Abstract

Measuring the live body weight of large-bodied animals can be impractical when equipment needed to weigh individuals is inadequate or unavailable. My objective here was to develop a model to accurately estimate the live body weight of black bears Ursus americanus floridanus in Florida based on the relationship between scale weight and sex, morphometric measurements, and age predictor variables obtainable in the field. I used an information-theoretic approach to evaluate simple and multiple linear regression models with 70% of the data, and evaluated the best model in the set using the remaining 30%. A sex-specific model was sustained because the intercept and coefficient of age variable in female and male modeled relationships differed significantly. Chest girth2 was the best single predictor of body weight in each sex. A model including age, age2, and body length variables was better supported than chest girth2 alone. I also created a reduced model to estimate body weight when personnel may not have an opportunity to determine a bear's age. Even though there was decreasing support for the reduced model, differences between the observed and estimated body weight of all models applied to the validation data set were not significant. The 95% confidence interval on the bias of the best model ranged from −1.9 to 1.6 kg in females and −1.4 to 2.1 kg in males. The 95% confidence interval of the reduced model ranged from −1.8 to 2.3 kg in females and −2.5 to 0.5 kg in males. The body weight estimation models can be used to provide more live body weight data from handled black bears in Florida that are not weighed with a scale.

Introduction

Body weight is a particularly important measure of health for American black bears Ursus americanus, and serves as an indicator of the spatial and temporal variation in food habits (Mahoney et al. 2001; McLellan 2011), nutritional condition (Cattet 1990; Noyce and Garshelis 1994; Cattet et al. 2002), and growth (Mahoney et al. 2001; Bartareau et al. 2012), and influences reproductive and survival success (Elowe and Dodge 1989; Stringham 1990; Kovach and Powell 2003; Costello et al. 2009). Smaller females cease embryo development and, as body weight increases, litter size increases while interbirth interval and age of primiparity decrease (reviewed in Stringham 1990; Noyce and Garshelis 1994; Samson and Huot 1995). Male reproductive success is dependent on the ability to thwart competitors, and larger males gain access to more females in estrus (Kovach and Powell 2003; Costello et al. 2009). Collecting body weight measurement is therefore recommended during handling because demographic and reproductive variables are functionally dependent on weight rather than age.

The ability to directly measure live body weight of black bears using calibrated scales is impractical when equipment needed to weigh individuals is inadequate or unavailable (e.g., in large-bodied animals, in remote localities). As an alternative method, body weight estimation models have been created based on the relationship between known measures of body weight and one or more predictor variables that are obtainable in the field (reviewed in Swenson et al. 1987, Cattet 1990, and Baldwin and Bender 2010). Several different models have been developed in different parts of the species' range and sex, age, chest girth, and body length have all been shown to affect model accuracy. Models with multiple predictor variables are generally more accurate than any single-variable model because different morphometric measurements describe body shape better than a single measurement alone (Cattet 1990). Sexual and interpopulation variation in published models indicates that the body weight–morphology relationship may differ among discrete populations (Swenson et al. 1987; Baldwin and Bender 2010).

My objective here was to develop a model to accurately estimate the live body weight of black bears Ursus americanus floridanus in Florida based on the relationship between scale weight and sex, age, and morphometric measurement predictor variables easily obtainable in the field. This ability will be useful to personnel conducting field research when scale weight is impractical to obtain. It will also enable retrospective estimates of the body weight of bears in cases where sex, age, and morphometric measurements are available but the individuals were not weighed.

