Abstract: Background: Predation risk declines non-linearly with one's own vigilance and the vigilance of others in the group (the 'many-eyes' effect). Furthermore, as group size increases, the individual's risk of predation may decline through dilution with more potential victims, but may increase if larger groups attract more predators. These are known, respectively, as the dilution effect and the attraction effect.
Assumptions: Feeding animals use vigilance to trade-off food and safety. Net feeding rate declines linearly with vigilance.
Question: How do the many-eyes, dilution, and attraction effects interact to influence the relationship between group size and vigilance behaviour?
Mathematical methods: We use game theory and the fitness-generating function to determine the ESS level of vigilance of an individual within a group.
Predictions: Vigilance decreases with group size as a consequence of the many-eyes and dilution effects but increases with group size as a consequence of the attraction effect, when they act independent of each other. Their synergetic effects on vigilance depend upon the relative strengths of each and their interactions. Regardless, the influence of other factors on vigilance – such as encounter rate with predators, predator lethality, marginal value of energy, and value of vigilance – decline with group size.

Abstract: During 1984-1987, 1992-1995, and 1998-2001, the author researched snow leopard, white lipped deer, kiang, and argali in Qinghai, Gansu, Xingiang, and Sichuan. He collected 644 snow leopard droppings, and analyzed kinds of foods and sources from perch. Snow leopard's foods include most main foods, main foods, comparative foods and lesser foods. Studied one another
index of faunistic congruence of foods species that from various distribution and variation both perch vertical variety and foods of snow leopard.

Abstract: In accordance with order of the Ministry of Nature and Tourism,
zoologists of our association have made surveys in three ways such as
reasons why snow leopards attack domestic animals, “Snow leopard” trial
operation to count them and illegal hunting in territories of Khovd,
Gobi-Altai, Bayankhongor, Uvurkhangai and Umnugobi provinces from
September 2009 to January 2010. As result of these surveys it has made
the following conclusions in the followings: Reason to hunt them illegally: the principal reason is that
administrative units have been increased and territories of
administrative units have been diminished. There have been four
provinces in 1924 to 1926, 18 since 1965, 21 since 1990. Such situation
limits movements of herdsmen completely and pastures digressed much than
ever before. As result of such situation, 70% of pastures become desert.
Such digression caused not only heads of animals and also number of
species. Guarantee is that birds such as owls, cuckoo, willow grouse in
banks of Uyert river, Burkhanbuudai mountain, located in Biger soum,
Gobi-Altai province, which are not hunted by hunters, are disappearing
in the recent two decades. For that reason we consider it is urgently
necessary for the government to convert administrative unit structures
into four provinces. This would influence herdsmen moving across
hundreds km and pastures could depart from digression.
Second reason: cooperative movement won. The issues related to management and strengthening of national
cooperatives, considered by Central Committee of Mongolian People's
Revolutionary Party in the meeting in March 1953 was the start of
cooperatives' movement. Consideration by Yu. Tsedenbal, chairman of
Ministers Council, chairman of the MPRP, on report "Result of to unify
popular units and some important issues to maintain entity management of
agricultural cooperatives" in the fourth meeting by the Central
Committee of Mongolian People's Revolutionary Party /MPRP/ on December
16-17, 1959, proclaimed complete victory of cooperative. At the end of
1959, it could unify 767 small cooperative into 389 ones, unify 99.3 %
of herdsmen and socialize 73.3 % of animals. The remaining of animals
amount 6 million 163 thousands animals, and equals to 26.7% of total
animals. This concerned number of animals related to the article
mentioned that every family should have not more that 50 animals in
Khangai zone and not more 75 animals in Gobi desert. It shows that such
number could not satisfy needs of family if such number is divided into
five main animals in separating with reproduction animals and adult
animals. So herdsmen started hunt hoofed animals secretly and illegally
in order to satisfy their meat needs. Those animals included main food
of snow leopard such as ibex, wild sheep, and marmot. Third reason is that the state used to hunt ibex, which are main
nutrition of snow leopards, every year. The administrative unit of the
soum pursued policy to hunt ibex in order to provide meat needs of
secondary schools and hospitals. That's why this affected decrease of
ibex population. Preciously from 1986 to 1990 the permissions to hunt
one thousands of wild sheep and two thousands of ibexes were hunt for
domestic alimentary use every year. Not less than 10 local hunters of every soum used to take part in big
game of ibexes. Also they hunted many ibexes, chose 3-10 best ibexes and
hid them in the mountains for their consummation during hunting.
Fourth reason: hunting of wolves. Until 1990 the state used to give
prizes to hunter, who killed a wolf in any seasons of the year. Firstly
it offered a sheep for the wolf hunter and later it gave 25 tugrugs /15
USD/. Every year, wolf hunting was organized several times especially
picking wolf-cubs influenced spread and population of wolves. So snow
leopard came to the places where wolves survived before and attack
domestic animals. Such situation continued until 1990. Now population of
ibexes has decreased than before 1990 since the state stopped hunting
wolves, population of wolves increased in mountainous zones. We didn't
consider it had been right since it was natural event. However
population of ibexes decreased. Fifth reason: Global warming. In recent five years it has had a drought
and natural disaster from excessive snow in the places where it has
never had such natural disasters before. But Mongolia has 40 million
heads of domestic animals it has never increased like such quantity in
its history before. We consider it is not incorrect that decrease of
domestic animals could give opportunities to raise population of wild
animals. Our next survey is to make attempt to fix heads of snow leopards
correctly with low costs.