University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Papers in Natural Resources Natural Resources, School of 5-30-2008 A Simple Morphological Predictor of Bite Force in Rodents Patricia W. Freeman University of Nebraska-Lincoln, [email protected] Cliff A. Lemen University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/natrespapers Part of the Natural Resources and Conservation Commons Freeman, Patricia W. and Lemen, Cliff A., "A Simple Morphological Predictor of Bite Force in Rodents" (2008). Papers in Natural Resources. 142. https://digitalcommons.unl.edu/natrespapers/142 This Article is brought to you for free and open access by the Natural Resources, School of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Papers in Natural Resources by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Published in Journal of Zoology 275:4 (2008), pp. 418–422; doi 10.1111/j.1469-7998.2008.00459.x Copyright © 2008 Patricia W. Freeman & Cliff A. Lemen; journal compilation copyright © 2008 The Zoological Society of London. Used by permission. http://www.interscience.wiley.com/jpages/0952-8369 Submitted December 14, 2007; revised April 7, 2008; accepted April 14, 2008; published online May 30, 2008 A Simple Morphological Predictor of Bite Force in Rodents Patricia W. Freeman and Cliff A. Lemen School of Natural Resources and University of Nebraska State Museum, University of Nebraska-Lincoln, Lincoln, NE, USA Corresponding author — P. W. Freeman, School of Natural Resources and University of Nebraska State Museum, 428 Hardin Hall, Uni- versity of Nebraska-Lincoln, Lincoln, NE 68583-0974, USA; email [email protected] Abstract Bite force was quantified for 13 species of North American rodents using a piezo-resistive sensor. Most of the species measured (11) formed a tight relationship between body mass and bite force (log 10(bite force) = 0.43(log 10(body mass)) + 0.416; R2 > 0.98). This high correlation exists despite the ecological (omnivores, grazers and more carnivorous) and taxonomic (Cricetidae, Hetero- myidae, Sciuridae and Zapodidae) diversity of species. Two additional species, Geomys bursarius (Geomyidae) and a Sciurus niger (Sciuridae), bit much harder for their size. We found a simple index of strength based on two measurements of the incisor at the 2 level of the alveolus (Zi = ((anterior-posterior length) × (medial-lateral width))/6) that is highly predictive of bite force in these ro- 2 dents (R > 0.96). Zi may be useful for prediction of bite force (log10 (Bite Force) = 0.566 log10 (Zi) + 1.432) when direct measure- ments are not available. Keywords: rodent, jaw, bite force, ecomorphology, biomechanics Introduction ing. We test this hypothesis with three indices that measure different aspects of strength. First the cross-sectional area Using a newly developed bite force sensor (Freeman & at location x on the jaw which is simply Lemen, 2008) we measured bite force in 13 species of ro- A = hw (1) dents. Part of our goal here was to see whether bite force in these rodents was correlated with their feeding ecology. We where h is the height of the beam and w, its width. A is an divided these species into trophic categories that included index of strength of a rectangular column to axially applied omnivores (Peromyscus, Perognathus, Dipodomys, Reithrodon- loads (Popov, 1999) because stress attributable to axial load- tomys, Spermophilus, and Onychomys), grazers (Microtus, Sig- ing is proportional to load/A. Note all strength indices used modon), nut eaters (Sciurus) and a fossorial species (Geomys) here are not absolute measures of strength. To obtain those along the same lines as Aguirre et al. (2002) in their study estimates the material properties of bone and teeth would of a bat community. Separation of these rodents into eco- have to be incorporated into the model. Our second index logical categories is a bit arbitrary (Landry, 1970), but we of strength is the section modulus Z (Popov, 1999): feel these categories have some validity. Z = wh2/6 (2) We also looked for morphological characteristics that can be used to predict bite force. We are not using a jaw where Z is an index of a rectangular cross-section’s ability mechanics approach where detailed information is needed to resist a bending moment. However, it does not take into on muscle mass, insertion points and input and output consideration the distance to the load. An index of bend- arms (Maynard Smith & Savage, 1959; Turnbull, 1970; Hi- ing strength that takes both Z and input arm into consider- iemae, 1971; Thomason, 1991). Ultimately such models try ation can be found by altering the stress equation for a rect- to combine force and input and output arms in a descrip- angular beam: tive model. Our approach