Why was lactase persistence selected for?

This paper has been discussed by Razib at GNXP, and probably others. I thought I would take a closer look at it myself.
One of the main findings here is the north-south gradient within England in the frequency of the lactase persistence allele.
But they also examine relationships between this genotype and health measures in order to uncover the mechanism by which lactase persistence may have been selected for.
For example, did lactase persistence arise due to the benefits (sugar, protein, fat) or because it enabled one to avoid the ill effects of lactose non-persitence (adverse health reactions)? In this paper, they test for associations between the LCT genotype and various health-related measures.
They also have a good discussion about the selection pressures that may have led to the lactase persistence trait being favored. Among the hypotheses, many of which I had never heard of, as outlined in the paper:

1) "nutritional (and survival) advantage of milk consumption in populations that have milk availability"

2) "the calcium absorption hypothesis which considers the ability to use milk as of particular importance for high latitude
populations with low ultraviolet light exposure who are thus subject to potential vitamin D deficiency and poor calcium absorption and for whom the calcium absorption-stimulating effect of lactose would increase fitness."

3) "a reduced diarrhoeal disease mortality hypothesis that considers that, in populations that have become high consumers of milk, this consumption will increase risk of diarrhoeal disease in individuals who are not lactase persistent and thus select for lactase persistence"

4) specifically for African populations: "in arid regions with animal husbandry practices allowing access to milk, the ability to use milk has a selective advantage through the provision of water and electrolytes"

5) "the enhanced fertility by early weaning hypothesis that postulates that lactase persistence leads to earlier weaning and that earlier cessation of breastfeeding reduces the infertile period following each birth"

It doesn't seem like this study provides any conclusive or even suggestive evidence in favor or against any of these hypotheses, although there is some data that does goes against the diarrhea hypothesis:

"the consequences of prolonged childhood diarrhoeal disease that might be expected in survivors – shorter body height, leg length and perhaps higher blood pressure – were not seen in our data"

Lactase persistence-related genetic variant: population substructure and health outcomes
George Davey Smith, Debbie A Lawlor, Nic J Timpson, Jamil Baban, Matt Kiessling, Ian N M Day and Shah Ebrahim
European Journal of Human Genetics advance online

Abstract: Lactase persistence is an autosomal-dominant trait that is common in European-derived populations. A basic tendency for lactase persistence to increase from the southeast to the northwest across European populations has been noted, but such trends within countries have not been extensively studied. We genotyped the C/T-13910 variant (rs4988235) that constitutes the putatively causal allele for lactase persistence (T allele representing persistence) in a general population sample of 3344 women aged 60–79 years from 23 towns across Britain. We found an overall frequency of 0.253 for the C (lactase non-persistence) allele, but with considerable gradients of decreasing frequency from the south to the north and from the east to the west of Britain for this allele. Daily sunlight was positively related to C (non-persistence) allele prevalence. However, sunlight exposure and latitude are strongly correlated, and it was not possible to identify which is the primary factor statistically underlying the distribution of lactase persistence. The C/T-13910 variant (rs4988235) was not related to drinking milk or bone health (although drinking milk itself was protective of bone health), and was essentially unrelated to a wide range of other lifestyle, health and demographic characteristics. One exception was general health being rated as being poor or fair, for which there was an odds ratio of 1.38 (1.04, 1.84) for women homozygous for the C allele; on adjustment for latitude and longitude of place of birth, this attenuated to 1.19 (0.87, 1.64). The lactase persistence variant could contribute to the examination of data for the existence of, and then statistical control for, population substructure in genetic association studies.