The stability of transient relationships

In contrast to long-term relationships, far less is known about the temporal evolution of transient relationships, although these constitute a substantial fraction of people’s communication networks. Previous literature suggests that ratings of relationship emotional intensity decay gradually until the relationship ends. Using mobile phone data from three countries (US, UK, and Italy), we demonstrate that the volume of communication between ego and its transient alters does not display such a systematic decay, instead showing a lack of any dominant trends. This means that the communication volume of egos to groups of similar transient alters is stable. We show that alters with longer lifetimes in ego’s network receive more calls, with the lifetime of the relationship being predictable from call volume within the first few weeks of first contact. This is observed across all three countries, which include samples of egos at different life stages. The relation between early call volume and lifetime is consistent with the suggestion that individuals initially engage with a new alter so as to evaluate their potential as a tie in terms of homophily.


Introduction
Humans are social animals and having strong and supportive relationships with others has large effects on both physical and mental health [31,27]. These social relationships are not static, but change over time due to two key processes. First, relationships have a natural tendency to weaken over time -to 'decay' [10].
Indeed, if no effort is made to maintain relationships, the level of emotional closeness between two individuals will tend to decrease [56] and the relationship will eventually drop out of the person's social network in terms of the meaningful ties they maintain with others [10]. Long-term studies of people's social networks (the set of relationships they maintain with their family and friends) show a degree of turnover in network members (alters), with some alters leaving the network and others joining [47,65]. Second, specific life events such as going away to study at university [56,51], entering a romantic relationship [35,59,43], having children [49,9], or getting divorced [42] can have an impact on the composition of social networks due to a decrease in the time available to maintain these relationships, or a change in the focus of attention (e.g. making new friends at university). What these various mechanisms highlight is that, despite the need and utility of stable relationships, over a period of time many relationships will cease to be active, i.e. many relationships are transient (e.g. Wellman finds that over a 10-year period, only about 27% of relationships remain active in Canadian adults [65]; see also [8] for a qualitative discussion).
Regardless of causal mechanisms, transient relationships form a considerable fraction of people's communication (see our results). They are also ubiquitous, judging by the number of studies that report them even when the research is focused on other types of relationships [10,47,65,56,51,49,9,42,60]. It is easy to appreciate that without them, adapting to the changing social needs of an individual would be impossible as this adaptation involves alters entering and leaving egos' social networks [60]. However, in contrast to longterm relationships, we know little about the amount of support they provide to a person, how many of them become long-term relations, or whether different individuals can handle more or less of them simultaneously.
In summary, we do not have a good understanding of transient relationships as part of dynamic ego social networks.
From a theoretical standpoint, the existing literature does not readily offer a clear picture or definition of transient relationships (only transient romantic relationships seemed to have received systematic attention [11]). On the one hand, the literature on relationship decay has identified a gradual decline in emotional intensity before the end of a relationship [10,56], suggesting that transient relationships may display a gradually decaying volume of communication. On the other, some research suggests that communication is set to an amount appropriate to the perceived quality of relationships, with longer-lasting relationships receiving a greater amount of communication [46,65,20]. In addition, the literature on homophily and friendship implies that an early and relatively fast assessment of relationships needs to take place in setting such a communication amount [41,20,4,37]. Under this picture, the volume of communication gauges the importance of a relationship [46,60] and the likelihood of the relationship ceasing after some lifetime. Thus, whilst research on emotional intensity indicates that relationships are constantly and gradually degrading in the absence of active maintenance, other research on homophily and patterns of communication suggests a rapid evaluation followed by a pattern of steady communication. Further complicating the situation, there is some evidence that emotional intensity and communication volume are monotonically related (see e.g. [51,60]). This begs the question: are these pictures consistent or contradictory?
Here, we study a variety of communication data sets, focusing on ties where measured communication is observed to cease, thus signaling a possible relationship hiatus or end. We call these relationships transient  [56]. However, this effect requires lifetimes to exceed a minimum threshold that we characterize and measure. We also find that the call volume an ego invests in a transient tie during the initial weeks of relationship is an informative quantity in estimating tie lifetime. Our results are remarkably robust across cohorts in different countries, of various age ranges, and under different life circumstances. Beyond providing empirical understanding about an important and overlooked class of social relationships, our study suggests that a full understanding of transient relationships requires collecting both objective (e.g. contact events) and subjective (e.g. emotional score) measures of relationship intensity.
Previous research on ego communication patterns has focused on a variety of related questions to the ones asked here such as overall properties of persistence and turnover in communication [60,45], phone communication survival with individual alters [44,50], or link prediction in broader communication contexts [3,52].
Whilst this research has provided new insights into both the patterns and dynamics of social relationships, it has not offered specific information on the temporal regularities of communication to individual alters, particularly transient ones.
Although in many areas the study of dynamic networks has gained considerable traction [30,22,54], analytical convenience has meant that many studies in the psychology literature on network structure treat relationships as if they are stable over time. Yet, in fact, they are intrinsically dynamic [65,60]. This dynamic property arises partly as a result of changing friendship opportunities and partly as a result of adjustments that people make over time in the value they place on individual relationships. Constraints on the availability of social time result in networks having a layered structure [28,62,38] between which individual alters are moved by increases or decreases in the time invested in them, including cases where communication virtually ceases leading to the effective removal of the alter from the layers. Understanding the processes involved in these decisions requires a better appreciation of the communication patterns involved.
It is important to note that the steadiness pattern we uncover here is not incompatible with the wellknown burstiness of human communication [6]. Instead, while burstiness indeed plays a role, especially at short time scales when the contrast between activity or inactivity is clearly demarcated, at longer temporal scales such burstiness leads to overall activity levels that can have their own long term patterns such as seasonality and trends. In this study, we are interested in this longer time scale.
Before moving on to the body of the article, we summarize how our findings contrast with the possible hypotheses that the current theory on relationship subjective decay suggests about transient relationships.
First, we find no gradual diminishing calling pattern trend. Second, the cessation of relationship communication is not generally presaged by reaching some low level of communication but, instead, is predicted by the volume of communication in the early periods of a relationship. Therefore, our results indicate that the view of transient relationships suggested by the literature on relationship emotional decay is incomplete.
Thus, the key aims of this study are to characterize the temporal communication patterns of transient alters, identify key variables and relations between those, and examine whether these patterns are consistent across different cohorts. We use three different mobile phone call data sets from the US, UK, and Italy, which include people of different ages, life stages, and cultural backgrounds. These data are from the time smartphones were not widely available in the respective countries and therefore do not suffer from the communication channel fragmentation of more recent data, where extensive use of multiple messaging services makes it more difficult to build up a complete picture of an ego's communication pattern to alters [5,53]. As a parenthetical note, the remainder is exclusively concerned with transient relationships, but we occasionally simply call them relationships for brevity.