Methods

Data collection

Personnel from the Florida Fish and Wildlife Conservation Commission live-captured 124 female and 185 male black bears spanning the full geographic range of the species in Florida from 2000 to 2012 (Table S1, Supplemental Material). The capture and handling procedures followed a standard data collection protocol that was approved by Florida Fish and Wildlife Conservation Commission and is consistent with that of the Gannon and Sikes (2007). Individual bears were captured using physical restraint (e.g., Aldrich spring-activated foot snares, cage traps) and a pole or projectile syringe used to remote deliver immobilizing drugs (Kreeger 1996). Each bear was immobilized with either a mixture of tiletamine hydrochloride and zolazepam hydrochloride (Telazol®) or a mixture of ketamine hydrochloride (Ketaset®) and xylazine hydrochloride (Rompun®) following the guidelines of Kreeger (1996). While immobilized, the scale weight, chest girth, and body length were measured and a first premolar tooth was extracted. Body weight was measured to the nearest pound using calibrated hanging spring scales, and weights were converted to kilograms. As the bear was lying on its side, chest girth was measured to the nearest centimeter using a nonstretchable tape measure pulled tight and allowed to relax at the largest circumference of the thorax. Body length was measured to the nearest centimeter as the distance along the contour of the spine between the distal hairline on the snout and tail. Age was determined by Matson's Laboratory LLC (Milltown, Montana) from counts of cementum annuli in the extracted premolar tooth (Willey 1974). The age of bears, except cubs of known birth date, was adjusted to the month of sampling assuming that average birth date was 1 February (Garrison et al. 2007).

Data analysis and model building

I conducted data analyses and model building following the techniques reviewed in Snee (1977), Zar (1999), Burnham and Anderson (2002), and Gergely and Garamszegi (2011) using Microsoft Excel® (Microsoft Corporation, Redmond, WA) and Statistix® 9.0 (Analytical Software 2008). Data were divided into two distinct data sets. I created candidate models using a model data set composed of 70% of the data (n = 86 females and 129 males). To assess how accurately the best fitted model in the set will perform in practice to the population the sample was chosen from, the validation data set was composed of the remaining 30% of the data (n = 38 females and 56 males). I split the data randomly by age so that a wide range of ages was present in each data set and the few young and old bears would not bias the models. I compared observed body weight with the estimated value and used the residual for descriptive statistics.

I fitted body weights and predictor variables to simple and multiple linear regression body weight estimation models of the form Y = B0 + B1X1 + B2X2 + … + BnXn + e, where Y is the dependent variable body weight (kg), B0 is the intercept, Bn is the coefficient of independent variable, Xn is the independent variable, and e is the random error. The predictor variables for model building included sex (S = 0 female and 1 male), age (A = yr), age2 (A2), body length (L = cm), chest girth (G = cm), and chest girth2 (G2). I initially created sex-specific models because growth curves show large differences between the sexes in rate of body size gain and mature weight (Mahoney et al. 2001; Costello et al. 2009; Bartareau 2011; Bartareau et al. 2012). I tested for sex differences in model intercept and coefficient of predictor variables and combined models if they did not differ. I assessed the effect of age as a quadratic function, assuming a nonlinear increase in growth to an asymptote (Mahoney et al. 2001; Bartareau 2011) and decrease in weight associated with senescence (Noyce and Garshelis 1994; Costello et al. 2009). I assessed the effect of body length because it is an indicator of skeletal size and maturity (Mahoney et al. 2001; Bartareau 2011). I assessed the effect of chest girth because it is an indicator of tissue growth and nutritional condition (Cattet 1990; Cattet et al. 2002). I also created a reduced model to allow application in bears of unknown age.

I used analysis of variance (F) to assess the differences between sexes in morphometric measurements and size ratios (i.e., body weight:chest girth, body weight:body). I used a Pearson correlation (r) matrix to assess the degree of linear association between body weight and the morphometric and age predictor variables. I used the corrected Akaike's information criterion (AICc) and Akaike weight (wi) to evaluate the suitability of candidate models in the set based on a balance of model fit and the accuracy of estimates. I used the Shapiro–Wilk test (W) to determine whether the residuals conform to a normal distribution and that this assumption for linear regression was met. I used the coefficient of determination (R2) to assess the relative goodness-of-fit of models. I assessed the accuracy of the models as applied to the validation data through the mean residuals (difference between estimated and observed), standard deviation of the residuals (SD), and 95% confidence intervals of the residuals. I used a paired t-test to compare observed weights from the validation data to the weights estimated by the models. All values are presented as mean ± standard error (SE).

