strain were assessed using standard t tests (state frequencies) or binomial tests (state compositions and transitions). The binomial test was conducted as follows: Let f1 and f2 be frequencies related to states 1 and 2, respectively, and N1 and N2 the number of occurrences. Let p~ f1N1zf2N2. N1zN2 If f1N1, f2N2,(N12x1) and (N22x2) are all larger than 5, then the statistic S~ rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃfﬃﬃ2ﬃﬃ{ﬃﬃﬃﬃfﬃﬃ1ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ follows a Normal law U(0, 1). pð1{pÞ N11 z N12 Correction for multiple observations was conducted using the Benjamini Hochberg procedure [25]. Briefly this procedure aims to control the false discovery rate (proportion of erroneous calls among all calls) in multiple statistical testing. Let p1ƒp2ƒ . . . ƒpm be the ordered observed p-values for each series of tests (e.g. tests of difference in transition probabilities between any two states) and q a false discovery rate threshold. If the set i=piƒ mi q is not empty then define k~max i=piƒ mi q . In this case the k most significant tests are called significant at the level q. Throughout the paper, q was set to 0.05. Results Maternal behavior in inbred and F1 hybrid mice In order to identify the period of the day (hour) where the highest amount of maternal care/behavior was observable in all four mouse strains, preliminary MANOVA of arched-back nursing, blanket nursing, and licking/grooming pups behaviors was performed. This analysis showed a main effect of hour (l = 0.831, F [3, 9] = 29.26, P = 0.001) for all behaviors analysed. Univariate results showed (Figure S1) that the first two hours of recording were different from the last two hours, with the highest amount of maternal behavior observable during the first phase of the daily observation. The following analyses were therefore performed on the behaviors recorded during the first two hours of the day. Two ANOVAs were performed on the number of pups of each litter. No effect of the strain was observed for this variable quantified in both inbred and F1 hybrid mothers. ANOVA of time in nest revealed a main effect of strain for inbred mothers (F [1, 50] = 34.3, P = 0.001) with C57BL/6 mothers showing more time in nest than BALB/c mothers (Figure 1A). No effect of strain was observed for the same variables measured in F1 hybrid mothers (Figure 1D). For inbred mothers, MANOVA of behavioral variables (see Table 1) revealed a significant main effect of strain (l = 0.103, F [20, 31] = 13.5, P = 0.001). Univariate results (see Table 1) showed that C57BL/6 mothers performed more arched-back nursing, licking/grooming pups, sniffing nest, carrying pup while BALB/c mothers performed more blanket nursing, eating, moving pups, rearing, digging, and sleeping. In order to evaluate if the strain effect observed for these variables was influenced by the size and sex ratio of each litter ANCOVAs of arched-back nursing, licking/grooming pups, sniffing nest, carrying pup, blanket nursing, eating, moving pups, rearing, and digging behaviors were performed. These analyses showed that the strain effect above described was not influenced by the size and the sex ratio of each litter. For reciprocal hybrid mothers, MANOVA of behavioral variables revealed a significant main effect of strain (l = 0.457, F [20, 56] = 3.3, P = 0.001). Univariate results (see Table 1) showed that C57BL/ 66BALB/c (B6xC) mothers performed more licking/grooming pups while BALB/c6C57BL/6 (CxB6) mothers performed more sniffing pups. ANCOVAs of licking/grooming pups and sniffing pups behaviors showed that the strain effect observed in reciprocal hybrid mothers was independent from the size and the sex ratio of each litter. For inbred mothers, repeated measures ANOVA revealed a significant effect of strain for licking/grooming pups (F [1, 20] = 50.5, HMM of Maternal Behavior P = 0.001; Figure 1B) and arched-back nursing (F [1, 20] = 14.8, P = 0.001; Figure 1C) with C57BL/6 mothers spending more time licking and grooming pups and performing arched-back nursing than BALB/c mothers. A significant effect of day was observed for licking/grooming pups (F [12, 240] = 3.73, P = 0.000; Figure 1B), and for arched-back nursing (F [20, 240] = 3.75, P = 0.000; Figure 1C) with these behaviors decreasing signifi- cantly during the postnatal period. For F1 hybrid mothers, repeated measures ANOVA revealed a significant effect of strain on licking/grooming pups (F [1, 18] = 7.91, P = 0.0115; Figure 1E), but not arched-back nursing (F [1, 18] = 0.63, P = 0.438; Figure 1F) with B6xC mothers performing more licking/grooming pups than CxB6 mothers. A significant effect of day on licking/grooming pups (F [12, 216] = 17.2, P = 0.001, Figure 1E) and arched-back nursing (F [12, 216] = 14.7, P = 0.001, Figure 1F) was observed with licking/ grooming pups and arched-back nursing decreasing significantly during the postnatal period. Together, these findings confirm previous reports of increased maternal care in C57BL/6 mothers compared to BALB/c mothers and demonstrate that only a small fraction of these differences are passed on to their reciprocal hybrid female offspring [3,6,10,15,16]. Building a robust hidden Markov model of behavioral sequences Based on our previous observations [10] we specified seven HMM states: blanket nursing (BLN), arched-back nursing (ABN), licking/grooming pups (LG), grooming (GRO), activity (ACT), eating (EAT), and sleeping (SLP). Initial conditions for the HMM were chosen consistent with our previous data (see Table S1, S2, and S3) [10] and a single final HMM, named MatHMM, was derived by application of the Baum-Welch algorithm to maternal behavior data from mothers of all four strains (Ntotal = 127) during the first postnatal week (Figure 2). We next tested whether our model MatHMM was sensitive to our choice of initial HMM architecture and initial model parameters. We show that, when the log-likelihood of the data converges to a plateau of about 2140000, which is the case for 11 out of 100 random initial models (Figure S2), all states of MatHMM, except GRO, are defined by the same probabilities of behavioral variables (Figures S3, S4, S5). This robustness to initial model settings is also true of state transition probabilities and initial state probabilities that do not vary much between MatHMM and the best randomized models (data not shown). Our model MatHMM with seven states fits the data better than MatHMM-derived models in which states ABN [resp. LG] and BLN [resp. GRO] were merged (see Table S4). In addition, we found that adding an eighth random state to MatHMM only leads to a small decrease of the BIC score (see Table S4), and that this modification does not change the structure of the final HMM (data not shown). HMM labeling of maternal behavior states To describe maternal behavior in more detail we used MatHMM to identify behavioral states and quantify their frequency, composition, and transitions. MatHMM (see Table S5, S6 and S7) was then used to label sequences of observed behaviors for each subject by applying the Viterbi algorithm (Figure 2). In this way, each observation in a sequence of maternal behavior was assigned an HMM state. HMM analysis of maternal behavior in C57BL/6 mice Initially we examined in detail HMM labelling of maternal behavior in the C57BL/6 strain. For illustration, several PLoS ONE | www.plosone.org 3 March 2011 | Volume 6 | Issue 3 | e14753