Results
Consider an ego i ∈ E, where E is one of the cohorts we study (a data set or subset thereof). The set of alters of i is denoted A i . To develop a clear picture of how an ego-alter relationship evolves over time, we focus on two quantities: the first is the observed lifetime ℓ i,x of the relationship, i.e. the number of days, reduced by 1, alter x ∈ A i remained in ego i's network from their first until their last observed phone call. The second is the observed elapsed duration a i,x of the relationship at the time of a phone call, i.e. the number of days between the first and a subsequent call between i and x, where the first call is defined to occur at a ix = 0. By definition, 0 ≤ a i,x ≤ ℓ i,x . To refer generically to the elapsed duration and observed lifetime of relationships without specifying the ego-alter pair, we simply use a and ℓ without subindices. For ease of reference, the symbols with their definitions and terms used in this paper are summarized in Table 1.
Since we are interested in studying relationships in which contact stops for a sufficiently long time that one can assume that the communication has either ceased or become dormant, in all our cohorts we eliminate from consideration ego-alter pairs that have contact with each other within a time window of ∆t w days before the last day T E of data for cohort E; the larger ∆t w , the more stringent our filter is in terms of which relationships we select as having ceased. Note that many relationships that cease communication may be dormant for a considerably longer time than ∆t w , as they may stop communication well before the end of a data set approaches; ∆t w is therefore a lower cutoff of the duration of time without contact (over all our datasets, on average transient relationships cease communication 238 days before the end of their studies).
Our method follows a similar logic to [44,50], and although a small percentage of relationships could become active again as indicated in these references (3% after 6 months), the level of error this induces is very small; note that, since longitudinal data is always limited, other criteria to determine tie end is very difficult, or even impossible, to apply. Finally, for each cohort E, we limit the relationship lifetimes we study to a maximum value L E to avoid issues of poor sampling (see details in Supplementary Information, Sec. S1). These filters lead to three cohorts for the UK, Italy, and the US; the Italian cohort is filtered one more time for additional analysis (so called IT n subcohort, see Sec. Data below, as well as Supplementary Information, Sec. S1.4.2).
To provide a sense for the magnitude of communication volume to transient alters, we note that for ∆t w = 60 days, each cohort exhibits large proportions of activity dedicated to transient relations. For ties that involved more than just casual exchanges (defined here as at least 3 calls): i) in the UK cohort they take up ≈ 45% of overall communication, ii) in the US cohort they receive ≈ 27% of overall communication, and iii) in the Italy cohort they take up ≈ 17% of overall communication.  The transient condition is ∆t w = 60 days, and for cohort IT n , the gap between the entry of an ego and the acceptance of an ego-alter pair is set to ∆t s = 50 days. The number of resulting ego-alter pairs induced by our selection criteria is reported in Table 2. Robustness checks with different values for parameters ∆ℓ, ∆a, ∆t w , and ∆t s are shown in the Supplementary Information, Sec. S3. The curves are stable for medium and long lifetime groups. For curves displaying stable regions, we show a dashed line that represents b(ℓ), the average number of phone calls to alters of a given ℓ during the stable regime of communication.

Stable volume of calls during the relationship
In order to study the evolution of attention allocation from ego to its alters, we focus on call volume as a function of the elapsed duration and observed lifetime of relationships. Specifically, we measure for each ego i the quantityf i (a, ℓ), namely the per alter average number of phone calls to alters whose lifetimes fall within ℓ and ℓ + ∆ℓ when the elapsed duration of the relationship is between a and a + ∆a (for definitions of ∆a, ∆ℓ, see Sec. Methods). If communication volume exhibits any general trend over the duration of ego-alter relations,f i (a, ℓ) would reflect such trend (in the Supplementary Information, Sec. 3.7, we show that another possible way to measure communication, time spent talking, is highly correlated with the number of calls).
To aid in our study off i (a, ℓ), and because any single ego i has few alters with a given combination a, ℓ, we also measuref (a, ℓ), the average off i (a, ℓ) over egos with a, ℓ (using the same ∆a and ∆ℓ asf i (a, ℓ)).
Intuitively,f i andf capture stable estimates of the communication volume (attention allocation) egos invest per alter.
We first focus on the UK cohort (as described in greater detail in Materials and Methods and Supplementary Information, Sec. S1) which is extracted from a study of students in their last months of secondary school and their first entire year of university study [58]. From this study, we form a cohort comprised of the transient relationships that egos form with alters after they transition to university (6 months from the start of the study) [56], and that also satisfies the transient relationship filter explained above.
The new alters that emerge after 6 months of the start of the study are almost certainly new social relationships for the egos, as prior research has shown that almost no relationships survive after 6 months without communication [20,44]. In this cohort, a and ℓ, respectively, approximate very well the actual duration and lifetime of transient relationships. In Fig. 1 (UK), we presentf (a, ℓ) for three groups of transient relationships based on their lifetimes: short starting with ℓ = 0, medium starting with ℓ = ⌊(L E −∆ℓ)/2⌋, and long starting with ℓ = L E − ∆ℓ; in all cases, ∆ℓ = 50, and ⌊⌋ represents the floor function. We standardize these ranges for this and subsequent analysis off (a, ℓ) andf i (a, ℓ) to avoid idiosyncratic choices, but see our comments about lifetime ranges in the discussion of Fig. 2. First, we note that alters with longer lifetimes receive a greater volume of calls (i.e.f (a, ℓ 1 ) >f (a, ℓ 2 ) if ℓ 1 > ℓ 2 ). Second, lifetime groups exhibit an initial period of slightly elevated activity up to an elapsed duration we label a s and, after this period, medium and long lifetime groups exhibitf (a, ℓ) that stabilize with respect to a, remaining close to constant for a long range of values of a, orf where ℓ s is the value of lifetime when the steady behavior sets in (see below). In other words, for ℓ > ℓ s , f (a, ℓ) approaches an a-independent value b(ℓ) from about a s (which corresponds to a value of 3 days, as described in the Supplementary Information Fig. S8) to just before the observed lifetime (a ≳ ℓ). Both b(ℓ) and ℓ s are determined by finding the range of a where, respectively,f (a, ℓ) andf i (a, ℓ) become steady. Note that ℓ s marks the upper bound for another type of transient relationship with ℓ < ℓ s , one that is too short and ephemeral to achieve any stability; in Fig. 1 lifetime. Fig. 1 shows the equivalent analysis of the UK subcohort, now for IT n , with remarkably consistent results.
As we show next, the robustness of the behavior of transient relations is such that even a more approximate measurement of a and ℓ continues to be informative. In the two bottom panels of Fig 1, we presentf (a, ℓ) for both the Italian and US cohorts still restricted to transient relationships but without restricting the timing of the entry of ego-alter pairs. The communication patterns in these cohorts are once again consistent with those of the UK and IT n . This should not be surprising because, given that one is selecting for transient relationships, the properties they possess lead to the same qualitative patterns (steadyf (a, ℓ) with a growing tendency as a function of ℓ). The nature of the approximation in using these cohorts is reflected in the measurement of ℓ, particularly if it is to be interpreted as actual lifetime of a relationship. If we definel and ℓ as, respectively, the actual and the observed lifetimes, then the Italian and US cohorts can have examples of ℓ > ℓ for particular relationships, whereas for the UK and IT n , one expectsl ≈ ℓ. In reality, only a fraction of ego-alter pairs in the unrestricted Italian and US cohorts are affected by this, because many relationships indeed start a considerable amount of time after an ego enters a study (average entry day per cohort: 119 UK, 287 IT n , 292 IT, and 283 US; complete distributions found in Supplementary Information, Fig. S2).
Below, we take advantage of the robustness with respect to the measurement of ℓ to perform the analysis leading to Figs. 4 and 5 with the UK, Italy, and US only since they provide larger statistical sampling.
As noted above, b(ℓ) is observed to increase as a function of ℓ. To provide further evidence for this observation, we present  Alter lifetime b( ) estimation UK IT n IT US Figure 2: b(ℓ) as a function of ℓ obtained through the stable region average method. The vertical axis is in logarithmic scale. Clearly, b(ℓ) has an increasing trend with respect to ℓ, with minor exceptions. The UK and US cohorts display a faster increase than IT and IT n . This could be a consequence of specific differences between details of the cohort participants, such as country, age, and/or personal circumstances of the participants; for example, since the Italian cohort is focused on adult parents with pre-teenage children, these participants may have less available time to invest in phone communication.
Whilef (a, ℓ) allows us to describe the temporal patterns of communication more easily, this is an average quantity over egos and therefore may not be representative off i (a, ℓ). However, it is the latter quantity that genuinely interests us because it captures a more accurate picture of how each ego generally behaves with its alters, i.e., what are the trends in communication over time. To examinef i (a, ℓ), we carry out two analyses.
The first one consists of determining the level of steadiness off i (a, ℓ) as a function of a. This is done ego by ego, taking for each time seriesf i (a, ℓ) two parts of equal duration in a around the mid-point of the series and excluding the first (a = 0) and last (a = ⌊ℓ/∆a⌋∆a) points (details found in Methods). The two ranges of elapsed duration generate for each ego two samples off i (a, ℓ) at points in a within each of the periods, and we perform a Kolmogorov-Smirnov test to determine if the values of the two samples come from the same distribution. Fig. 3A captures the results of the test. Overwhelmingly, the test shows non-significant differences between the values off i (a, ℓ) before and after the mid-point, ego by ego. Moreover, the average  Supplementary Information, Fig. S15), not merely rejecting the possibility of change, but confirming a high probability that communication volumes remain largely unchanged between time periods. In other words,f i (a, ℓ) remains steady between the first and second periods of the lifetime. The second analysis pertains to the robustness of b(ℓ) as a good approximation forf i (a, ℓ) or, more precisely, that each individualf i (a, ℓ) does not deviate much from b(ℓ). We test this by calculating b i (ℓ) for each ego and form its distribution over i (see Fig. 3B). The results show that indeed the values of b i (ℓ) are typically close to those of b(ℓ) and, therefore, can be treated as approximately equal, i.e.
The results illustrated by Figs. 1, 2, and 3 together support the following interpretations. First, the pattern of communication that each ego maintains with its transient alters does not exhibit systematically increasing or decaying trends, that is, no trend is dominant (unless ℓ < ℓ s , in which case there do not seem to be stable relationships). This steadiness due to the absence of trends is strongly supported by the lack of statistically significant results, and indeed large p-values approaching 1, from the Kolmogorov-Smirnov test comparing the first and second time periods of each ego's call volumesf i (a, ℓ). The steadiness is a surprising result that indicates that communication related to transient relationships does not tend to gradually fade away in parallel with measures of emotional closeness [56]; when communication ceases, it appears to do so without warning. Second, the similarity between b(ℓ) and the set of b i (ℓ) (that is, b i (ℓ) ≈ b(ℓ)) shows that the b i (ℓ) follow a growing trend with ℓ. This trend, displayed in Fig. 2   Box plots for all cohorts using the 1.5 interquartile range convention for p-values from Kolmogorov-Smirnov tests for egos in medium (teal) and long (purple) lifetimes in all cohorts. The per alter call averagesf i (a, ℓ) are divided into two equally-sized ranges of a, the early range ∆a ≤ a < ⌊(1/2) (⌊ℓ/∆a⌋ − 1)⌋∆a and the late range ⌊(1/2) (⌊ℓ/∆a⌋ − 1)⌋∆a ≤ a ≤ ⌊ℓ/∆a⌋∆a − ∆a). Large p-values mean that the early and late ranges off i (a, ℓ) are not distinguishable, and thus, show no trend with a; small p-values mean there is a trend in a. We draw a dashed line at the 0.05 significance threshold and the averages over all egos are represented with the symbol ×. As it is clear from the plot, the vast majority of egos show no trend with a. Panel B: Average values of b i (ℓ) (circles) and standard error of the means (whiskers) for medium (teal) and long (purple) lifetimes for all cohorts. Superimposed to each circle and associated whisker is a symbol × that represents the value of b(ℓ) for the corresponding cohort, which matches well the averages of b i (ℓ) across cohorts and lifetimes.