Results

Descriptive statistics

The sample of bears represented the population in Florida by sex, age, and morphometric measurements (Table 1). The ages of bears overlapped, though the mean age of females was significantly greater than males (P < 0.001). Body weight was the most variable morphometric measurement in both sexes followed by chest girth and body length. The mean body weight of males was significantly greater than that of females (P < 0.001), whereas chest girth (P = 0.399) and body length (P = 0.747) were homogenous between sexes. Males had significantly greater body weight:body length size ratio than did females (P = 0.018), whereas body weight:chest girth was homogenous between sexes (P = 0.089). Individual bears of a given body length differed in chest girth and weight. For example, among females that measured 149 cm (n = 4), chest girth ranged from 83 to 96 cm and scale weight ranged from 65.8 to 90.7 kg. Among males that measured 150 cm (n = 7), chest girth ranged from 80 to 102 cm and scale weight ranged from 56.7 to 103.4 kg.

Table 1.

Descriptive statistics for age and morphometric measurements of 124 female and 185 male black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where CI is 95% confidence interval, CV is the coefficient of variation, and F1,307 and P are the analysis of variance values comparing the differences between sexes.

Descriptive statistics for age and morphometric measurements of 124 female and 185 male black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where CI is 95% confidence interval, CV is the coefficient of variation, and F1,307 and P are the analysis of variance values comparing the differences between sexes.
Descriptive statistics for age and morphometric measurements of 124 female and 185 male black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where CI is 95% confidence interval, CV is the coefficient of variation, and F1,307 and P are the analysis of variance values comparing the differences between sexes.

Body weight estimation models

Pearson correlation coefficient values indicated that body weight was significantly (P < 0.001) correlated with all morphometric measurements, age, and each other (Table S2, Supplemental Material). Body weight showed the strongest correlation with chest girth (female r = 0.957, n = 124, P < 0.001; male r = 0.963, n = 185, P < 0.001) and body length (female r = 0.802, P < 0.001; male r = 0.878, P < 0.001). Body weight was also correlated with age, but less so in females (r = 0.555, P < 0.001) than males (r = 0.751, P < 0.001).

A sex-specific model was sustained because female and male models differed significantly in intercept (P < 0.001) and coefficient of age (P = 0.018) and body length (P = 0.009) variables (Table 2). The coefficient of the remaining predictor variables was homogenous between the sexes (P > 0.05). There was a high level of significant coefficients in predictor variables. Chest girth2 had the strongest relationship to body weight according to t-value.

Table 2.

Estimated beta, standard error (SE), t-value, and corresponding P-value for predictor variables in multiple linear regression models to estimate the body weight (kg) of 86 female and 129 male black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where predictor variables are age (A = yr), age2 (A2), chest girth (G = cm), chest girth2 (G2), and body length (L = cm).

Estimated beta, standard error (SE), t-value, and corresponding P-value for predictor variables in multiple linear regression models to estimate the body weight (kg) of 86 female and 129 male black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where predictor variables are age (A = yr), age2 (A2), chest girth (G = cm), chest girth2 (G2), and body length (L = cm).
Estimated beta, standard error (SE), t-value, and corresponding P-value for predictor variables in multiple linear regression models to estimate the body weight (kg) of 86 female and 129 male black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where predictor variables are age (A = yr), age2 (A2), chest girth (G = cm), chest girth2 (G2), and body length (L = cm).

The AICc and wi values indicated a preference for the same models as R2 and SD (Table S3, Supplemental Material). The R2 value indicated that chest girth2 described the greatest amount of variation in body weight in each sex (R2 = 0.944 female and 0.973 male). A sex-specific model including age, age2, and body length was better supported than chest girth2 alone or any other multiple predictor variable modeled relationships (wi = 0.986 female and 0.738 male; R2 = 0.962 female and 0.985 male) as follows:

 
formula
 
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The residuals of the models provided good dispersion about the mean and conformed to a normal distribution in both the model (female W = 0.969, P = 0.058; male W = 0.987, P = 0.251) and validation data set (female W = 0.955, P = 0.126; male W = 0.954, P = 0.051), indicating constancy of variance.

