The Miura Map on the Line

The Miura map (introduced by Miura) is a nonlinear map between function spaces which transforms smooth solutions of the modified Korteweg - de Vries equation (mKdV) to solutions of the Korteweg - de Vries equation (KdV). In this paper we study relations between the Miura map and Schroedinger operators with real-valued distributional potentials (possibly not decaying at infinity) from various spaces. We also investigate mapping properties of the Miura map in these spaces. As an application we prove existence of solutions of the Korteweg - de Vries equation in the negative Sobolev space H^{-1} for the initial data in the range of the Miura map.Comment: 33 page

On the regularity of the composition of diffeomorphisms

For $M$ being a closed manifold or the Euclidean space we present a detailed proof of regularity properties of the composition of $H^s$-regular diffeomorphisms of $M$ for $s > 1/2\dim M + 1$

Genetic regulation of parasite infection: empirical evidence of the functional significance of an IL4 gene SNP on nematode infections in wild primates

Background Susceptibility to parasite infection affects fitness-related processes, such as mate choice and survival, yet its genetic regulation remains poorly understood. Interleukin-4 (IL4) plays a central role in the humoral immune defence against nematode parasite infections, inducing IgE switch and regulation of worm expulsion from the intestines. The evolutionary and functional significance of single nucleotide polymorphisms (SNPs) in IL4-genes is known, yet empirical information on the effect of IL4 SNPs on gastro-intestinal infections is lacking. Using samples from a population of wild red-fronted lemurs (Eulemur fulvus rufus, Primates: Lemuridae), from western Madagascar, we explored the association of IL4-gene promoter polymorphisms with nematode infections and investigated a possible functional role of the IL4 polymorphism on male reproductive success. Results Using sequence analyses of lemur DNA we detected a new SNP in the IL4 gene promoter area. Carriers of the genotype T/T showed higher nematode infection intensities than individuals of genotypes C/T and C/C. Genetic population analyses using data from more than 10 years, suggested higher reproductive success of T/T males than expected. Conclusions Our results suggest a regulatory effect of an IL4 gene promoter polymorphism on the intensity of parasite infections in a natural population of red-fronted lemurs, with a seemingly disadvantageous genotype represented in low frequencies. Long-term population analyses, however, point in the direction of a negative frequency-dependent association, giving a fitness advantage to the rare genotype. Due to low frequencies of the genotype in question conclusive evidence of a functional role of IL4 polymorphism cannot be drawn here; still, we suggest the use of IL4 polymorphism as a new molecular tool for quick assessment of individual genetic constitution with regard to nematode infection intensities, contributing to a better understanding of the actual components of the immune response that mediate protection against gastro-intestinal parasites

The Behavioral Ecology of the Tibetan Macaque

This open access book summarizes the multi-disciplinary results of one of China’s main primatological research projects on the endemic Tibetan macaque (Macaca thibetana), which had continued for over 30 years, but which had never been reported on systematically. Dedicated to this exceptional Old World monkey, this book makes the work of Chinese primatologists on the social behavior, cooperation, culture, cognition, group dynamics, and emerging technologies in primate research accessible to the international scientific community

Catalyzing Transitions to Sociality: Ecology Builds on Parental Care

In the context of social evolution research, great emphasis on kin-selected benefits has led to an understanding of parental care as one of the activities that helpers can perform in extended cooperative families. Nevertheless, this perspective might have precluded a deeper understanding of the implications of parental care for social evolution. We argue that parental care is a broader set of processes playing a key role both before and during the emergence of sociality. The care system of a species may be understood as the result of long coevolutionary processes with environmental pressures during pre-social stages that impact transitions to sociality. We evaluate the present framework against evidence on the evolution of parental care and transitions toward sociality in subsocial and parasocial vertebrate and invertebrate species. Moreover, following previous evidence for the importance of modes of foraging and resting, we structure our inquiry by classifying societies into three types. Our results suggest that in “central place foragers” and “fortress defenders”, ecological factors promoting the evolution of parental care foster a set of coevolutionary feedback loops resulting in increases in parental effort and offspring needs. Offspring needs alone or in combination with limited breeding options enhance the relative benefits of positive social interactions, catalyzing transitions to sociality. In “itinerant foragers”, sociality is associated with colonizing new niches. Changes in predation pressure entail changes in the modes of care or selection for certain types of care already present in solitary ancestors. Further changes in the form of collective defense may be needed for permanent sociality to evolve. We conclude that there is evidence that social transitions to different types of societies are the result of long coevolutionary processes between environmental pressures and the care systems in a wide variety of taxa. Therefore, advances in the study of the origins of sociality may require further investigation of parental care evolution in solitary ancestors of today's social species

Refuge sharing network predicts ectoparasite load in a lizard

Living in social groups facilitates cross-infection by parasites. However, empirical studies on indirect transmission within wildlife populations are scarce. We investigated whether asynchronous overnight refuge sharing among neighboring sleepy lizards, Tiliqua rugosa, facilitates indirect transmission of its ectoparasitic tick, Amblyomma limbatum. We fitted 18 neighboring lizards with GPS recorders, observed their overnight refuge use each night over 3 months, and counted their ticks every fortnight. We constructed a transmission network to estimate the cross-infection risk based on asynchronous refuge sharing frequencies among all lizards and the life history traits of the tick. Although self-infection was possible, the network provided a powerful predictor of measured tick loads. Highly connected lizards that frequently used their neighbors’ refuges were characterized by higher tick loads. Thus, indirect contact had a major influence on transmission pathways and parasite loads. Furthermore, lizards that used many different refuges had lower cross- and self-infection risks and lower tick loads than individuals that used relatively fewer refuges. Increasing the number of refuges used by a lizard may be an important defense mechanism against ectoparasite transmission in this species. Our study provides important empirical data to further understand how indirectly transmitted parasites move through host populations and influence individual parasite loads

A reply to “Ranging Behavior Drives Parasite Richness: A More Parsimonious Hypothesis”

This preprint has been reviewed and recommended by Peer Community In Ecology (https://dx.doi.org/10.24072/pci.ecology.100001). In a recent article, Bicca-Marques and Calegaro-Marques [Bicca-Marques JC, Calegaro-Marques C (2016) Ranging behavior drives parasite richness: A more parsimonious hypothesis. American Journal of Primatology 78: 923–927.] discussed the putative assumptions related to an interpretation we provided regarding an observed positive relationship between weekly averaged parasite richness of a group of mandrills (Mandrillus sphinx) and their daily path lengths (DPL), published earlier in the same journal [Brockmeyer T, Kappeler PM, Willaume E, Benoit L, Mboumba S, Charpentier MJE (2015) Social organization and space use of a wild mandrill (Mandrillus sphinx) group. American Journal of Primatology 77: 1036–1048.]. In our article, we proposed, inter alia, that “the daily travels of mandrills could be seen as a way to escape contaminated habitats on a local scale”. In their article, Bicca-Marques and Calegaro-Marques proposed an alternative mechanism that they considered to be more parsimonious. In their view, increased DPL also increases exposure to novel parasites from the environment. In other words, while we proposed that elevated DPL may be a consequence of elevated parasite richness, they viewed it as a cause. We are happy to see that our study attracted so much interest that it evoked a public comment. We are also grateful to Bicca-Marques and Calegaro-Marques for pointing out an obvious alternative scenario that we failed to discuss and for laying out several key factors and assumptions that should be addressed by future studies examining the links between parasite risk and group ranging. We use this opportunity to advance this discourse by responding to some of the criticisms raised in their discussion of our article. In this reply, we briefly contextualize the main object of criticism. We then discuss the putative parsimony of the two competing scenarios