modern linguistics, cognitive neuroscience and neo-Darwinian evolutionary theory has begun to make important contributions to our understanding of the biology and evolution of language. I review some of this recent progress, focusing on the value of the comparative method, which uses data from animal species to draw inferences about language evolution. Discussing speech first, I show how data concerning a wide variety of species, from monkeys to birds, can increase our understanding of the anatomical and neural mechanisms underlying human spoken language, and how bird and whale song provide insights into the ultimate evolutionary function of language. I discuss the ‘‘descended larynx’ ’ of humans, a peculiar adaptation for speech that has received much attention in the past, which despite earlier claims is not uniquely human. Then I will turn to the neural mechanisms underlying spoken language, pointing out the difficulties animals apparently experience in perceiving hierarchical structure in sounds, and stressing the importance of vocal imitation in the evolution of a spoken language. Turning to ultimate function, I suggest that communication among kin (especially between parents and offspring) played a crucial but neglected role in driving language evolution. Finally, I briefly discuss phylogeny, discussing hypotheses that offer plausible routes to human language from a non-linguistic chimp-like ancestor. I conclude that comparative data from living animals will be key to developing a richer, more interdisciplinary understanding of our most distinctively human trait: language

Call Cultures in Orang-Utans?

BACKGROUND: Several studies suggested great ape cultures, arguing that human cumulative culture presumably evolved from such a foundation. These focused on conspicuous behaviours, and showed rich geographic variation, which could not be attributed to known ecological or genetic differences. Although geographic variation within call types (accents) has previously been reported for orang-utans and other primate species, we examine geographic variation in the presence/absence of discrete call types (dialects). Because orang-utans have been shown to have geographic variation that is not completely explicable by genetic or ecological factors we hypothesized that this will be similar in the call domain and predict that discrete call type variation between populations will be found. METHODOLOGY/PRINCIPAL FINDINGS: We examined long-term behavioural data from five orang-utan populations and collected fecal samples for genetic analyses. We show that there is geographic variation in the presence of discrete types of calls. In exactly the same behavioural context (nest building and infant retrieval), individuals in different wild populations customarily emit either qualitatively different calls or calls in some but not in others. By comparing patterns in call-type and genetic similarity, we suggest that the observed variation is not likely to be explained by genetic or ecological differences. CONCLUSION/SIGNIFICANCE: These results are consistent with the potential presence of 'call cultures' and suggest that wild orang-utans possess the ability to invent arbitrary calls, which spread through social learning. These findings differ substantially from those that have been reported for primates before. First, the results reported here are on dialect and not on accent. Second, this study presents cases of production learning whereas most primate studies on vocal learning were cases of contextual learning. We conclude with speculating on how these findings might assist in bridging the gap between vocal communication in non-human primates and human speech

Gestural communication of the gorilla (Gorilla gorilla): repertoire, intentionality and possible origins

Social groups of gorillas were observed in three captive facilities and one African field site. Cases of potential gesture use, totalling 9,540, were filtered by strict criteria for intentionality, giving a corpus of 5,250 instances of intentional gesture use. This indicated a repertoire of 102 gesture types. Most repertoire differences between individuals and sites were explicable as a consequence of environmental affordances and sampling effects: overall gesture frequency was a good predictor of universality of occurrence. Only one gesture was idiosyncratic to a single individual, and was given only to humans. Indications of cultural learning were few, though not absent. Six gestures appeared to be traditions within single social groups, but overall concordance in repertoires was almost as high between as within social groups. No support was found for the ontogenetic ritualization hypothesis as the chief means of acquisition of gestures. Many gestures whose form ruled out such an origin, i.e. gestures derived from species-typical displays, were used as intentionally and almost as flexibly as gestures whose form was consistent with learning by ritualization. When using both classes of gesture, gorillas paid specific attention to the attentional state of their audience. Thus, it would be unwarranted to divide ape gestural repertoires into ‘innate, species-typical, inflexible reactions’ and ‘individually learned, intentional, flexible communication’. We conclude that gorilla gestural communication is based on a species-typical repertoire, like those of most other mammalian species but very much larger. Gorilla gestures are not, however, inflexible signals but are employed for intentional communication to specific individuals