Taccachantrieri, for the beginning - I don't buy your view that stereotypies (which you equal to pacing, which is wrong, btw.) are very invariable within species and related to species behavioral ecology.
Why? Because:
1) study which you read has layers upon layers of bad design,
2) In captivity, there is huge variation depending from age and sex, and also individual. And stereotypy in most individuals can be induced by poor management or reduced to nill.
3) In nature, many species of carnivore readily colonize very diverse habitats, changing territory size, behavior and even social system. So in fact, median or minimal territory is of little value.
How do hard substrates increase the rate of stereotypic behaviour? If anything the increased discomfort associated with walking over hard surfaces constantly should dissuade polar bears from walking back and forth. Not surprisingly when the Oregon Zoo introduced rubber flooring to replace their concrete floors activity levels of their elephants increased (Meller CL (Meller, Carnie L.), Croney CC (Croney, Candace C.), Shepherdson D (Shepherdson, David). 2007). Stereotypical behavior also increased because it was also more comfortable for the animals to engage in. If some Zoo's were to change their substrates and flooring in polar bear exhibits to softer substances I would actually expect polar bear pacing to increase not decrease! this suggests that a lot of polar bears are even worse off than we expect

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Because they give wrong simulation to feet, there is no comfortable resting place, they lack even this minimal variety of smell and touch of sandy/grassy surface. Zoos which changed concrete to soft substrate in all animals noticed improvement in behavior - except some ungulates which must wear hooves.
Snow Leopards are kept in very similar situations to other species of large solitary cats. If stress from being in unnatural social conditions contributed to their pacing than surely we would expect similar rates in other big cats like tigers and jaguars. In reality rates of stereotypical behavior are higher in certain species as can be shown in the following rates of stereotypical behavior used by Mason and Clubb (2007): Cheetahs 24.6%; jaguar 20.08%; tiger 16.43%; mountain lion 11.75%; and snow leopard 7.43%. Home range does show a correlation with these behavioral tendencies (all results are averages for the species and expressed as square kilometers): Cheetah 60; jaguar 54.3; tiger 67; snow leopard 38.9; mountain lion 37.8. Polar bears actually somewhat congregate around shores waiting for ice to form, and so are probably not any less social than other species of bear. Polar bears have the highest infant mortality of any bear in captivity and high rates of pacing. Most bears are kept in similar social situations so you cannot use polar bear captive social grouping as an explanation for their unnatural behaviors in captivity, however you could use the fact that they have larger home ranges and travel longer distances per day.
As far as enclosure size goes Jurek7 pay attention to the quote I gave and my comments on how snow leopard enclosures are actually much smaller than polar bear enclosures because it refutes the argument you're making in quite a tidy manner.
Taccachantrieri, first, I consider this data as artifact, because of non-randomly sampling, small samples and excluding non-pacing individuals.
Second, I consider this data as artifact, because territory size in the wild is so flexible. Serious scientist would not give average or minimal territory size for large carnivore. Average territory size of leopard? Where - in rain forests of India or marginal semidesert of Arabia? How to include vast areas where leopard territories were unstudied? With natural prey density, current density usually lowered by man, or animal exploiting man-made food source?
Finally, it is unrealistic to invent and refute rules to which each species can fit. Like that territory size important/important, because one species - snow leopard - doesnt behave this way.
Polar bears live in very open environments in the wild and feel very comfortable in vast rather bare spaces with long sightlines because of their camouflage. How can the fact that captive environments are so open increase their stress so significantly? I would certainly expect animals that live in very closed environments in the wild like rainforest's to feel more exposed and stressed in open captive enclosures than polar bears.
Two wrong points:
- I see no reason of your idea, that polar bears would unconditionally like open areas because they live in them. Do they also like white walls more than other colors?
- Problems for other animals are often: no resting places, no possibility to withdraw from conspecifics, little simulation.
The age argument falls through as well because age is somewhat reflected in phylogeny. Bears live longer than big cats, so age was actually controlled for in this experiment.
Age - I meant age of animal. Old animal which developed stereotypy may not change it. Surely, all carnivores are young, mature and aging?
About phylogeny - polar bears are actually phylogenetically nested among brown bears. Phylogenetical approach here is doubly wrong.
Sorry, this study is so full of wrong approaches that I cannot list them all. Not all are revelant to polar bears, but I just wanted to show you to treat studies with criticism and open head.
I have more faith in reports of enrichment, even anecdotal. Because these show actual success in reducing stereotypies in polar bears.
BTW, the same authors, I think, committed a study [BTW - are you professionally related to them?] comparing result of various enrichment. Food came as most effective, and toys as least effective - even common enichment.
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My own observation of bears and elephants is that pacing/weaving occurs often when animals not have access to all exhibit area. Especially, animals denied access to indoor area, often pace before closed doors.
I would definitely start practice of giving animals access to all exhibit space normally 24/365, except really extreme weather. If necessary, raise fences a little and install small light outside not to let animal panic in starless night. During cleaning time, I would distract animal closed away by small amount of food. I would limit practice of luring animals with food to get them in/out, perhaps restrict to give them special treats.