Introduction

White-tailed deer (Odocoileus virginianus) is one of the most important wildlife species in Mexico due to the number of animals that are hunted annually (^{Clemente-Sánchez, F., Cessa-Reyes, V., Cortez-Romero, C., Tarango-Arámbula, L. A., & Arenas-Baez, 2015}). Established regulations for the harvest of white-tailed deer by institutions in North America usually allow different numbers of animals to be harvested depending upon their sex, having a preference for males (^{Lindsay & Belant, 2008}; ^{Riley et al., 2003}). It is necessary to obtain information about the number of females and males inhabiting an area to facilitate compliance with applicable laws and to estimate harvesting rates more accurately to avoid the hunting pressure over the males (Lindsay & Belant, 2008). Sex determination in wild populations is also essential for understanding the structure and dynamics of the population, habitat use, behaviour, and the mating system (^{Morden, Weladji, Ropstad, Dahl & Holand, 2011}; ^{Shaw, Wilson & White, 2003}). Historically, faeces have been used as indexes of animal abundance (^{Kobelkowsky-Sosa et al., 2001}; ^{Lounsberry et al., 2015}), a source for animal identification (^{Brinkman et al., 2010}), and as a means for determining diet (^{Homolka, Heroldová & Bartoš, 2008}), parasite infestation (^{Myers, Foreyt, Talcott, Evermann & Chang, 2015}), and hormone metabolites (^{McCoy & Ditchkoff, 2012}), which indicate physiological stress in the animals and their reproductive status.

Some non-molecular methods for sex identification that are used for several species of deer are difficult to carry out and are not entirely reliable; for example, direct observation of the genital region (^{Morden et al., 2011}), analysis of the hormone levels in the blood, and pelvic morphology have been used for several species of deer. These techniques cannot always be readily used in free-living animals (^{Shaw et al., 2003}) since the animals need to be captured, which is problematic or harmful (^{Han, Lee, Cho, Oh & Oh, 2009}). For these reasons, non-invasive monitoring techniques, such as deoxyribonucleic acid (DNA) faecal extraction or pellet morphometry, have been used (^{Morden et al., 2011}).

Using DNA extracted from epithelial cells shed from the intestinal lining present in faeces, it is possible to obtain an individual animal’s DNA and to genotype the animal (^{Huber, Bruns & Arnold, 2002 2003}; ^{Tolleson, Randel, Stuth & Neuendorff, 2005}). Since faeces can be easily collected without disturbing any species, genotyping using DNA obtained from faeces has become a promising tool in studies of behaviour, ecology, and wildlife management (Huber et al., 2003). The determination of sex from DNA extracted from the faeces of wildlife species has become more feasible recently (^{Han et al., 2009}; ^{Yamauchi et al., 2000}) due to the amplification of specific fragments of DNA associated with a sex chromosome, the SRY gene (^{Bryja & Konečný, 2003}; ^{Han et al., 2009}; ^{Yamauchi et al., 2000}), with PCR. The SRY gene produces a transcription factor of a high mobility group (HMG) that recognises specific DNA sequences and binds to them. This process begins with the embryonic differentiation of testicles. Therefore, it is a gene of males, and it is present in a single copy in the non-recombinant region of the Y chromosome in most mammals (^{Bryja & Konečný, 2003}).

Information obtained from faecal groups can be used to estimate ecological parameters in mammals, and this information can be an excellent tool for researchers, particularly if information about the sex and age of the animals can be obtained from the faeces (^{Sánchez-Rojas, Gallina & Equihua, 2004}). Several studies have been able to identify age using faecal pellet morphometry of white-tailed deer (^{Ezcurra & Gallina, 1981}), reindeer (Rangifer tarandus platyrhynchus) (^{Morden et al., 2011}), and Sonoran pronghorn (Antilocapra americana sonoriensis) (^{Woodruff, Johnson & Waits, 2016}). Additionally, the sex of moose (Alces alces) (^{MacCracken & Van Ballenberghe, 1987}) and mule deer (Odocoileus hemionus) (^{Sánchez-Rojas et al., 2004}) was determined by using the morphometry of faecal pellets. To determine the age and sex of deer populations based on the features of faecal pellets has significant implications for the management, use, and conservation of species, especially when the animals are difficult to track and see (^{Sánchez-Rojas et al., 2004}).

This work aimed to generate classification functions using neural networks and fuzzy logic approaches to predict animal sex from faecal pellet morphometry in white-tailed deer. Sex was used as the dependent variable and faecal pellet morphometry as the independent variable. Results obtained from the amplification of faecal DNA using the SRY gene marker were contrasted to obtain the percentage of correct classifications.

