Quantifying gender preferences in human social interactions using a large cellphone dataset

In social interactions between humans, gender and age play a key role in the communities and social structures they form and the dynamics therein. For the caller–callee interactions in mobile communication there are four fundamental possibilities, namely male to male, male to female, female to male, and female to female, which together with age, kinship, and different levels of friendships affect the strengths of social interactions, giving rise to a wide scope of human sociality. The studies of primate brain size and its relation to their average social group size suggest that humans are able to maintain of the order of 150 stable relationships (Dunbar number) [1–3]. In addition the Social Brain hypothesis suggests that on the basis of emotional closeness human social networks can be divided into four cumulative layers of 5, 15, 50 and 150 individuals, respectively [4]. The concept of emotional closeness is, in general, hard to quantify, but previous studies have shown how it can be associated with the frequency of communication between two individuals [5, 6]. This makes the concept quantifiable such that one can observe how much an individual shares social resources with his or her contacts of different gender and age.

Over the past decade or so, much research on human communication patterns has been done by using “digital footprints” data from modern communication technologies such as mobile phone calls and text messages as well as social media like Facebook, and Twitter [7–9]. Of these the mobile phone communication data of call detail records (CDRs) has turned out to help us in getting insight into the structure and dynamics of social networks, human mobility and behavioural patterns in much finer details than before [7]. It has also revealed how microscopic properties related to individuals translate to macroscopic features of their social organization such as networks. As a result of these studies we now have quite a good understanding of a number of structural properties of human social networks such as degree, strength, clustering coefficient, community structure, and motifs [10–12].

Apart from these basic structural properties of networks, more recent studies have given us insight into a number of other aspects of social networks, namely their dependence on temporal, geographic, demographic, and behavioral factors of individuals in the network [13–17]. One such observation pertains to the shifting patterns of human communication across the reproductive period of their lives, which appears to reflect parental care [18, 19]. Another is a study using the postal code information in the data to show that the tie strength is related to geographical distance [20]. In addition, it has been shown that there is a universal pattern of time allocation to differently ranked social contacts [21]. Finally, recent studies indicate variation in connections and the number of friends with the age and gender [22, 23]. The importance of the strength and significance of communication with top-ranked contacts have also been studied in detail [18, 22].

In the present study, we focus on measuring the relative strengths of the four possible pairwise caller–callee interactions over their lifespans as a function of the caller’s age. From the point of view of call initiation, we find that females play a more active role during their reproductive years as well as during their grandmothering period [24, 25]. The grandmothering hypothesis is usually studied in the context of human longevity and evolutionary benefits. The notion deals with the focus of post-menopausal on their grandchildren. In general, the social focus of women are known to shift from the opposite gender in the same age cohort, when they are young, to the age cohort of their children, as they grow older. We observe that while females of grandmothering age are found to give more attention to their children, males up to the age of 50 years still keep stronger connection with their spouses of slightly younger age. Furthermore, the fraction of calls to individuals of different generations indicates that mothers tend to call their daughters more than their sons, whereas fathers call their sons more than their daughters. For younger individuals, most of their calls go to contacts of the same generation, whereas older people call younger people more frequently. The calling activity of older adults with the younger individuals who are below or around their reproductive age would signify parental and alloparental care, that is, caring for the children of children. We group these kind of behaviour as affection flows downward.

In this study we analyse mobile phone communication records of a particular European mobile service provider containing time series of call detail records or CDRs of caller–callee pairs. This dataset also includes demographic information such as age and gender of the callers. By using the gender information we measure the relative strengths for the four basic calling pattern such that we count the total fraction of calls for the caller–callee pairs of the same or of different genders by assuming a cut-off for the minimum call duration. We analyse all the CDRs for the year 2007 on a month-by-month basis for more than 2.4 million subscribers where both the caller’s and the callee’s demographics are known, totaling over 30 million calls. Since datasets of this kind are susceptible to error due to multiple subscriptions, we filtered out customers who have multiple subscriptions under the same contract number. Our study based on CDRs allows obtaining anonymized data from a very large population, but is in contrast to small-scale studies where volunteers are recruited and cross-validation of results is possible by collecting information from the participants through questionnaires [21, 26].