Survival of alters
The increase of the b i (ℓ) with respect to ℓ suggests that it may be possible to estimate ℓ for transient with ℓ suggests that, for a randomly chosen x ∈ A i , g i,x is likely to increase with ℓ. To confirm this, we define the probability P (a | a o , a f , g) over a set of egos (cohorts or combinations thereof) and their transient alters with lifetimes ≥ a o that one of those alters, randomly chosen, with call volume g within the window a o ≤ a ≤ a f is still active for elapsed durations a > a o (note that a can be smaller or larger than a f ). The intuition of this quantity is that if we take, for example, the number of calls g(a o , a f ) placed by an ego to one of its alters in a given period of the relationship (when a is between a o and a f ), the probability that the relationship will still be active for a > a o would grow with the number of calls g(a o , a f ) received by the alter; in other words, the more calls received, the longer the lifetime. The period comprised by a o ≤ a ≤ a f can be chosen with some level of flexibility, but if it corresponds to an early period in the observation of the relationship (for example, the second complete month of activity), it may provide an early forecast for the lifetime of the relation. Due to the discreteness of the g and the finite sample size, we slightly modify the probability we study to include a range of values of g, and represent the quantity by P (a | a o , a f , γ), where γ characterizes a range of values of g (specifically, γ is defined as the exponent characterizing the bin 3 γ ≤ g < 3 γ+1 ).
In Fig. 4, we combine the UK, Italy, and US cohorts to show that there is a monotonically increasing relation between P (a | a o , a f , γ) and γ, i.e. that the survival probability of a specific alter in an ego's network grows based on the number of calls ego makes to alter between days a o and a f (here taken to be 30 and 60, respectively) of the observed relationship. The monotonic behavior is robust to different choices of parameters and cohorts (see Supplementary Information, Fig. S18). Note that we deliberately used an extremely simple test that captures an early period of relationships, even including the challenging choice of a o , a f < ℓ s which means that many alters we consider do not reach steadiness. Nevertheless, the measurement clearly shows the monotonicity of P (a | a o , a f , γ) with γ. Since this survival analysis is meant to illustrate the relation between ℓ and g, we refrain from developing this point further, as a more precise prediction of the continuation of relationships may require the use of additional variables beyond call volume. A selection of such variables may be informed by several considerations, including other work that has explored the related (but not identical) question of alter persistence [50]. 1 ≤ g < 3 3 ≤ g < 9 9 ≤ g < 27 27 ≤ g < 81 We use the combined data for UK, Italy and US, and therefore, we only look at relationships active for ℓ < L US = 220 days or less, in order to include data for all three cohorts. The bins represented by γ as the exponent in 3 γ ≤ g < 3 γ+1 are γ = 0, 1, 2, 3. As γ increases, the probability of survival also increases, i.e. for

