Ageing red deer alter their spatial behaviour and become less social

Social relationships are important to many aspects of animals’ lives, and an individual’s connections may change over the course of their lifespan. Currently, it is unclear whether social connectedness declines within individuals as they age, and what the underlying mechanisms might be, so the role of age in structuring animal social systems remains unresolved, particularly in non-primates. Here we describe senescent declines in social connectedness using 46 years of data in a wild, individually monitored population of a long-lived mammal (European red deer, Cervus elaphus). Applying a series of spatial and social network analyses, we demonstrate that these declines occur because of within-individual changes in social behaviour, with correlated changes in spatial behaviour (smaller home ranges and movements to lower-density, lower-quality areas). These findings demonstrate that within-individual socio-spatial behavioural changes can lead older animals in fission–fusion societies to become less socially connected, shedding light on the ecological and evolutionary processes structuring wild animal populations. Using 46 years of individually monitored data for European red deer, the authors show that older individuals become less socially connected, with correlated changes to their spatial behaviour.

I dentifying the drivers of a wild animal's social connectedness is important for understanding diverse processes like pathogen transmission 1-3 , information acquisition 4,5 , and fitness 6,7 . In particular, individual ageing provokes broad phenotypic changes, and is therefore likely to impact sociality through a range of mechanisms 8 (Table 1). Despite growing knowledge concerning senescent changes in wild animals 9,10 , including several examples of senescing behavioural traits [11][12][13] , relatively little is yet known about the mechanisms underlying age-related declines in sociality ('social senescence'). In recent years, the popularity of social network analysis has facilitated a profound growth in our knowledge of the ecology and evolution of sociality in wild animals 14,15 . Similarly, a recent deeper understanding of senescence in the wild has allowed researchers to identify within-individual declines separate from other demographic processes 9,10 . Combining these two knowledge bases (social networks and senescence in the wild) could lend useful insights into the role of ageing in shaping animal behaviour and structuring wild animal societies, thus informing a wide range of ecological and evolutionary phenomena 16 .
Social senescence might occur for many reasons, ranging from individual to population level in scale (Table 1) 16 . At the individual level, physiological changes may render older individuals less competitive 17 ; they may therefore avoid associating with (younger) conspecifics to avoid being outcompeted, or they may be actively excluded. Similarly, ageing individuals may show increased 'social selectivity' , replacing disadvantageous or aggressive interactions over the course of their lives with fewer, more positive interactions 12 . In humans, age-related physiological declines (and resulting healthcare requirements) are associated with friends being replaced with family members in the ageing individual's social network 18 . Alternatively, rather than being driven by physiological decline, such changes could be driven by changing motivations with age-for example, where sociality is beneficial in earlier life but not in old age [19][20][21] .
In species with relatively fluid social systems, an individual's observed sociality can be influenced by its movement within its environment; in such systems, age-related changes in spatial behaviours could be associated with concurrent changes in observed social connectedness, without actually being driven by a reduction in social behaviour per se 14,22 . As such, providing evidence for social senescence may require demonstrating that the observed changes are robust to changes in spatial behaviour. For example, if older individuals have smaller home ranges, they will probably also make fewer unique contacts 22 . Further, ageing individuals may select less desired habitats or prefer areas that other individuals tend to avoid (and which therefore host lower conspecific densities), both of which will likewise reduce social connections 3,14,23 . The relevance of each of these processes will probably depend on the social system of the animal in question: for example, in species with highly stable social groups that move and forage together, it may be unlikely that age-related changes in spatial behaviours underlie changes in sociality.
Notably, observed age-related patterns may not originate from within-individual changes: if certain individuals have higher mortality rates than others, then an apparent age-related pattern might emerge at the population level (that is, 'selective disappearance') 9,10 . For example, if more social individuals are more likely to die because of greater levels of competition, a population-level pattern of decreasing sociality with age would emerge without requiring any within-individual decline in sociality. Identifying and differentiating selective disappearance from within-individual senescence requires longitudinal analyses following known individuals 9,10 . Similarly, because an animal's observed sociality depends on surrounding population structure 22,24,25 , demographic changes could produce apparent age-related social declines. For example, if an animal forms relationships when it is young that are not replaced when those contacts die 26,27 , then older animals will be less socially connected as a result. Social connectedness has recently been shown to correlate with age in chimpanzees, macaques, ibex and marmots 12,28-31 , but the relative roles of these spatial, demographic and within-individual drivers have yet to be investigated. Untangling these processes could shed a light on the relative importance of within-individual age-related behavioural changes (compared with physiological or demographic processes) in determining population structure in wild animals. Ultimately, doing so will help to inform the role that ageing individuals play in a system's ecology through processes such as pathogen transmission, cooperation or competition with its associates.