In order to analyze the gender preferences of individuals in interaction with others at different stages of their lives we choose the age of the caller and count the total number of calls within a time window. We apply a threshold for minimum call duration, such that calls shorter than the threshold value are considered not to be indicative of emotional closeness while calls longer than that are taken to indicate a meaningful emotional or social exchange relationship between the caller and the callee. Then we calculate the relative probabilities for the four possible types of caller to callee interaction. As it is difficult to decide a priori where the borderline between meaningless and meaningful is, we will vary the threshold for minimum call duration in measuring how the probabilities of the four ways of interaction vary with age and gender of the callers.

In Fig. 1 we show snapshots of the four interaction types for a call duration threshold of one minute. By considering callers and callees between 20 and 70 years of age we have calculated the calling or interaction probabilities for the same and different gender pairs. Here the probability is determined as the ratio between the total number of calls to the specific age callee and the total number of calls to all the callees within the age range of 20 to 70 years. From these communication patterns, the signature of a generation gap becomes evident. For example, the calling pattern between two females exhibits a rather clear signature of being triple lobed with the side lobes separated from the same age group center lobe by a generation gap up and down. This is indicative of frequent interactions between mothers and their daughters over the two generation gaps.

For callers with age g, we first divide the (outgoing) calls into four sets according to the genders of the caller–callee pairs, namely, FF, FM, MF and MM, where ‘M’ denotes males and ‘F’ denotes females. Then we further divide the sets by the duration of the calls (t, measured in seconds). For a given duration t, we calculate the relative probabilities among the four possible caller–callee pairs such that, \(f_{\mathrm{FF}}(g,t)+f_{\mathrm{FM}}(g,t)+f_{\mathrm{MF}}(g,t)+f_{ \mathrm{MM}}(g,t)=1\). In case female-female pairs, \(f_{\mathrm{FF}}(g,t)\) = (total numbers of outgoing calls of duration t from female callers with age g to female callees)/(total number of outgoing calls of duration t from any caller (male or female) with age g), and likewise for other types of pairs. In Fig. 2 we show these probabilities as a function of the call duration t for different age groups of callers, i.e. 21–25, 31–35, 41–45, 51–55, 61–65, and 71–75 years. We find that the relative ranking between them is strongly dependent on call duration. At younger ages (21–25 years), the MM calls tend to be relatively short, with interactions peaking around 10 secs and being of the highest rank up to 100 secs then decaying, suggesting that these calls are concentrated on their same gender friends. However, as men age, they get married and change their interaction preference to their opposite gender partners (see the panels for the age groups of 31–35 and 41–45 years). At the same time the distribution of call duration becomes flatter making the average call duration longer, a trend also evident among the older age groups (51–55, 61–65, and 71–75 years). On the other hand, the ranking for the FF calls tend to be rather low for all the age groups up to a call duration of 100 secs. The distribution of call duration is initially quite flat and small in value, but it starts increasing at about the age of women bear their first child, peaking at around 1000 secs. This suggests frequent interactions between the daughter and her mother, and seems to indicate that the grandmothering effect has set in. As for opposite gender pairs, we find that below the age of 35 years, the FM and MF interactions show quite high values for medium to high call duration. This can be interpreted as an indication of strong bonding between spouses. But with age, the FM-interactions start decreasing while MF-interactions increase, thus showing inverse relationship from the age of 40 years onward for medium to high call duration. This observation suggests that as women age they shift their attention from their spouses to their children.