Relation between early call volume and relationship lifetimes
The results displayed in Fig. 4 demonstrate that knowing g i,x (a o , a f ) for relationship i, x provides information about ℓ i,x . Next, we perform two analyses that further illustrate and quantify this.
First, we present the symmetric uncertainty U (ℓ, g) between the two random variables ℓ and g measured for each ego-alter pair in each cohort as well as for all unique cohorts combined. This quantity ranges from 0, when ℓ and g are independent, to 1, when ℓ gives complete information on g and vice versa. Concretely, U is a monotonically increasing function of how tightly interdependent two variables are to each other and it is therefore a function of the joint distribution of the variables. Symmetric uncertainty is a normalized version of the more well-known concept of mutual information I(ℓ, g) (see Sec. Methods). Combining all cohorts, U (ℓ, g) = 0.09, while separate cohorts yield U (ℓ, g | UK) = 0.3632, U (ℓ, g | IT) = 0.1044, U (ℓ, g | IT n ) = 0.0998, and U (ℓ, g | US) = 0.1597. Although these values are not near 1, they are nevertheless quite significant, and to interpret them we must take into account that g is measured very early in relationships, ignoring other variables related to the value of ℓ [50].
The interpretation of Fig. 4, along with the consistency of the results over various cohorts, suggests another interesting possibility: by quantifying the behavior of one cohort, one may be able to predict the behavior of another. In our final analysis, we examine whether P (a | a o , a f , γ) calculated from the combined cohort made of the US and UK data sets can predict the behavior of the Italian cohort.
The results of our analysis are shown in Fig. 5, generated as follows: combining the US and UK cohorts, represent, we obtain the ordered sequence yellow, purple, teal, and red. This order of colors is the same we encounter as we travel the contour map in the direction of increasing a, which means that longer lifetimes are less probable. However, note that we can travel along the increasing a direction on a variety of parallel paths each corresponding to a fixed value of γ. Since the lines that separate the colored regions of the contour map bend upwards as γ increases, it means that traveling in the increasing a direction along a line that has a large fixed γ, the probability of survival decays more slowly with increasing a, indicating that lifetime increases with increased calling in the period between a o and a f .
To understand the connection between the Italian cohort (represented by the symbols in the panels of  The match in location between the symbols and the colored regions means that the behavior of different cohorts is consistent, supporting the reliability of g as a helpful predictor of ℓ.

Discussion
In this study, we use three mobile phone data sets from the UK, US, and Italy to examine the temporal evolution of communication between an ego and those of its alters that show a considerable communication which has been previously associated with further longevity in relations [56], and sampling of the reasons why people effectively cease to communicate with their alters. Indeed, understanding the interplay between objectively and subjectively measured relationship characteristics may be relevant to understand a variety of aspects of human communication, including how transient and long-term relationships are associated with well-being [27].
It is reasonable to think that our definition of transient relationships will require further qualitative and quantitative studies because, as research into short-and long-term romantic relationships demonstrates [11], At a practical level, our results also have implications in designing research protocols, because they suggest that even relatively short time series of mobile data (say between 100 and 180 days, but above the ℓ s limit) are sufficient to distinguish among alters who will go on to have different lifetimes in the network over a longer time period. As participant drop-out is a key issue in longitudinal studies [34,40], this finding may enable researchers to design studies that optimize the balance between the length of the study and the likelihood of participant drop-out.
Whilst we found robust relationships between early call volume and lifetime in transient relationships in all three countries, there were some limitations to this study that may have impacted our research findings.
First, the focus of this study was on understanding the temporal patterns of communication in transient relationships independent of individual characteristics. Thus, factors such as gender [23,15], personality [13,61], or whether a relationship is between friends or romantic partners [15,58], may all affect these temporal patterns of communication. Therefore, future research could examine how ego and alter characteristics may modify the patterns we have identified. Second, given our initial motivation for testing whether gradual decay in subjective ratings also translated into objective gradual decay in communication volume, we focused our study on patterns of call volume. However, as has been shown in the context of related questions [50], different characterizations of temporal signals may be informative. In the future, an expanded exploration of different temporal characterizations of communication in transient relationships may provide further valuable information about how such relationships evolve. Third, the lack of data that couples high temporal resolution subjective ratings with call patterns prevents us from understanding subjective ratings at a level of detail equivalent to that of calling data. Until such data are available, our understanding of the mismatch between objective and subjective measurement of transient relationship temporal behavior will remain unclear.
Another question pertains to patterns of communication as these increasingly shift from mobile calls and texts to messaging platforms and social media sites such as Whatsapp [5], Twitter, Instagram [53,25,32], and WeChat [48]. The diversity of these platforms makes collecting communication data more complex than relying solely on mobile data, but the development of applications that passively collect accurate data on mobile application use provides new opportunities for research in this area [21,63,55]. This variety of platforms and channels is not relevant to the present study due to the time frame when our data were collected (before the widespread use of smartphones in the respective countries). However, based on the fact that communication regularities seen in phone calls also appear in channels such as email [24] and Facebook [18], once the various channels of communication are aggregated, the overall signal may show a great deal of similarity with our present findings.
The connection between early call volume and lifetime of transient relationships may suggest support for a description of the effect of homophily in relationships called the "Seven Pillars of Friendship." This description is made up of a set of seven cultural dimensions that define the individual and the cultural community they belong to [20]. These dimensions include: dialect, place of origin, career trajectory, hobbies/interests, moral/religious views, musical tastes, and sense of humour. Friendship quality has been shown to depend on the number of these friendship dimensions that an ego and a particular alter share [14], reflecting the extent to which friendships are dominated by homophily -the tendency for 'birds of a feather to flock together' [14,16,41]. It has been suggested that, after first meeting, dyads initially devote time to checking out each others' respective positions on the seven pillars, and then adjust their rate of contact to that appropriate for the quality of relationship defined by the number of pillars they share [62,16].  The UK data set is further filtered (as explained in Sec. Results) to ego-alter pairs that appear only after 6 months of the study, when participants begin university study. We also exclude relationships with less than 3 calls since such relations are uninformative. Further filtering is applied to determine transient relationships (see Sec. Transient alter selection). Finally, the IT n cohort is constructed by further filtering relationships to those in the Italian data that do not commence until after a minimum number of days since the entry of the participant. These filters define our four cohorts UK, US, IT, and IT n . All data sets were collected before smartphones became common and thus capture the bulk of people's non-face-to-face communication.