There was decreasing support for a reduced model excluding the effects of age (wi = 0.012 female and < 0.01 male; R2 = 0.956 female and 0.976 male) as follows:

 
formula
 
formula

The residuals of the reduced models conformed to a normal distribution in both the model (female W = 0.979, P = 0.195; male W = 0.995, P = 0.072) and validation data set (female W = 0.974, P = 0.496; male W = 0.959, P = 0.056). Sex differences in the intercept and coefficient of predictor variables in the reduced model were similar to that of the best model. The effect of age in the model was to increase the intercept and decrease the coefficient of chest girth2 and body length parameters.

The differences between the observed and estimated body weight was not significant in the model and validation data set (Table 3). The mean residual of my best model was −0.13 kg ± 0.86 in females and 0.32 kg ± 0.84 in males. The 95% confidence interval on the residuals of best model ranged from −1.9 to 1.6 kg in females and −1.4 to 2.1 kg in males. The 95% confidence interval on the residuals of the reduced model ranged from −1.8 to 2.3 kg in females and −2.5 to 0.5 kg in males.

Table 3.

Residual (Mean ± SE) and 95% confidence interval (CI) in body weight estimation model of black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where predictor variables are age (A), age2 (A2), chest girth (G), chest girth2 (G2), body length (L), paired t-test (t), degrees of freedom (df), and P-value comparing differences between body weight estimated by the model (n = 86 female and 129 male) and observed body weight from the validation data set (n = 38 female and 56 male).

Residual (Mean ± SE) and 95% confidence interval (CI) in body weight estimation model of black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where predictor variables are age (A), age2 (A2), chest girth (G), chest girth2 (G2), body length (L), paired t-test (t), degrees of freedom (df), and P-value comparing differences between body weight estimated by the model (n = 86 female and 129 male) and observed body weight from the validation data set (n = 38 female and 56 male).
Residual (Mean ± SE) and 95% confidence interval (CI) in body weight estimation model of black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where predictor variables are age (A), age2 (A2), chest girth (G), chest girth2 (G2), body length (L), paired t-test (t), degrees of freedom (df), and P-value comparing differences between body weight estimated by the model (n = 86 female and 129 male) and observed body weight from the validation data set (n = 38 female and 56 male).

Discussion

It is more difficult to directly measure a black bear's body weight than other morphometric measurements, so estimation has been undertaken with scale weight–predictor variable relationships using simple and multiple regression models in many black bear populations (Swenson et al. 1987; Cattet 1990; Baldwin and Bender 2010). An important question is whether results of the modeled relationships on the sample can be extended to the population from which the sample has been chosen. Previously, uncertainty in the selection of a given modeled relationship and model validation were overlooked and accuracy consisted of quoting the R2 values in the model data set. The application of modeled relationships without rational selection and independent validation of the obtained models could result in a model with biased parameter estimates and inaccurate inference on new subjects (Whittingham et al. 2006; Gergely and Garamszegi 2011). By using an information-theoretic approach to evaluate competing models and then comparing observed and estimated body weight measurements through a validation data set, I have shown that live weight of black bears in Florida can be estimated with a high degree of accuracy based on the sex-specific relationship between scale weight, morphometric measurements, and age predictor variables obtained in the field.

