The issue/concern of animal bylaws came up at the Ottawa meet. Here in Hamilton there was a major change to the animal by-laws a few years ago. Here is in part what is in the by-law:

No person shall keep animals belonging to the following orders:
Anseriformes (e.g. ducks, geese, swans and screamers), except located on rural or
agricultural premises zoned under a City zoning by-law permitting such a
use;
Artiodactyla (e.g. cattle, goats, sheep, pigs, deer, elk, alpacas and llamas), except:
(a) a Vietnamese pot-bellied pig with a current, valid licence on February 8, 2012; or
(b) located on rural or agricultural premises zoned under a City zoning by-law permitting such a use;
Carnivora (e.g. otters, wolves, bears, coyotes, foxes, tigers, leopards, cougars, lions, lynx, mink, skunks, weasels, badgers, mongooses and racoons), except dogs, cats and ferrets;
Chiroptera (e.g. bats, myotis and flying foxes);
Crocodylia (e.g. alligators, crocodiles, gavials and caimans);
Edentates (e.g. anteaters, sloths and armadillos);
Galliformes (e.g. pheasants, grouse, guinea fowls, turkeys, chickens and peafowls), except located on rural or agricultural premises zoned under a City zoning by-law permitting such a use;
Lagomorpha (e.g. hares and pikas), except domestic rabbits;
Marsupialia (e.g. koalas, kangaroos, opossums and wallabies), except sugar gliders derived from self-sustaining captive populations;
Perissodactyla (e.g. horses, donkeys, jackasses, mules, zebras and ponies), except located on rural or agricultural premises zoned under a City zoning by-law permitting such a use;
Primates (e.g. chimpanzees, gorillas, monkeys and lemurs);
Raptors (e.g. eagles, hawks, falcons and owls), except as provincial falconry licence;
Rodentia (e.g. porcupines, prairie dogs, nutria and chinchillas) except Rodentia:
(a) where neither the female nor the male of the species exceeds or will exceed 1,500 grams in weight before or at maturity; and
(b) that are derived from a self sustaining captive population; Squamata (e.g. lizards and snakes) except:
(a) non-venomous snakes where neither the female nor the male of species exceeds or will exceed 3 metres in length from nose to tip of tail before or at maturity; and
(b) non-venomous lizards (not including Iguana iguana) where neither the female nor the male of the species exceeds or will exceed 2 metres in length from nose to tip of tail before or at maturity; or
Struthioniformes (e.g. ostriches, rheas, cassowaries, emus and kiwis), except ostriches, emus or kiwis located on rural or agricultural premises zoned under a City zoning by-law permitting such a use.
No person shall keep or permit to be kept an animal that produces any poison, venom or toxin, except Grammostola rosea (Chilean Rose), Brachypelma smithi (Mexican Red-Knee) and Avicularia avicularia (Pink-Toe) Tarantulas.
Despite sections 10.1 and 10.2, a provincially authorized wildlife custodian may keep an animal prohibited under this By-law in accordance with the authorization.
No person shall keep or permit to be kept any insect, spider or squamata permitted under this By-law except in an escape-proof enclosure.
No person shall keep or permit to be kept any lagomorph, marsupial or rodent permitted under this By-law except in a suitable enclosure

At the time, I ended up looking up most of the names as I had no clue what they really included. For example: Galliformes
The Galliformes are a clade of bird species of cosmopolitan distribution that, with the Anseriformes, belong to the branch Galloanserae. The group have more than 270 living species and includes the megapodes, chachalacas, guans, curassows, turkeys, grouse, New World quails, pheasants, partridges and guinea fowl. They are, with Neoaves, the two main lineages of Neognathae.