In this Article, we investigated age-related declines in social behaviour using a wild, long-term study population of individually monitored red deer (Cervus elaphus) 32 . The deer, which have been studied since 1973, inhabit a ~12 km 2 area in the north block of the Isle of Rum, Scotland. They are individually followed from birth, and exhibit a fission-fusion social system characterized by substantial mixing but with repeatable social phenotypes based on spatio-temporal grouping patterns 22 . The deer are well suited to studying social senescence: they experience strong age-related declines in ranging behaviour 11 and fitness 33 , and they have well-characterized spatially structured social networks structured by a combination of spatio-temporal drivers and individual phenotypes 22 . Importantly, these data are observational, and are not able to differentiate between all the hypothetical drivers of social decline that we outline in Table 1. Nevertheless, by fitting a series of spatially explicit network models, we examine how age-related declines in social behaviour could arise through within-individual senescence, changes in spatial behaviour, and demography, beginning to untangle the potential causes of age-related social changes in wild mammals.

results
Evidencing social declines. Using 46 years of census data containing over 200,000 observations of spatio-temporal grouping patterns in 712 individually known female deer, we fitted generalized linear mixed models (GLMMs) to investigate the phenotypic drivers of three correlated annual measures of social connectedness: mean group size, degree centrality and connection strength. Although representing slightly different elements of sociality, these metrics are all taken to be broadly descriptive of general social connectedness, and are used throughout the literature for this 34 . We uncovered age-related declines in all three measures when accounting for a range of other intrinsic and extrinsic drivers (model set 1; Fig. 1a-c). Older females had smaller groups, fewer contacts and weaker social connections (Fig. 1a-c). Ageing 1 year came with a reduction in average group size of 0.24 individuals (95% credibility interval (CI) −0.29, −0.19; P < 10 −6 ; Fig. 1a), 0.65 fewer unique contacts (CI −0.82, −0.50; P < 10 −6 ; Fig. 1b) and 0.05 weaker network connection strength (CI −0.07, −0.04; P < 10 −6 ; Fig. 1c).
Testing selective disappearance. An age-related decline in social connectedness could be produced if highly social individuals are more likely to die (that is, 'selective disappearance'), creating an apparent population-level decline in sociality. To test this possibility, we sequentially added individual identity and longevity (age at death) to a model constructed on the subset of individuals with known death year (90% of individuals; model set 2). Longevity was positively associated with group size (0.09; 95% CI 0.03, 0.16; P = 0.002), degree centrality (0.08; 95% CI 0.03, 0.13; P < 0.001) and connection strength (0.08; 95% CI 0.03, 0.13; P = 0.002), indicating that individuals with more and stronger contacts were likely to live longer (Fig. 1d). However, incorporating individual identity and longevity did not notably change or remove the negative age effect estimates, demonstrating that the observed senescence did not originate from selective disappearance of more-social individuals (P < 10 −6 ; Fig. 1d).
Testing demographic drivers. We tested whether the death of associates could be driving age-related social declines by examining the relationship between an individual's summed social connections to individuals that had died in the preceding year and the individual's own sociality in the focal year (model set 3). We found that the death of associates was not predictive of social metrics, regardless of whether these associates had died naturally or had been shot; although the strength of associations with dead individuals improved the group size model, and shot friends the strength model (Supplementary Table 1; change in deviance information criterion (ΔDIC) >2), the 95% CI for both effect estimates overlapped with 0. This finding implies that mortality-associated loss of associates is offset by the acquisition of new connections with surviving individuals.