Previous body weight estimation models for black bears have been based on the strong relationship with chest girth (Swenson et al. 1987; Baldwin and Bender 2010) and improved by including body length and age predictor variables (Cattet 1990). Whether the model used differs between sexes is not known outside a few populations and there is no consensus. I found that there were enough significant differences between parameters in modeled relationships to necessitate the use of sex-specific models. My model including chest girth2, body length, age, and age2 predictor variables was better supported than any other modeled relationships in the model data set. The results indicate that morphometric data pooled across sexes and ages in modeled relationships concealed sex-specific size-at-age variability in body weight–predictor variable relationships and the accuracy of estimates was decreased. Even though there was decreasing support for a reduced model that can be applied to bears when age cannot be accurately determined, differences between the scale and estimated body weight of each model in the validation data set was not significant.

The proportion of a bear's body weight to its chest girth dimension was homogenous between females and males and this result signifies the strong correlation of weight with chest girth in each sex. In contrast, the proportion of body weight to length dimension was significantly greater for males than females, suggesting that limitations in some biological or ecological factor impede female growth. Generally, as a black bear's body weight is gained or lost, the thickness of the subcutaneous muscle and adipose layers increases and decreases (Cattet et al. 2002). The modeled relationships in this study show that bears of a given body length differ in weight, and chest girth measurements vary predictably as weights increase or decrease. Adding the predictor variable age as a quadratic function with chest girth and body length further improved the modeled relationships in ways assumed by body weight variation related to age. The coefficients of age predictor variables enumerate the significant sex-specific size-at-age variability in body weight. Sex differences in the coefficients of age parameters indicate that male-biased sexual size dimorphism in this species results in part because males grew faster and at an older age than females.

Management Implications

Many black bears are immobilized and handled annually in Florida, but their large size means they are not always weighed because the personnel often do not have the equipment needed to weigh individuals in the field. The Florida Fish and Wildlife Conservation Commission maintains a database that contains the needed chest girth, body length, and age data to estimate the body weight of many bears that could not be weighed with a scale. Although direct measurement using a calibrated scale is preferable to a body weight estimation model, the models presented can be used to provide more live body weight data from bears handled in Florida that are not weighed with a scale, and the estimate will be more accurate than visual estimates.

Supplemental Material

Please note: The Journal of Fish and Wildlife Management is not responsible for the content or functionality of any supplemental material. Queries should be directed to the author for the article.

Table S1. Data file (.xls) of sex, age, chest girth, body length, and body weight obtained from live captures of 124 female and 185 male black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida.

Found at DOI: http://dx.doi.org/10.3996/012016-JFWM-003.S1 (57 KB XLS).

Table S2. Pearson coefficient values for correlation between age and morphometric measurements of 124 female and 185 male black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida. All values P < 0.001.

Found at DOI: http://dx.doi.org/10.3996/012016-JFWM-003.S2 (53 KB DOC).

Table S3. Coefficient of determination (R2), standard deviation (SD), corrected Akaike's information criterion (AICc), and Akaike weight (wi) for simple and multiple linear regression body-weight-estimation models of 86 female and 129 male black bears Ursus americanus floridanus captured from 2000 to 2012 in Florida, where predictor variables are age (A), age2 (A2), chest girth (G), chest girth2 (G2), and body length (L).

Found at DOI: http://dx.doi.org/10.3996/012016-JFWM-003.S3 (72 KB DOC).

Acknowledgments

This study was made possible thanks to the Florida Fish and Wildlife Conservation Commission and many people who assisted with data collection. Thanks to B. Crowder, E. Leone, T. O'Meara, B. Scheick, Editor-In-Chief, Associate Editor, and three anonymous reviewers for constructive comments that improved the quality of the manuscript, and L. Pulliam for diligence in sourcing literature.

Any use of trade, product, website, or firm names in this publication is for descriptive purposes only and does not imply endorsement by the U.S. Government.

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Author notes

Citation: Bartareau TM. 2016. Estimating the live body weight of American black bears in Florida. Journal of Fish and Wildlife Management 8(1):234-239; e1944-687X. doi:10.3996/012016-JFWM-003

The findings and conclusions in this article are those of the author(s) and do not necessarily represent the views of the U.S. Fish and Wildlife Service.

Supplementary data