Transient alter selection
Each communication event (outgoing phone call) between ego i and alter x occurs on a particular day a ix after their first observed communication, where the first day corresponds to a ix = 0. From the perspective of when each cohort E begins, the first observed contact between i and x occurs on day t (1) ix which is a number between 0 and T E − 1. If there are n ix total observed calls between i and x, the last call occurs on day t (nix) ix of the study, which corresponds to ix . In our study, we exclude any alter x such that T E − t (nix) < ∆t w where ∆t w is an excluded window that provides confidence that a relationship has indeed stopped communicating for a significant amount of time.
The call volume f ix (a ix , ℓ ix ) between i and x captures the evolution of relationship ix over time, but it is a considerably noisy signal, generally with few samples for given values of a = a ix and ℓ = ℓ ix . To address the possibility that egos have a systematic trend over time in communicating with their alters, we average over alters of i in A i (ℓ, ∆ℓ) ⊂ A i , the set of alters x such that ℓ ≤ ℓ ix < ℓ + ∆ℓ. The bin size in the main text has been chosen as ∆ℓ = 50 days, but other values are shown in the Supplementary Information, Sec. S3.3.
From these definitions, as well as a window of a such that a ≤ a ix < a + ∆a (with ∆a = 15), we introduce where θ(·) corresponds to the step function (θ(x) = 1 if x > 1, and 0 otherwise), and || produces the cardinality of a set. Note that any trend consistently present in f ix (a ix , ℓ ix ) would be inherited by both f (a, ℓ) andf i (a, ℓ).

Kolmogorov-Smirnov test forf i (a, ℓ)
We study the level of steadiness off i (a, ℓ) as a function of a ego by ego, taking for each time seriesf i (a, ℓ) two parts of equal duration in a that exclude the first (a = 0) and last (a = ⌊ℓ/∆a⌋∆a) points of the time series.
These two points are excluded for specific reasons. The first point is affected by initial tendencies to have communication that has not stabilized, as can be seen in Fig. S8. The last point is excluded because, unless ℓ is a perfect multiple of ∆a, the call volume captured by the last time point of the series is likely to have less call volume simply because it is not fully used (there is a period between ℓ and ⌊ℓ/∆a⌋∆a with no activity). After excluding these two points, the two resulting ranges of elapsed duration (∆a ≤ a < ⌊(1/2) (⌊ℓ/∆a⌋ − 1)⌋∆a and ⌊(1/2) (⌊ℓ/∆a⌋ − 1)⌋∆a ≤ a ≤ ⌊ℓ/∆a⌋∆a − ∆a) generate for each ego two samples off i (a, ℓ) at points in a within each of the periods, and we perform a Kolmogorov-Smirnov test to determine if the values of the two samples come from the same distribution. The result of the Kolmogorov-Smirnov test for each ego is a p-value that, the closer it is to 1, the more likely it is that the seriesf i (a, ℓ) is steady. Let us label the p-value obtained for each ego as p i . We conduct these tests for egos with medium and long lifetimes. consecutive increases of q, i.e. when q changes from value q x to q x + 1 and from q x + 1 to q x + 2, we take q x as the beginning of the approximately 0-average slope of u(a). If the average slope sign alternation condition is never met, or if the average slope is always identical to 0, the algorithm stops when the range of a cannot be truncated any further, which is when q = ⌊ℓ/∆a⌋, and in this case, we make q x = 2 which means that we revert to looking at all but the two endpoints of u(a) (although the algorithm is deemed to have failed to converge and we use its results differently). Using the resulting q x (converging or non-converging), we measureū(a), the average of u(a), using all u(α∆a) with ⌊q x /2⌋ ≤ α ≤ ⌊ℓ/∆a⌋ − ⌊(q x + 1)/2⌋. When u(a) corresponds tof (a, ℓ), then b(ℓ) =ū; when u(a) corresponds tof i (a, ℓ), then b i (ℓ) =ū.
The method described above also yields the minimum lifetime ℓ s at which stable regions begin to emerge.
As noted above, q x = 2 when the method does not converge, otherwise, the method converges and therefore, at a = ⌊q x /2⌋∆a a flat region of u(a) begins. Noting that this a is equivalent to the shortest possible value of lifetime, we equate ℓ s with ⌊q x /2⌋∆a and take u(a) to bef i (a, ℓ). This produces a sample of ℓ s , one for each ego, and provides a statistical picture for the smallest lifetimes that exhibit a steady regime.
P (a | a o , a f , γ) computation

Mutual information
The measurement of mutual information between the random variables ℓ and g is performed for all the combined cohorts together and also for individual cohorts. Mutual information I(X, Y) between two random variables X and Y is defined as the amount of information one of the random variables contains about the other. Specifically, for discrete random variables, where Pr(X = x, Y = y) is the joint probability to draw x and y simultaneously, Pr(X = x) the marginal probability to draw x, and Pr(Y = y) the marginal probability to draw y. I(X, Y) is measured in bits, which we can normalize to a symmetric uncertainty U (X, Y), where H(X) and H(Y) are the entropies of X and Y, respectively, defined as H(X) = − x∈X Pr(X = x) log 2 Pr(X = x) (and similarly for H(Y)). The advantage of using U (X, Y) is mostly its interpretation.
When the two variables are independent, U (X, Y) = 0, and when there is complete information about one variable from the other, U (X, Y) = 1.

Computational and statistical tools used
In this article, most of the statistical functions employed have been programmed from scratch, using Python Elapsed duration Observed elapsed duration in days of the relationship between ego i and alter x. ℓ i,x Lifetime Observed lifetime in days of alter x in ego i's network. ∆t s -Exclusion days at the start of IT data to create IT n . If ego calls alter for the first time at or after ∆t s days, we identify the relationship as new. ∆t w -Exclusion days before the end of the cohort data. If the last contact between an ego-alter pairs occurs ∆t w days or more before the end of data in their cohort, we identify a relationship as transient. Probability that an alter is active at elapsed duration a, given that it had activity 3 γ ≤ g < 3 γ+1 during the interval [a o , a f ] I(ℓ, g) Mutual Information Mutual information between ℓ and g. It quantifies the amount of information that can be obtained from one variable by observing the other. U (ℓ, g) Symmetric uncertainty Symmetric uncertainty between ℓ and g. It measures the same as I(ℓ, g), but in a scale that goes from 0 (when the variables are independent) to 1 (when the information one variable gives about the other is complete).  Medium lifetime Long lifetime  UK, IT, and US combined  303  7625  ---UK  30  920  483  90  76  IT n  142  2736  1102  278  157  IT  143  4052  1369  447  313  US  130  2653  1415  399  319   Table 2: Number of transient ego-alter pairs by cohort with ∆t w = 60 days and ∆t s = 50 days (for IT n only). The last three columns show the exact number of relationships specifically used in the lifetime groups of Fig. 1 which represent a subset of all the transient relationships contained in the data.
The Mobile Territorial lab data used in this study are not freely available on an open repository for privacy reasons. However, they are available upon request by contacting the authors at lepri@fbk.eu. The data will be made available in a timely manner and in compliance with any ethical or legal requirements.

S Supplementary Information
As a general note, in this document the term relationship between ego-alter pairs refers to transient relationships. In many instances, we simply write relationship for brevity, but this should always be understood to mean transient relationships. The only exception to this rule is encountered in Sec. S.1.2. and its only figure   (Fig. S1).

S.1 Construction of cohorts for each study
A succinct explanation of the data is provided in the main text (Sec. Methods). These data sets have been fully described in previous articles, and the corresponding citations can be found below in the respective subsections.
Here we expand on some details of the studies that generated these data, namely the timing of entry of participants into the study and the life circumstances of the participants in each study. These details affect the way in which we choose the transient relationships we analyze here. After these descriptions, we elaborate on the filters we apply to arrive at the final cohorts in this study.