Next, aggregating calls over the different durations we calculate the relative probabilities as functions of age g, such that for a given g, we have, \(f_{\mathrm{FF}}(g)+f_{\mathrm{FM}}(g)+f_{\mathrm{MF}}(g)+f _{\mathrm{MM}}(g)=1\), where \(f_{\mathrm{FF}}(g)\) = (total numbers of outgoing calls from female callers with age g to female callees)/(total number of outgoing calls from any caller (male or female) with age g), and likewise. In Fig. 3, we depict these relative probabilities for the four caller–callee interaction categories as functions of the caller’s age, for call durations greater than 30 sec, 60 sec, 120 sec, and 240 sec, respectively. The probabilities are rather stable when the calls of very low duration are filtered out. If we concentrate only on the behavior observed for threshold values of 120 sec and 240 sec (see the two bottom panels), our observations are as follows: For individuals older than 30 years, MM interactions become less frequent, which can probably be attributed to men getting married and thus giving priority to their opposite gender spouses over the same gender friends. This picture is also supported by observing the age-wise variation of the MF-interactions, where we see that up to the age of 45 years men call their spouses more than they call others. However, MF-interactions also show a minimum around the age of 50 years after which they start increasing again from the age of 55 years on. This may be attributed to men’s more frequent interactions with women one generation younger which corresponds to the age cohort of the daughters. On the other hand, the FF-interaction curve starts from a low value at about 27 years of age, after which it shows a steadily increasing trend. This observation indicates again that before marriage, females call less frequently to other females. After the age of 27, the FF-interaction curve grows rapidly up to the age of about 65 years. This behavior lends support once more to the grandmothering effect. Finally, the curve for FM-interactions indicates that after the age of 35 years, the focus of women on their spouses starts progressively decreasing. A similar observation also presents itself when we consider only top-ranked calls (ranked by their call duration) as shown in the Appendix (see Fig. 7).

In Fig. 4(A), the fraction of calls having duration greater than 100 seconds (out of all the calls made) is shown as a function of the caller’s age. Here, the fraction of longer calls for the four different pairs of interactions all peak around callers aged 30 years, after which the interactions decrease till about 50 years of age, followed by an increase till about 60 years of age, at which point the interactions seem to plateau. It should be noted that, for the FF curve, the increase from 50 to 60 years of age can again be taken as clear evidence of grandmothering. In Fig. 4(B), we measure the average call duration as a function of caller’s age for the four different types of interactions of the same or different gender pairs. From the MM curve, it is evident that the average call duration for male-to-male calls is low throughout their lifespan. The FM and MF curves show that at younger ages (i.e. before marriage) both male-to-female and female-to-male participate in long phone calls. But after typical marrying age for this population (27 years, as indicated in the national statistics), call duration drops significantly. The FF curve shows that initially the fraction increases with age (up to the age of 40 years), then rapidly falls. It is nevertheless clear that after the age of around 35 years, the call duration for female-to-female calls is the highest among the four possible types of interaction, which again can be interpreted as a signature of the grandmothering effect.

In Fig. 5, we show the fraction of outgoing calls from a caller to a callee who is either one generation older or one generation younger. The caller–callee pairs with a generation gap are chosen such that the magnitude of the difference between the age of the caller and the age of the callee is greater than 20 years. Here we observe that FF-interactions always have the highest value for any age, which can be taken as evidence of a large amount of communication between mothers and their daughters. Before the age of 27 years (the average age of marrying in this population), measurement of MF interactions indicates that sons are also strongly attached to their mothers. After the age of 40 years, the MF and FM interactions are very close to each other, suggesting that sons get the same amount of attention from both parents. On the other hand, the tie strength between fathers and their sons are reflected in the curve for MM interactions, which show a similar trend as the other interaction types. Notice that female callers are, relatively speaking, closer to the other generation than the same age male callers. In addition, the calling patterns of older people suggest that sons and daughters get different amounts of attention from their parents. In other words, from the mothers’ point of view, daughters get more attention than the sons, while sons get more attention from their fathers than daughters do. We find that, at younger ages, the fraction of calls going from one generation to another is around 10% to 30% of the total number of calls. On the other hand, when the age of the callers reaches 60 years, they are found to mostly communicate with their children (ranging from 50% to 70%), which supports the claim that affection flows downward. A similar pattern emerges from an analysis of just the top ranked calls, as elaborated in the Appendix, see Fig. 8.

In this study, we have measured the relative interaction probabilities for the four possible caller–callee pairs of the same and opposite gender. We have observed that in general the interaction probabilities are strongly dependent on the age and gender of the caller in relation to the age and gender of the callee. Also, we observed the communication over the generation gap as depicted in Fig. 1 showing the lobed structure and in the Appendix in Fig. 9, where we depict the distribution of calls made by the callers of certain age to callees as a function of callees’ age showing it to be bimodal [18, 19, 22].

