# Bite force quotient

Bite force quotient (BFQ) is a numerical value commonly used to represent the bite force of an animal adjusted for its body mass, while also taking factors like the allometry effects.
The BFQ is calculated as the regression of the quotient of an animal's bite force in newtons divided by its body mass in kilograms. The BFQ was first applied by Wroe et al. (2005) in a paper comparing bite forces, body masses and prey size in a range of living and extinct mammalian carnivores, later expanded on by Christiansen & Wroe (2007). Results showed that predators that take relatively large prey have large bite forces for their size, i.e., once adjusted for allometry. The authors predicted bite forces using beam theory, based on the directly proportional relationship between muscle cross-sectional area and the maximal force muscles can generate. Because body mass is proportional to volume while muscle force is proportional to area, the relationship between bite force and body mass is allometric. All else being equal, it would be expected to follow a 2/3 power rule. Consequently, small species would be expected to bite harder for their size than large species if a simple ratio of bite force to body mass is used, resulting in bias. Applying the BFQ normalizes the data allowing for fair comparison between species of different sizes in much the same way as an encephalization quotient normalizes data for brain size to body mass comparisons. It is a means for comparison, not an indicator of absolute bite force. In short, if an animal or species has a high BFQ this indicates that it bites hard for its size after controlling for allometry.
Hite et al., who include data from the widest range of living mammals of any bite force regression to date, produce from their regression the BFQ equation:
$BFQ=100\left({\frac {BF}{10^{0.5703(\log _{10}BM)+0.1096}}}\right)$
Or equivalently
$BFQ=77.7\left({\frac {BF}{BM^{0.5703}}}\right)$
where BF = Bite Force (N), and BM = Body Mass (g)

## Carnivore BFQs

| Animal | BFQ |
| Aardwolf | 77 |
| European badger | 109 |
| Asian black bear | 44 |
| American black bear | 64 |
| Brown bear | 78 |
| Domestic cat | 67 |
| Cheetah | 119 |
| Cougar | 108 |
| Coyote | 88 |
| Dhole | 132 |
| Dingo | 125 |
| African wild dog | 138 |
| Domestic dog | 114 |
| Singing dog | 100 |
| Arctic fox | 97 |
| Cape genet | 48 |
| Gray fox | 80 |
| Red fox | 92 |
| Gray wolf | 136 |
| Brown hyena | 123 |
| Spotted hyena | 124 |
| Jaguar | 134 |
| Jaguarundi | 75 |
| Leopard | 98 |
| Clouded leopard | 137 |
| Lion | 128.1 |
| Northern olingo | 162 |
| Sand cat | 137 |
| Sun bear | 160 |
| Least weasel | 164 |
| Spotted-tailed quoll | 179 |
| Tasmanian devil | 181 |
| Tiger | 139 |
| Thylacine | 166 |
Table sources (unless otherwise stated):

## Sex Differences for BFQ in Canids

In a 2020 paper, the results of an estimation of the BFQ of various canid species separated by sex were published. Below there is a table with the BFQ averaged from the BFQ for each espécimen of each sex and for each species. BFQ coming from a single specimen for each sex in a given species will be marked with an asterisk.
| Common Name | Scientific Name | Male BFQ | Female BFQ |
| Short-eared dog | Atelocynus microtis | 120.25 | 144.65 |
| Senegalese wolf | Canis lupaster anthus | 140.66 | 126.24 |
| *Golden jackal | *Canis aureus | *113.98 | *113.25 |
| Coyote | Canis latrans | 132.65 | 131.88 |
| Grey wolf | Canis lupus | 130.59 | 141.06 |
| Dingo | Canis lupus dingo | 133.67 | 127.57 |
| New Guinea singing dog | Canis lupus hallstromi | 130.26 | 107.31 |
| *Red wolf | *Canis rufus | *182.41 | *124.33 |
| Ethiopian wolf | Canis simensis | 144.27 | 158.21 |
| Crab-eating fox | Cerdocyon thous | 118.24 | 116.41 |
| Maned wolf | Chrysocyon brachyurus | 131.59 | 112.87 |
| Dhole | Cuon alpinus | 148.80 | 147.85 |
| Side-striped jackal | Lupullela adusta | 111.21 | 107.21 |
| Black-backed jackal | Lupullela mesomelas | 126.95 | 115.11 |
| Culpeo | Lycalopex culpaeus | 128.62 | 120.07 |
| *Darwin's fox | *Lycalopex fulvipes | *154.63 | *140.60 |
| South American gray fox | Lycalopex griseus | 135.27 | 124.87 |
| Pampas fox | Lycalopex gymnocercus | 127.1 | 116.76 |
| Sechuran fox | Lycalopex sechurae | 128.84 | 138.14 |
| Hoary fox | Lycalopex vetulus | 123.09 | 122.13 |
| African wild dog | Lycaon pictus | 144.71 | 146.08 |
| Common raccoon dog | Nyctereutes procyonoides | 136.49 | 134.94 |
| Bat-eared fox | Otocyon megalotis | 107.14 | 126.26 |
| Bush dog | Speothos venaticus | 160.28 | 154.63 |
| Gray fox | Urocyon cinereoargenteus | 146.30 | 121.51 |
| Island fox | Urocyon littoralis | 109.27 | 108.22 |
| Bengal fox | Vulpes bengalensis | 128.47 | 139.10 |
| Cape fox | Vulpes chama | 96.98 | 87.21 |
| Arctic fox | Vulpes lagopus | 120.59 | 115.34 |
| Kit fox | Vulpes macrotis | 109.77 | 110.99 |
| Pale fox | Vulpes pallida | 89.47 | 98.21 |
| Rüppell's fox | Vulpes ruepellii | 135.31 | 121.97 |
| Swift fox | Vulpes velox | 122.57 | 120.38 |
| Red fox | Vulpes vulpes | 116.25 | 118.97 |
| Fennec fox | Vulpes zerda | 113 | 129.62 |