S.1.1 Detailed information about each National study
UK study The UK dataset was collected between 2007 and 2008, with all participants (egos) starting the experiment simultaneously. The timing of data collection was chosen to start observing participants during the last few months of secondary school and then continue to observe them for a time period that would capture an entire first year of university study. All participants were recruited from the same cohort in one school. The transition from secondary school to university occurs around six months after the start of data collection. With this design, participants begin the study while interacting generally with well-established network members (alters), and after six months, participants start to engage with a host of contacts that can be taken to be newly met alters (for details see [58]). Of the total cohort of 30, only 2 participants did not transition to university but their networks were still deeply disrupted due to the loss of alters and new personal circumstances.
US study The US dataset was collected between 2010 and 2011, with a pilot phase lasting 6 months, and then a second phase of 12 months in which an additional larger pool of participants is recruited at the beginning of this phase. This means that the egos did not all start simultaneously (for details see [1]).
Effectively, this produced a sample of approximately 17 months.
The circumstances of the participants (egos) in the US data set are generally steady in time, i.e. the participants were not intentionally recruited to capture a particularly large change in their circumstances.
Furthermore, egos do not generally enter synchronously in the phases of the study.
Italian study The Mobile Territorial Lab experiment recruited participants in two groups, one beginning their participation in early 2013 and the second in early 2014 [12]. As with the US dataset, egos were not selected to be in a particularly dynamic stage of their lives where large changes to their circumstances could be foreseen. As with the US data set, egos in this study do not begin synchronously.

S.1.2 Bounds on lifetimes by cohort
The numbers of ego-alter relationships in all data sets decrease as a function of observed lifetimes. These decreases begin at a steady rate for all data sets, but as the lifetimes start to reach values that resemble the duration of the study, and in most cases considerably less time, the number of ego-alter pairs drop off at increased rates. With all the values of L E on hand, the ego-alter pairs we study are those that satisfy

S.1.3 Calculation of initial relationship times for asynchronous ego entry
The US and Italian studies add participants in an asynchronous way, i.e. not all participants become active at the same time. This becomes relevant for some measurements presented in the main text and in this supplementary document.
To deal with this effect, for each ego i in both the Italian and US data sets, we define an entry time ϵ i , equal to the day t of the study that i belongs to when this ego is seen to make the first contact with any of its alters A i (defined in the Methods, main text). Then, for ego-alter pair ix, we generate a relative start ix is the day of first contact between i and x measured from the first day of the study to which i belongs. Thus, τ o,ix measures the number of days since ego i entered his/her study before i and x were observed to begin contact.
We use this information in two different ways. First, we use it in determining how many transient relationships in each national study begin at or after a certain number of days from the entry of an ego into the study (see Sec. S.2). The second way we use this information is the construction of the IT n cohort, described next.

S.1.4 Construction of cohorts
We develop four cohorts. Two of the cohorts (UK and IT n ) are meant to characterize transient relationships where there is a high chance the initial contact is observed within the data. Two other cohorts (IT and US) are not adjusted to specifically try to capture the initial contact of ego-alter pairs but, as we see in Sec. S.2, this occurs for most contacts due to chance.
All the cohorts explained next satisfy the following: i) each ego-alter pair ix has at least 3 contacts, so as to avoid studying meaningless relationships, ii) no lifetimes ℓ ix are larger than the L E , where i ∈ E, and iii) ego-alter pairs comply with the transient relationship filter ∆t w , explained in the main text.
The Italian (IT) and US cohorts are fully defined by the three filters just mentioned. The other two cohorts satisfy additional conditions.
Construction of UK cohort Beyond the conditions stated above, the UK cohort is generated by only using ego-alter pairs that become active after 6 months or more from the start of the study. All egos have activity and therefore the cohort has all egos that enter the study from the beginning. Alters seen entering ego networks at that point are believed to be almost all new.
Construction of IT n cohort This sub-cohort of the Italian cohort, in addition to conditions i, ii, and iii, includes a filter such that an ego-alter pair ix is used only if τ o,ix ≥ ∆t s , where ∆t s is an exclusion window at the start of a participant's time in the study. This condition means that if pair ix is active before the ego has been in the study at least ∆t s days, the relationship is ignored. This filter is a way to reduce the number of ego-alter pairs analyzed for IT n that may have been active before the actual start of the study.
As we show in Sec. S.2, a large portion of transient relations actually begin after the start of the study and therefore, the filter introduced by using ∆t s further lessens the likelihood of using an ego-alter pair that was in communication before the start of the study.
The result of the application of all the filters stated above is cohorts where the sample size is indicated in Table 2 of the main text.

S.2 Starting and ending times of relationships inside each study
As explained in the main text, even though in the US and Italian studies, some ego-alter pairs may have been active before the start of the study, the majority of transient relationships begin well after an ego enters his/her respective study (see next). This goes a long way in explaining why the various analyses we undertake in this study work similarly well when using UK and IT n or US and IT.
To provide evidence for this interpretation, we present the cumulative distribution for τ o (that is, the random variable associated with the individual τ o,ix for concrete ix pairs), separated by cohorts (Fig. S2A).
Each curve shown provides, per cohort, the percentage of ego-alter pairs that are first seen to be active on or before day τ o . Clearly, although many relationships are first observed for small values of τ o , they are by no means the majority. For instance, in most studies, 40% of relationships require that τ o reaches a value of ≈ 50 days. The US is the only exception, starting at ≈ 40% when τ o is still quite small. By contrast, IT n requires well over 100 days to reach 40% of transient relationships.
A similar analysis can be carried out with regards to the final contact between ego i and alter x, which days before the end of each study. This is relevant when assessing how close to the filter ∆t w each pair ix gets. As Fig. S2B shows, this filter is not commonly reached. Thus, for example, in most cohorts only about 40% of ego-alter pairs remain in touch when there still over 100 days before the end of the study.
These two analyses provide support for the consistency seen in the results coming from cohorts UK, IT n , IT, and US because, although for the first two a, ℓ more strictly measure the actual elapsed duration and lifetime of transient relationships than the latter two, in practice many transient relationships are well contained inside the time boundaries of the studies, effectively making all four cohorts similar.

S.3 Robustness check forf (a, ℓ)
This section is concerned with robustness checks for the results and interpretation off (a, ℓ), presented in with an additional subsection that testsf (a, ℓ) against ∆t s in IT n .

