Here you will find links for your research on the roles of animals (wild and domestic) in the Ancient Roman world.
General:
http://www.societasviaromana.net/Collegium_VitaQuotidiana/pets.php
http://blogs.transparent.com/latin/part-i-of-ancient-roman-pets-popular-pets/
http://www.mariamilani.com/ancient_rome/ancient_roman_animals.htm
Cats:
http://www.playfulkitty.net/2014/09/16/cats-ancient-rome/
Dogs:
http://www.ancient.eu/article/184/
Pets in Egypt (influence on romans)
http://www.ancient.eu/article/875/
Pet epitaphs (gravestone inscriptions):
https://www.thedodo.com/9-touching-epitaphs-ancient-gr-589550486.html
Animals in the Colosseum:
http://www.tribunesandtriumphs.org/colosseum/wild-animals-at-the-colosseum.htm
http://www.livescience.com/53615-horrors-of-the-colosseum.html
http://www.smithsonianmag.com/travel/how-ancient-romans-got-wild-animals-colosseum-180955580/
http://www.metmuseum.org/toah/hd/play/hd_play.htm
https://en.wikipedia.org/wiki/Venatio
hunting:
http://www.liquisearch.com/boar_hunting/history/ancient_greece_and_rome
Hunting in the Roman world: anthropology, animal bones and ancient literature
http://www.endangeredspecieshandbook.org/persecution_roman.php
food (including animals):
http://www.crystalinks.com/romecuisine.html
http://www.the-romans.co.uk/food.htm
http://vroma.org/~plautus/foodweise.html
https://en.wikipedia.org/wiki/Ancient_Roman_cuisine
More scholarly:
http://penelope.uchicago.edu/Thayer/E/Journals/CJ/44/4/Household_Pets*.html
http://animalstudiesrepository.org/cgi/viewcontent.cgi?article=1011&context=acwp_sata