is purely descriptive; to find an σ = l P/Z (3) easily measured morphological index that accurately corre- x lates with bite force measured in the field. Body weight can where σ is the bending stress in a beam at location x, lx is the be used to predict bite force. However, this overlooks pos- distance from the load to location x and P is the load. Equa- sible differences in species based on feeding ecology and tion (3) is intuitively satisfying because it is a ratio of bend- not size, as in the difference in the wolf and the bone-crush- ing moment (numerator) and cross-sectional strength (de- ing hyena (Binder & Van Valkenburgh, 2000; Meers, 2002; nominator), but it is not an index of strength. First, stress but see Wroe et al., 2005). We assume that the more pow- is inversely related to strength so we use the reciprocal of erful the bite, the stronger the jaws must be to resist break- stress. Second, equation (3) includes the load P which is not 418 S IMPLE M ORPHOLOGICAL P REDICTOR OF B ITE F ORCE IN R ODENT S 419 part of the beam’s strength. To fix this we substitute a load and incisor. Other regular shapes, such as an oval could of 1 into equation (3) to yield be used, but they would only differ by a constant from our calculations. After mean mass was found for a species, two S = Z/l (4) x museum specimens of similar mass were measured and av- where S is an index of bending strength. Note that equa- eraged to supply the morphological data. tion (4) is simply the ratio of a cross-section’s ability to re- Freeman & Lemen (2008) noticed that in some condi- sist a bending moment divided by the input arm length. It tions (cold stress), animals did not bite as hard. Therefore is this ratio that determines the relative strength of a cross- we only trapped on mild nights (temperature > 7 °C) for section relative to its input arm (Van Valkenburgh & Ruff, this study. There may still be a problem even when care is 1987). taken to reduce stress; if some animals do not bite at their Two locations on the dentary were chosen for measure- hardest, they will create outliers at the low end of bite ment: the base of the incisor and the midpoint of the di- force. To test for the problem of such outliers, we ran re- astema (Figure 1). We test the usefulness of these indices gressions on the data using both the standard least squares and body mass for predicting bite force. model (lm model in R; R Development Core Team, 2005) and a robust regression (rlm in MASS package in R us- Materials and methods ing Huber method). Further when computing relative bite force as residuals from the regression of bite force to body We measured bite force on 94 individuals of 13 species mass, we used both mean and median to test for the impact (Cricetidae: Microtus ochrogaster, Neotoma floridana, Ony- of outliers. chomys leucogaster, Peromyscus leucopus, Peromyscus manic- Although absolute bite force is important, we also found ulatus, Reithrodontomys megalotis, Sigmodon hispidus; Geo- the relative bite force by using the residuals from a linear myidae: Geomys bursarius; Heteromyidae: Dipodomys ordii, regression of the log 10 transformations of body mass and Perognathus flavescens; Sciuridae: Sciurus niger, Spermophilus bite force. What group of species should be used in the re- tridecemlineatus; and Zapodidae: Zapus hudsonius) by using gression? On the surface it seems all species should be in- a piezo-resistive sensor as described in Freeman & Lemen cluded. The problem with this approach is that two of the (2008). Animals were removed from the trap and tested im- larger species in our study were the durophagus S. niger mediately. In all cases bite force was measured at the inci- and fossorial G. bursarius. Because of their size and power- sors as the rodent bit the sensor. The strongest bite of each ful bites, they would have a large amount of leverage in the animal was recorded. Testing only lasted about a minute regression analysis. This solution would not give the best before the animal was weighed and released. Because the body mass to bite force relationship. Therefore we chose to bites of the larger rodents could cause damage, thin metal use only cricetids to define the regression line. The range in disks were used for a protective covering over the sensor size of these rodents incorporated nearly the entire range (see Freeman & Lemen, 2008). of sizes in the study, and these species were more similar in The rodent mandible is complex, but the distal end can phylogeny and ecological habit. be seen as a beam (Landry, 1970 and Figure 1). The beam We use the AIC method on the log 10-transformed re- is made up of the front incisor and the diastema portion of gressions for model selection (Burnham & Anderson, 2002).