S.3.1 Standard error of each value off (a, ℓ)
The results presented in Fig. 1 in the main text consider the stable volume of communication for the aggregated alters and egos of a given lifetime range. In order to show that variation exists at the individual level, we support our results with those from Fig. 3B in the main text. Additionally, as an alternative visualization for the variation among individual egos, we show one standard error for each point off (a, ℓ) in Fig. S3 as shaded regions in a color corresponding to their lifetime group.
For all cohorts, as lifetime increases, so does the standard error. This is due to the fact that the number of transient alters decreases with ℓ, as seen in Fig. S1. (a, ℓ) for a between ℓ and ℓ + ∆ℓ

S.3.2 Decay inf
Our method for measuringf (a, ℓ), although effective in terms of generating a reliable estimate of the per ego per alter calling volume of each ego to their alters, also has the unintended consequence of frequently generating a fast decaying tail forf (a, ℓ) for ℓ ≤ a ≤ ℓ + ∆ℓ visible in medium and long lifetimes (Fig. 1 of the main text as well as figures of the robustness checks of the current section). Here, we explain the origin of this effect, which is not a behavioral feature of egos, but rather a statistical nuisance effect.
As defined in the main text,f (a, ℓ) is given bȳ where θ(·) corresponds to the step function (θ(x) = 1 if x > 1, and 0 otherwise), and || produces the cardinality of a set. In the range of a starting with ℓ and ending at ℓ + ∆ℓ, there is a progressive reduction of the numerator of Eq. 6 that occurs because not all individual egos have alters until a = ℓ + ∆ℓ. Instead, any given ego typically has activity until a value of a somewhere in the middle of the range between ℓ and ℓ + ∆ℓ. Let us assume that the ego in question is i. If the last active alter with lifetime between ℓ and ℓ + ∆ℓ in ego i's network stops activity at a In Fig. S4, we show the number of egos still active in the range between ℓ and ℓ + ∆ℓ respective to each of the cohorts shown in Fig. 1 of the main text. As it is clear from these plots, the number of active alters decays rapidly from a value of |A i (ℓ, ∆ℓ)| to 0 causingf (a, ℓ) to also decay within this temporal range. This effect leads to the generation of the fast drops seen in most of the curves in Fig. 1. However, we should note that the decay can be partially attenuated if, by random chance, a group of egos in some lifetime group ℓ to ℓ + ∆ℓ remains active until closer to ℓ + ∆ℓ and/or the total call volume among those egos near the end of the time series fluctuates upwards (see e.g. medium lifetime for Italy in Fig. 1).

S.3.3 Robustness in ∆t w
In our study, we exclude any alter x such that T E − t (nix) ix ≤ ∆t w which means that we study ego-alter pairs that stop communicating at some point in the study and remain without communication until the end of the study and for a minimum of at least ∆t w days. This is effectively our transient relationship operational criterion.
The main text presents results with ∆t w = 60 (fourth row in Fig. S5). Here, we test robustness by also checking ∆t w = 10, 30, 50, 90. As Fig. S5 shows, using different values of ∆t w does not affect either the steadiness nor the monotonicity features.

S.3.4 Robustness in ∆ℓ
The value of ∆ℓ of each lifetime group in Fig. 1 of the main text has been chosen as ∆ℓ = 50 days (circles in In addition to the ∆a above, we also apply ∆a = 1 to estimate the value a s . However, given that this quantity appears across values of ℓ, we usef (a, ℓ ≥ ℓ s ). This has the additional advantage of improving our sample size. As Fig. S8 shows, the first set of points on the plot, a = 0, 1, and 2, all show a steady decreasing trend before the curve begins to stabilize. Therefore, we believe that a s = 2 constitutes a lower bound for the applicability of Eq. 1 in the main text.

S.3.7 Volume and duration of calls
To study the temporal signal of communication, one can study numbers of calls or call durations. However, these two choices are known to be correlated for the UK data we use here [60]. In order to provide a full  (a, ℓ). In this section, we discuss an alternative method to obtain b(ℓ) and b i (ℓ) to the stable region average presented in the main text, Methods section.

S.4.1 Mann-Kendall method to identify b(ℓ)
As an alternative to the Stable Region Average method presented in the main text, here we give an alternative calculation of b(ℓ), using the Mann-Kendall test [36,39], explained further in [26], to detect trends in the data. We use the Python implementation provided by [33]. The basic intuition of the test can be understood as a simplification first proposed by Mann [39] of the Kendall rank-correlation test [36]. In particular, for a signal such asf (a, ℓ) orf i (a, ℓ) (which for generality we denote as u(a)), one defines a test statistic

S.4.2 Results from application of the Mann-Kendall method
In this section, we show results for b(ℓ) done across the values of ℓ with the Mann-Kendall method described above. This result can be seen in Fig. S11. From the plot, we see that b(ℓ) increases with ℓ almost universally, with the exception of minuscule fluctuations early in IT and IT n , and again for the longest ℓ for IT n . This last deviating point occurs because the introduction of ∆t s effectively eliminates a great deal of the ego-alter samples that are available for equivalent lifetimes of IT, thus reducing statistical sampling. Overall, the trends are clear and highly consistent across cohorts (see Fig. 2 in the main text).
The fact that b(ℓ) is increasing with ℓ also supports the claim made in the main text that the selection of the medium and long lifetimes used in Figs. 1 and 3 is mostly arbitrary and for the purposes of illustrating the behavior off (a, ℓ) for concrete values of ℓ. However, these choices of ℓ are not restrictive and in fact one can work with values of ℓ from ℓ s and up.
One last observation is that, while the trends of b(ℓ) are increasing, there are differences among the cohorts, with the US and UK showing a more rapid growth than the Italian cohorts, which start roughly steady and then begin their marked increase for larger values of ℓ. This may have implications in terms of how effectively one can distinguish medium lifetimes in Italian ego-alter pairs in comparison to the other cohorts on the basis of early phone call activity. This will require further research.
Results for b i (ℓ) and ℓ s are presented in Sec. S.5 as they pertain to ego-level features, the subject of that section.

S.5 Individual ego tests
The features captured byf (a, ℓ) are also shared byf i (a, ℓ) for individual egos. This is supported in the main text through the results displayed in Fig. 3, and further tested in other parts of the main manuscript, namely, those that check if the increase off (a, ℓ) with ℓ has predictive power such as Figs. 4 and 5. In this section, we complement this evidence by showing primary analyses that allows us to construct the results presented in the main text, as well as additional robustness checks for the main text results.

S.5.1 Visual inspection of random sample off i
A simple and illuminating check for the consistency betweenf i for individual egos and the aggregate resultf is to plot the series together. Fig. S12 shows thef reported in the main text (dark curves), Fig. 1, as well as Smirnov test for each ego is a p-value that, the closer it is to 1, the more likely it is that the seriesf i (a, ℓ) is steady. Let us label the p-value obtained for each ego as p i . We conduct these tests for egos with medium and long lifetimes.
In the main text, we show box plots of the {p i } i∈E obtained from the tests (Fig 3A) for all cohorts E.
Here, we present the probability distributions of these {p i } i∈E (Fig. S15)