Materials and Methods

Results

Faecal DNA from 398 fresh faecal groups collected in both UMA were extracted. By amplifying the SRY gene marker, 385 faecal groups were assigned to one sex, achieving 96.7% success in the PCR analysis. By calculating the faecal pellets volume, 31 faecal groups were assigned as fawns, 241 as yearlings, and 113 as adults; at the same time, 219 faecal groups were classified as female and 166 were classified as male (Table 1).

Differences among seasons were found; autumn and summer showed higher values than winter and spring in width and radius (F _{3, 1148} = 3.8787, p < 0.009 and F _{3, 1148} = 3.8787, p < 0.0099, respectively). The length/width had higher values in winter and spring than in autumn and summer (F _{3, 1148} = 3.99, p < 0.0088). Regarding the interactive effects, it was only found differences between sex in width, radius (F _{6, 1148} = 33.9, p = 0.013), and length/width (F _{6, 1148} = 33.95, p = 0.0111) in the data from the adult white-tailed deer faeces collected in the winter. Since the statistical differences were only found in the interaction sex-age-season, specifically in faecal groups from adults collected in winter, the data from 23 faecal groups of adults collected in the winter were used to perform the sex classification functions.

The variable width showed the lowest (8.59%) coefficient of variation, and volume presented the highest value (22.10%). As age increased, the coefficient of variation values in all the morphometric variables increased (Table 2); however, homoscedasticity assumption was not violated.

For the neural network analysis, it was tested from two to 40 neurons in the hidden layer, and the model that included 22 neurons showed a lowest percentage error (5%). The weights, w_ij and w_jk, and the constants, α _j and α _k , were calculated, organised, and substituted in the model for neural network classification (Table 4), a predicted classification rate of 94.4% was obtained by correctly assigning four of the five faecal groups of the males and all of the faecal groups of the females. Through fuzzy logic analysis, a predicted classification rate of 86.9% was obtained by correctly assigning four of the five males and 16 of the 18 females (Table 3).

The membership values to convert the real variables to binary form to use in fuzzy logic were as follows: width ≥ 8.2 mm = 1 (male), length ≥ 15.2 mm = 0 (female), radius ≥ 4.1 mm = 1 (male), volume ≥ 730 mm³ = 1 (male) and length/width ≥ 1.8 = 0 (female).

Discussion

The use of faecal DNA for sex identification of individuals is a feasible and non-invasive tool to generate information of great importance for the management of wildlife species (^{Lindsay & Belant, 2008}; ^{Shaw et al., 2003}). Unlike other studies, which have relied on the amplification of two or more genes (^{Huber et al., 2002}; Lindsay & Belant, 2008; Shaw et al., 2003; ^{Yamauchi et al., 2000}), the amplification of the SRY gene marker to identify sex in the faecal groups was used. Since the SRY gene is exclusive to males, it generates enough information with a single pair of PCR primers. Lindsay & Belant (2008) observed that in white-tailed deer, with only the amplification of this gene, the sex of individuals can be identified from DNA in faeces. The lack of PCR product for the SRY gene marker is not the result of a failed reaction, but rather the absence of the Y chromosome (^{Huber et al., 2002}).

In this study, sex classification by faecal pellet morphometry was successful only with adult faecal groups collected in winter. The classification functions were able to correctly classify a high percentage of the adult faecal groups into sex by using morphometric variables from the faecal pellets. However, the neural network classification function was more accurate than the fuzzy logic classification function. In the classification performed by ^{Sánchez-Rojas et al. (2004)} for mule deer using mean stepwise discriminant analysis with the faecal pellet morphometry variables, adult males were correctly assigned in 100% of the cases, and adult females were assigned in 91.66%. By using fuzzy logic, they were able to classify 100% of the males and 75% of the females. ^{MacCracken & Van Ballenberghe (1987)} successfully identified the sex of moose faecal groups using a stepwise discriminant analysis in 92% of the males and 91% of the females. Finally, Yu-Chun et al. (2008) correctly classified faecal groups from eld’s deer (Cervus eldi hainanus) in 76.17% of males and 42.22% of females by discriminant analysis; also, they classified 19.49% of males and 20.02% of females by fuzzy analysis.

The variables that mostly contributed to the differentiation of the winter faecal groups of adult females and males collected with neural networks, in order of importance, were width, radius, length, length/width, and volume. Regarding the fuzzy logic analysis, the most critical variables to determine sex in the faecal groups were width and the length/width; and the less important variables were radius, length, and length/width. ^{MacCracken & Van Ballenberghe (1987)} classified the sex of moose by faecal morphometry with the variables volume and width-width₂ by using a stepwise discriminant analysis. ^{Sánchez-Rojas et al. (2004)} found that the best variables to classify sex in mule deer were width and volume in faeces by fuzzy logic and discriminant analysis. ^{Morden et al. (2011)} classified sex in reindeer with the combination of variables width, length, and depth in faeces using a discriminant analysis.

