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Some properties of quantum Lévy area in Fock and non-Fock quantum stochastic calculus

100%

Chen S. , Hudson R.

tom Vol. 33, Fasc. 2

425--434

We consider the analogue of Lévy area, defined as an iterated stochastic integral, obtained by replacing two independent component onedimensional Brownian motions by the mutually non-commuting momentum and position Brownian motions P and Q of either Fock or non-Fock quantum stochastic calculus, which are also stochastically independent in a certain sense. We show that the resulting quantum Lévy area is trivially distributed in the Fock case, but has a non-trivial distribution in non-Fock quantum stochastic calculus which, after rescaling, interpolates between the trivial distribution and that of classical Lévy area in the “infinite temperature” limit. We also show that it behaves differently from the classical Lévy area under a kind of time reversal, in both the Fock and non-Fock cases.

Seasonal reproduction in Mexican cottontail rabbits Sylvilagus cunicularius in La Malinche National Park, central Mexico

70%

Vazquez J. , Martinez Chacon A. J. , Hudson R. , Rodriguez-Martinez L. , Martinez-Gomez M.

tom 52

nr 4

361-369

Mexico has the largest number of leporid species in the world but most have been little studied. The endemic Mexican cottontailSylvilagus cunicularius (Waterhouse, 1848) is the largest Mexican rabbit, and although not in danger of extinction, it is increasingly threatened. Since little is known about its annual pattern of reproduction, we studied this species in La Malinche National Park, central Mexico, whereS. cunicularius is still common. For 7 years we trapped and marked 157 different individuals (plus 59, sometimes multiple, re-captures), determining across the year the percent of adult females that were reproductively active, the number of juveniles as a percent of total captures, and the percent of males with scrotal testes. Reproductively active females were present throughout the year but with a notable peak from March to October, juveniles were present throughout the year but with a peak from September to December, and adult males had scrotal testes throughout the year with no seasonal change in testis length. Onset of the breeding season coincided with increasing day length and temperature, and births with high rainfall. Thus, in central MexicoS. cunicularius breeds throughout the year but particularly during the warmer, wetter summer months. We therefore recommend that hunting only be permitted from November to February.

A comparison between vegetation and diet records from the wet and dry season in the cottontail rabbit Sylvilagus floridanus at Ixtacuixtla, Central Mexico

61%

Hudson R. , Rodriguez-Martinez L. , Distel H. , Cordero C. , Altbacker V. , Martinez-Gomez M.

tom 50

nr 3

Mexico has eight endemic lagomorph species, several of which are endangered. For conservation reasons it is necessary to know more about their diet. In a first step we applied the method of fecal pellet analysis to the cottontailSylvilagus floridanus (Allen, 1890). Since it is common in Mexico, information on its diet should provide a useful baseline with which to compare the diets of other Mexican lagomorphs. At Ixtacuixtla, we recorded vegetation and analyzed fecal pellet content once in August (wet season) and once in March (dry season) at 4 sampling sites representing different habitat types. The comparison of vegetation and diet records suggestedS. floridanus to occupy the same dietary niche in the different habitats. Measures of niche breadth showedS. floridanus to be neither a generalist nor a specialist. Nevertheless, it appeared to be quite selective in consuming particular herb and grass species even when they became scarce during the dry season. Since the vegetation record only poorly represented the rabbits’ diet, a more focused approach is suggested for future studies: first, to identify the relevant food species in the diet, second, to obtain data on the availability of these, and third, to concentrate on time points when changes in resource state could be a limiting factor.