S.5.4 Analysis of ℓ s
The functionsf i (a, ℓ) do not always stabilize to a flat region. This almost always occurs because ℓ is too small, i.e. when lifetimes are short as described in the main text (small fractions off i (a, ℓ) do fail the Kolmogorov-Smirnov test for medium or long lifetimes too, but at rates between 0% and 4% over the different cohorts, thus a negligible effect). As explained in Sec. S.4.1, the stable region and Mann-Kendall methods may fail to converge, which means they never find a region in which the average slope off i (a, ℓ) is close to 0. On the other hand, when ℓ starts to become large, if a stable region is found, we track the values of the smallest a at which such stable regions begin for each ego. In the methods described in Sec. S.4.1, these values are labelled a m . At the threshold between ℓ being too small, not showing a steady regime, and starting to show stability, a m and ℓ are very similar as a M is not too far above a m . Therefore, as a conservative approximation, we equate a m to the smallest lifetimes at whichf i (a, ℓ) for a given ℓ can become stable.
Mostf i (a, ℓ), as ℓ is increased, eventually exhibit a stable region starting at some a m (q x ) = ⌊q x /2⌋∆a. We collect all such values over egos of a cohort and label them ℓ s , the minimum lifetime for stable communication.
In Fig. S16 we present distributions of ℓ s for each of the cohorts, the vertical scale is logarithmic and the horizontal scale is linear. The shape of these plots resembles exponential distributions which suggest a narrow set of possible values for ℓ s .
To provide estimates for the values of ℓ s at which, generally,f i (a, ℓ) becomes steady, we take two approaches. First, we directly calculate the averages of ℓ s of each of the cohort distributions. These averages can be found in Table S3. We also create a single combined cohort that produces an average ℓ s of 55.94. A second approach is to assume that the distributions indeed are well approximated by the exponential form ∼ e −ℓs/υ , and estimate υ. In turn, υ can be used to provide estimates for ℓ s . This second approach is well supported by the similarity of the distributions for the different cohorts (Fig. S16B), which suggests that ℓ s has similar quantitative properties across cohorts. This is a surprising result given the diversity of the egos.
To perform this second approach based on curve fitting we assume Pr(ℓ s ) = Ce −ℓs/υ where C is the  shorter windows of observation, even down to 15 days. Third, the curves for γ < 2 appear to be smoother than those for higher values of γ. This occurs due to the number of alters in these bins, as shown in Table S4.
Finally, when a o and a f − a o both increase, the curves P (a | a o , a f , γ) separate very widely as functions of γ, signalling the much greater ability of g to predict lifetime. The caveat to this is that, since the purpose of using early call volume within a limited time window is mostly to provide some early estimates of ℓ, it is not practical to increase both a o and a f − a o because in that case the measurement of g in fact amounts to a full measurement of relationship call volume.

S.7.1 Variations on contour plots
We also test the robustness of the results of Fig. 5 to cohort selection. In that figure of the main text, we combined data from the UK and US to explore how well they predict the Italian cohort. Here, we change our cohort selection in order to test how robust these results are.
In Figs. S20 and S21 we show two combinations of two countries used to produce the contour plots shown, and the third country is contrasted against those contours. In all cases, as in the main text, the third country's behavior is reasonably predicted. The limited quality in comparison with that of the Fig. 5 in the main text is that the Italian cohort is, by far, the best sampled one leading to a cleaner match of symbols and contours in  Fig. 1 of the main text with the addition of one standard error (above and below) for each point off (a, ℓ), represented as a shaded region with color corresponding to those used for each lifetime group in the paper. All other parameters are the same as those presented in the main text, Fig. 1.  Figure S4: Number of egos with active alters at elapsed durations in the ranges ℓ ≤ a ≤ ℓ + ∆ℓ for all countries and lifetime cohorts shown in Fig. 1, main text. Left column shows medium lifetimes, the right columns shows long lifetimes. The colors consistent with the main text, Fig. 1. From these plots, one can observe how the number of active egos decays steadily within the window between ℓ and ℓ + ∆ℓ, generating the fast decaying effect seen in Fig. 1, a purely statistical effect of the definition off (a, ℓ). In the main text, ∆ℓ = 50 days is used. Each row corresponds to a cohort, and each column to a lifetime group. For small ∆ℓ, as expected, the signal fluctuates more. The only qualitative change observed across all the plots is in the column for short lifetimes: as ∆ℓ increases, we observe the gradual emergence of weak plateaus, specially as ∆ℓ → ℓ s , the minimum value at which steadiness emerges forf (a, ℓ).     Alter lifetime b( ) estimation UK IT n IT US Figure S11: b(ℓ) as a function of ℓ obtained through the Mann-Kendall method, cohort by cohort. The vertical axis is in logarithmic scale. Clearly, b(ℓ) has an increasing trend with respect to ℓ, with minor exceptions. This result, remarkably similar to Fig. 2 in the main paper, highlights the consistency between the Mann-Kendall and stable region average methods.

Short lifetime
Medium lifetime Long lifetime Figure S12: Visual comparison of a sample off i (a, ℓ) curves (light color) with their respective cohort averagē f (a, ℓ) (dark color). Cohorts are indicated in each plot. As expected, individual egos exhibit larger fluctuations than their cohort average, yet the fluctuations are generally centered around the averages, providing evidence that the general behavior of individual egos is qualitatively similar to that of the cohort average with respect to monotonicity with respect to ℓ, and steadiness with respect to a. More quantitative evidence for these features being present in thef i is provided by the Kolmogorov-Smirnov test shown in the main text, Fig. 3, as well as below in Fig. S14 3 −1 Medium Lifetime Long Lifetime    Table S3: Calculation/estimation of average ℓ s by cohort, all cohorts combined, and exponential fit for all cohorts combined (Eq. 7). When all cohorts are combined, results are obtained from an ordinary least square (OLS) estimation (Fig. S16A). For the individual cohorts as well as the combined cohort, averages are obtained directly from the ℓ s of all relationships for which the calculation of b i (ℓ) converges. Their distributions are shown in Fig S16B.  Each plot corresponds to a single cohort (indicated in each plot), in contrast to the main text which includes UK, IT, and US. The smaller samples that make up each cohort do lead to noisier results as well as step-wise jumps on the plots. The bins represented by γ as the exponent in 3 γ ≤ g < 3 γ+1 are γ = 0, 1, 2, 3. As γ increases, and even though the plots display noisier behavior than in Fig. 4 of the main text, the probability of survival also increases in all cohorts, i.e. for γ ′ > γ, P (a | a o , a f , γ ′ ) > P (a | a o , a f , γ), consistent with the conclusions of the main text.
There is a noticeable decrease in the number of alters, as γ increases. Just as for Fig. S19, a combination of the three countries was used for this Table  0  We use the combined data for UK, Italy and US, and therefore, we only look at relationships active for ℓ < L US = 220 days or less, in order to include data for all three cohorts. The bins represented by γ as the exponent in 3 γ ≤ g < 3 γ+1 are γ = 0, 1, 2, 3. The most important effects observed are that if a o is chosen early in the relationship (say a o = 0), survival curves are closer together and even show inconsistency for the smallest call bin γ = 0. Also, curves with increasing γ do not separate as broadly. Larger a f − a o , on the other hand, leads to greater separation between curves of increasing γ, although increasing the window of observation is somehow antithetical to the idea of using g measured in a small time window to predict relationship lifetime. In any case, for reasonable a o (one that is not too small) we still find, as in the main text, that as γ increases the probability of survival also increases, i.e. for γ ′ > γ, P (a | a o , a f , γ ′ ) > P (a | a o , a f , γ). The match in location between the symbols and the colored regions is reasonable throughout values of the probability. However, quality is degraded slightly in comparison to the main text, Fig. 5, as the sample for the UK cohort is considerably smaller than the one for Italy (which forms the symbols of the main text). Overall, the qualitative trend of the results presented is still consistent with those of the main text. . The match in location between the symbols and the colored regions is best achieved for largest probabilities, i.e. dark yellow and purple regions. For lower probability regions, the match is not as good although it has the correct trend of dependence of survival with respect to g, namely, more calling means longer survival. The smaller size of the US cohort plays a role. Overall, the qualitative trend of the results presented is still consistent with those of the main text.