and transitions between identified behavioral states. Surpri- singly, only a limited subset of these differences in maternal behavior were observed in reciprocal hybrid offspring, suggesting that the maternal effect on this behavior is limited to critical elements of the maternal strategy. However these differences were detected after HMM analysis and were not really ob- servable with classical statistical methods. We therefore demon- strate the power of HMM to extract behavioral patterns that are not revealed by simple frequency analysis alone and provide a detailed description of the maternal effect on behavior in mice. Materials and Methods Animals Three week old C57BL/6J@Ico (C57BL/6) and BALB/ cByJ@Ico (BALB/c) male and female mice were purchased from Charles River Laboratories (Calco, Italy). Reciprocal F1 hybrid females were obtained by breeding C57BL/6 females and BALB/ c males (B6xC mothers) and BALB/c females and C57BL/6 males (CxB6 mothers). To reduce differences in maternal behavior due to genetic differences of their offspring, maternal behavior of inbred mothers was assessed in C57BL/6 (N = 26; litter size = 6.3360.55) and BALB/c (N = 26; litter size = 5.9960.59) females mated at 8 weeks of age with BALB/c and C57BL/6 males, respectively. Maternal behavior of reciprocal F1 hybrid mothers was assessed in B6xC (N = 36; litter size = 6.8560.47) and CxB6 (N = 39; litter size = 6.7460.52) females mated at 10–12 weeks of age with C57BL/6 males. For all breeding, fathers were removed before parturition and mothers and offspring left undisturbed and without cage changing until postnatal day 21 at which time pups were weaned, housed 3– 5 per cage, and weekly cage cleaning was resumed. No special effort was made to normalize litter sex composition or size. Food and water were provided ad libitum, and mice were housed on a 12 h light/dark cycle with lights on at 7:00 AM. All animals were handled in strict accordance with good animal practice as defined by the relevant national and local animal welfare bodies. All experiments of this study were approved by the ethics committee of the Italian Department of Health and therefore conducted under license/approval ID #:91/2007-B, according with Italian regulations on the use of animals for research (legislation DL 116/ 92) and NIH guidelines on animal care. Behavioral observation Maternal observations (60 observations/hour) were performed for 3 h during the light period (10:00–11:00 AM, 2:00–3:00 PM, and 6:00–7:00 PM) and 1 h during the night period (7:00–8:00 PM) each day from postnatal day 1 to 19. All observations were conducted by V.C. The following behaviors were scored in the nest: arched-back nursing (mother is immobile and in a upright arching posture with rigid limbs placed directly underneath or slightly away from the body, head depressed, and with all or most pups attached to the nipples), arched-back nursing,half litter (more than half of pups outside nest), blanket nursing (mother is less immobile and in a low arching posture with some rigid limbs or lying flat on the pups with little or no limb support), blanket nursing,half litter (more than half of pups outside nest), licking/ grooming pups, licking/grooming pups,half litter, nest building, self grooming, sniffing pups, and sniffing nest. Time in nest was calculated by summing time spent in all these states. The following behaviors were scored outside the nest: carrying pups (retrieval of pups form outside nest), carrying tail, climbing (on the cage top), digging, drinking, eating, moving pups, rearing, self-grooming, sniffing cage, and sleeping. HMM of Maternal Behavior Statistics The effect of the hour of the day and strain on behavioral measures was first analyzed by multiple analysis of variance (MANOVA) followed by univariate ANOVA and in cases of significance (P,0.05), post-hoc comparisons using Duncan’s test. The effects of postnatal day and interaction between strain and postnatal day were analyzed by repeated measure ANOVA. Analysis of covariance (ANCOVA) was performed to evaluate if the litter size and sex ratio affect/influence the strain effect observed/detected. All statistical analyses were carried out with the help of Statistica (StatSoft, Tulsa, OK) and SPSS (SPSS, Chicago, IL) software. HMM analysis and statistics Sequences of observed behaviors for the training of HMM states were defined as consecutive behavioral observations taken once a minute for one hour. A hidden Markov model (HMM) is characterized by its state transition probability matrix A (chance to go from one state to another), its observation matrix B (contribution of each behavior to each state), and initial state probability matrix p (chance of being in a given state at the start of a sequence). In our analysis we defined seven HMM states: blanket nursing (BLN), arched-back nursing (ABN), licking/grooming pups (LG), grooming (GRO), eating (EAT), activity (ACT) and sleeping (SLP). A single HMM was derived by applying the Baum- Welch algorithm to observed behavioral sequences from mothers of all four strains starting from an initial HMM (A0, B0, p0). This algorithm is an iterative procedure in which the HMM matrices are re-estimated at each step n to increase the fit between the model and the data until it reaches an optimum [17]. The final HMM, MatHMM (Aend, Bend, pend) that corresponded to the optimal fit was used for our analysis. We tested the robustness of this MatHMM to the choice of the initial model. First we tested whether the final model matHMM depended on our choice of initial parameters (A0, B0, p0). For this we ran the Baum-Welch algorithm on the data from all four strains for 100 different initial models where all state transition, observation and initial state probabilities were assigned a random number between 0 and 1 following a uniform distribution. Next, to test whether the choice of seven states lead to the best model we computed the Bayesian Information criterion (BIC) [24] for the model MatHMM and models in which the two states ABN and BLN were merged and/ or the two states GRO and LG were merged. Briefly the BIC states that the best model is the one which minimizes the following quantity: BIC~{2 log Likelihoodzd log p: where p is proportional to the size of the data, d is the number of free parameters in the family of models and Likelihood is the likelihood of the data given the HMM, as computed through the forward-backward procedure [17]. In the case of Hidden Markov models, d can be calculated as follows: d~N{1zNðM{1ÞzNðN{1Þ: where N is the number of states and M is the number of distinct behavioral variables. Finally, MatHMM was used in conjunction with the Viterbi algorithm to assign HMM states to each observed behavioral observation. The labeling data was then used to calculate the frequencies, compositions, and transition probabilities among HMM states for each of the four strains. Significant effects of PLoS ONE | www.plosone.org 2 March 2011 | Volume 6 | Issue 3 | e14753