We present the symmetric Hadamard representation for scalar and photon Feynman Green's functions. We use these representations to give a simple definition for their associated renormalized stress tensors. We investigate the connection between the accuracy of the WKB approximation and the vanishing of the trace anomaly for these fields. We show that, although for scalars there is a direct connection, this is not true for photons, and we discuss the relevance of these results to the approximation of renormalized stress tensors in static Einstein space-times.
The response of migrating humpback whales to biopsy sampling was investigated off North Stradbroke Island, South East Queensland. Whales were allocated a behavioral category prior to biopsy sampling according to the general behavior of their pod. Behavioral reactions were recorded after each attempt. Sex was determined using a molecular genetic technique.
Detectable reactions occurred in 41.6% of successful biopsy attempts, a significantly lower response rate than that reported by two studies carried out on the feeding and breeding grounds of the North Atlantic. There was no difference in the response rate of whales on their northward or southward migration. Pod size was not an important factor in predicting the response of an individual. Females responded to biopsy sampling at a significantly higher rate than males.
Our results indicate that a substantial difference in response rate can occur between studies. Factors such as the type of boat used and the prior exposure of whales to human impact may be of importance. Our study suggests that female humpback whales may be particularly responsive to human disturbances. Overall, however, biopsy sampling has minimal impact on humpback whales.
Existing population models for humpback whales assume that all individuals within a population undertake the annual migration from feeding areas in high latitudes to breeding areas in tropical waters. An excess of males was recorded in the commercial whaling catches near breeding areas in the southern hemisphere, but no account of this was taken in developing population models, because it was believed that this bias was a result of whalers selecting against females with young calves. Here we demonstrate that the sex ratio of migrating humpback whales near a breeding area is highly skewed towards males. A biopsy study carried out in 1992 throughout the northward and southward migrations revealed a sex ratio of 2.4 males: 1 female in the population of humpback whales migrating along the east Australian coast (n = 180). A reanalysis of the catches made during commercial whaling in this and other areas of the southern hemisphere gave a sex ratio of the same order. The most plausible explanation, supported by some evidence, is that some females remain in the feeding areas throughout winter. The results reported here show that existing management models require major revision to take account of these findings.
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