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.