Differences between females and males were found only in the width, radius, and length/width variables in winter for adults were found in this study. Likewise, ^{Sánchez-Rojas et al. (2004)} found differences between age and sex only in the width and volume variables in the faecal pellets from mule deer in all the seasons they sampled. The morphometric method is based on the assumption that the measures of the faecal pellets depend on the body size of the individual, and this, in turn, depends on age and sex (^{Camargo-Sanabria & Mandujano, 2009}). ^{MacCracken & Van Ballenberghe (1987)} suggested that the pellet morphometry technique would work best in species that exhibit strong sexual dimorphism. White-tailed deer is a dimorphic species; this dimorphism could be more evident in winter, since this is when the breeding season occurs and the production of testosterone increases (^{Clemente-Sánchez et al., 2015}). Males have well-developed antlers, flared necks, and an accumulation of body fat to maintain themselves during the winter and breeding season (^{Dostaler, Quillet, Therrien & Côte, 2011}; ^{Galindo-Leal & Weber, 1998}). ^{Sánchez-Rojas et al. (2004)} attributed the success of their sex classification in the faecal groups of mule deer to the high degree of sexual dimorphism in the species. Since the faecal pellet morphometry technique has shown good results in species with marked sexual dimorphism, ^{Camargo-Sanabria & Mandujano (2009)} suggested that faecal pellet morphometry was not successful in their study, because white-tailed deer living in the tropical areas shows less sexual dimorphism than those in the north of Mexico, and they did not consider the seasons of the year or fawns in their classification function.

Additionally, seasonal vegetation changes in North America are well known. In Northern Mexico, in the summer or rainy season, the available vegetation becomes more abundant, and its quality increases. Meanwhile, in the dry season or winter, the number of forage species available decreases, and the quality of the plant species is reduced (^{Dostaler et al. 2011}). ^{Barboza & Bowyer (2000)} mentioned that increases in the size of the digestive tract are associated with seasonal vegetation changes in female white-tailed deer and with pregnancy and lactation in domestic ruminants. However, the digestive morphology may not change in males of dimorphic species. These vegetation changes are reflected directly in the defecation rate and faecal pellet size (^{Ball, 2010}; ^{Clemente et al., 2005}; ^{Tolleson et al., 2005}). ^{Alvarez (1994)} found seasonal differences in the morphology of the pellets of red deer (Cervus elaphus) and fallow deer (Dama dama). ^{Morden et al. (2011)} also found these differences between seasons, comparing the dimensions of the faecal pellets of reindeer. ^{Camargo-Sanabria & Mandujano (2009)} commented that faecal pellets in summer can be larger and present considerably more variation in their morphometry due to the change in diet resulting from the change in vegetation. In this study, faeces of the adults in the summer had the largest volume and width (table 2). With respect to the coefficients of variation, all the morphometric variables ranged from 9% to 35% (Table 2); meanwhile, ^{Sánchez-Rojas et al. (2004)} obtained CV of 5% to 23%. This indicated small or medium variance between the individual pellet groups. It was observed that, as the age increased, the CV was higher. The morphometric variable with the highest CV value in this study was volume. ^{Sánchez-Rojas et al. (2004)} found highest CV values in the same variable.

Regarding age groups, the average of the morphometric variables was always higher in the adults than in the yearlings and fawns. This assumption agrees with the findings by ^{MacCracken & Van Ballenberghe (1987)} for moose, ^{Camargo-Sanabria & Mandujano (2009)} for white-tailed deer, ^{Morden et al. (2011}) for reindeer, ^{Woodruff et al. (2016)} for Sonoran pronghorn, and ^{Hanya et al. (2017)} for sika deer. ^{Sánchez-Rojas et al. (2004)} found that in mule deer, the faecal pellets belonging to the yearlings were more rounded, and the length/width proportion was lower in the yearlings than in the adults, but no significant differences were observed. It was found in this work that, as age increased, the length/width proportion decreased, and the faecal pellets became more rounded in the males than in the females (Table 2).

Conclusions

Based on the statistical analysis results, differences between females and males in faecal morphometric variables were found only in faeces from adults collected in winter. This was caused due to the influence of the season over vegetation and the changes in diet, at the same time, over faecal pellets size mostly in the summer. Moreover, the pellet size was influenced for body size given by the age and sex of the animals. Then, the technique of faecal pellet morphometry to classify sex in faecal groups could be applied in adults surveyed in winter. Both classification functions, neural network and fuzzy logic, showed high percentage of successfully classification of faecal groups. However, the neural network function was even more accurate (94.4%) than the fuzzy logic (86.9%). Neural network sex classification function can serve as a tool to identify sex from faecal groups without disturbing or endangering the populations of white-tailed deer.