Our findings from the study of the distributions of call duration for different age groups of the caller (Fig. 2) shows that the MF interactions tend to increase with call duration up to age 50 years, suggesting that men have a strong emotional connection with their opposite gender spouse of about the same age. In contrast, the FM interactions indicate that women are not as active after the age of 35 years, and have a decreasing trend for medium or long call duration with age. On the other hand, the MM interactions show initially greater probability for short call duration at younger ages, after which this becomes least probable for medium and higher call duration for any age of the caller. The FF interactions start with the lowest probability of all at younger ages, then shows a steadily increasing trend for medium and higher call duration with the age of the caller.

In the investigation of the relative probabilities for the four types of interaction as a function of the caller’s age with calls above certain threshold value (30 sec, 60 sec, 120 sec and 240 sec) (Fig. 3), we show that the FF interactions have an increasing trend with the caller’s age. This is due to frequent interactions between the daughter and her mother, an indication that the grandmothering effect has set in. An opposite trend is observed for the FM interactions, i.e. the relative probability shows a decreasing trend with age. On the other hand, the MF interactions show a high probability for ages ranging from 20 to 50 years. After that, it shows a decreasing trend up to the age of 55 years, and then beyond that again shows an increasing trend. The MM interaction curve shows the weakest interaction after the age of 25 years.

The effect of the difference in the number of male and female subscribers on the counting of pairs and the results shown in either of Fig. 2 and Fig. 3 is understood with the help of the scores calculated using the null model. These scores reveal how the populations of males and females influence the counting of pairs. Moreover, zero being a reference for the score, the latter is able to differentiate between contrasting cases, that is between negative (below the expectation with respect to the null model) and positive scores (above the expectation). For example, in Fig. 6(A) that corresponds to Fig. 2, scores for female-female calling are found to change from negative to positive with age of the caller. Overall, the scores lend support to our original results yet bringing clarity on the nature of the results.

Looking at the fractions of calls of duration more than 100 sec as a function of the caller’s age (Fig. 4) revealed that for the FF interactions there is an increase from 50 to 60 years of age, which once again is taken as a clear evidence of grandmothering setting in. We have also found that on the basis of the average call duration that around 35 years of age the duration of female-to-female calls is highest among the four possible types of interaction. This can again be interpreted as a signature for the grandmothering effect. Furthermore, we showed (Fig. 5) that there is a fraction of total calls going from callers to callees who are either one generation older or one generation younger. Here we observed that for female callers the fraction of calls going to a different generation is, for all ages, always greater than for male callers. More precisely, the FF interactions show the highest probability, most likely reflecting strong ties between mothers and their daughters. On the other hand, at a younger age, a large fraction of calls go from males to females, suggesting that sons are strongly attached to their mothers before marriage. After the age of 40 years, the MF and FM interaction curves are very close to each other, suggesting that sons get the same amount of attention from both parents. More generally, we have found that younger callers, most of the calls (70–90%) to callees of the same generation. On the other hand, for older people, most of their calls go to their children (i.e. contacts who are younger by a generation), which supports the claim that affection flows downward. Broadly speaking, our conclusions regarding the preference of communicating individuals as a function of their age, and in particular, the preference of women in their post-reproductive period, is based on the observed variation in the quantities, namely the relative frequency of outgoing calls, the propensity to make calls of longer duration, and the proliferation of cross-generational calls. However, the consistency with alternative hypotheses could as well be investigated but those should be able to explain the patterns of communication taking into account the age dependent variation in kinship and different levels of friendship.

The advent of newer channels of digital communication in the last decade has rapidly supplemented the usage of mobile phones. The pattern of communication availing multiple modes, for example, voice calling in conjunction with text-messaging or through social networking services, is in turn able to characterize the nature of sociality [32–34]. However, the fact that variability in calls can also serve as an important factor, has been rather overlooked. In previous works by some of the authors we had focussed on undirected communication and tried distinguishing communication between peers, partners and kins for individuals of different gender and age [19]. Here, we investigate outgoing calls specific to gender and age, and consider duration of calls in the same spirit as multiple available channels. On one hand the current study stands consistent with the earlier works that revealed patterns in sociality like grandmothering, on the other the study might be indicative of gender and age differences in selecting different channels of communication. The understanding of the immediate social neighbourhood of individuals as well as the preferences in the style of communication would be valuable inputs to the developing fields of mobile health and medicine [35, 36].