Examining spatial autocorrelation. Accounting for spatial positioning is important in social network ecology because spatial autocorrelation may produce confounding between response and explanatory variables, potentially rendering analyses less conservative 35 . Specifically, in social network analyses, individuals that live in closer proximity to one another may exhibit more similar social phenotypes because they experience similar environments, and they socialize with each other more frequently 22 . We fitted stochastic partial differentiation equation (SPDE) effects to consider spatial autocorrelation by accounting for spatial variation in the response variable across the landscape (Methods). We found that fitting the SPDE effect substantially improved the fit of our models (ΔDIC >462) and reduced age effect estimates in model sets 1 and 2 (Fig. 1); the age effects remained significant for group size (P = 1.2 × 10 −5 ) and strength (P = 0.0009), while degree centrality became non-significant (P = 0.10). The SPDE effect also removed the effect of longevity on group size in model set 2 (P = 0.5; Fig. 1; for full effect estimates, see Supplementary Table 2). Age was heavily spatially structured (ΔDIC 299): individuals with more similar ages lived in closer proximity, with younger individuals in the centre of the study area, and with age increasing to the fringes of the population (Fig. 2a). This trend implied that age-dependent changes in spatial behaviour could be contributing to the observed declines in social connectedness. Spatial behaviour changes* Older individuals alter spatial behaviours like habitat selection, with their social positions changing as a result. tested using the SPDE extensions of all model sets, and using the spatial behaviour metrics in model sets 4-6.
Selective disappearance More social individuals are more likely to die earlier (for example, through competition), creating an apparent age-related decline. tested using model sets 2 and 5.
Demographic changes Older individuals' associates die as they age, and are then not replaced. tested using model set 3.
Asterisks denote within-individual changes (that is, processes that drive 'social senescence' per se), while mechanisms without asterisks are processes that could drive apparent age-related changes but without necessitating any within-individual changes. Note: our data were not able to identify roles of competition avoidance or exclusion.
Testing selective disappearance for spatial behaviours. Following our protocol for social metrics (model set 2), we added longevity to investigate how selective disappearance could affect observed spatial metrics' relationships with age (model set 5; Extended Data Testing spatial explanations for social declines. We then fitted spatial metrics as explanatory covariates to test whether they could explain age-related declines in social metrics (model set 6). We found that social metrics were positively associated with local density and home range area, agreeing with previous findings 22 . Additionally, social metrics were negatively associated with distance from the population centre (P < 10 −6 ). Fitting these effects as explanatory variables in the GLMMs did not fully supplant the negative effects of ageing (P < 0.001; Extended Data Fig. 2 and Supplementary Table 4), although it did substantially reduce the size of the estimated effects (Extended Data Fig. 3). Including the SPDE effect alongside these three spatial covariates likewise did not remove these effects (P < 0.03; Extended Data Fig. 2b and Extended Data Fig. 3).

Discussion
These observations demonstrate senescent declines in social connectedness in a wild ungulate, while providing much-needed insights into the potential underlying drivers. We uncovered no evidence for selective disappearance or demographic mechanisms governing age-related declines in social connectedness; instead, our results suggest that such declines occurred at the within-individual level. We found that generalized spatial phenotypes also changed with age, as represented by a correlated suite of spatial metrics: older individuals were generally found with smaller home ranges, farther from the centre of the population, in areas of lower density, and with lower-quality grazing. This altered spatial behaviour did not fully explain age-related declines in social connectedness, implying the partial involvement of a non-spatial driver of social senescence. Moreover, owing to the reciprocal relationships between spatial and social behaviour 14,36,37 and our use of an observational dataset, it is possible that the changes in spatial behaviour arose from the changes in social connectedness, rather than vice versa. Nevertheless, these observations support the value of examining spatial context when considering the intrinsic drivers of social network structure 3,14,22 , particularly when combining long-term data with spatially explicit network models. Social senescence could emerge from generalized reductions in spatial activity caused by physiological decline and inhibited movement ability 11,16 . This mechanism would be supported if older individuals' ranges gradually shrank within themselves, while moving less in space. This explanation was not supported for several reasons: first, although an age-related decline in home range area was evident (supporting earlier findings 11 ), it was not robust to controlling for spatial autocorrelation, which implies that this finding could originate from age-related changes in spatial locations or spatially structured observation effort rather than smaller home ranges per se. Second, older individuals' home ranges did not increasingly fall within their previous home ranges, implying that they inhabited different areas rather than smaller subsets of the same area. Third, age-related declines in shifts in average annual location were very weak and not robust to controlling for spatial autocorrelation, demonstrating that home ranges shifted at a relatively constant rate across the landscape through an individual's life rather than notably slowing down in old age. Taken together, these observations imply that ageing females exhibit similar spatial activity levels but in different areas of the landscape.
Although reduced activity did not appear to be responsible, altered spatial behaviour did contribute to age-related declines in social connectedness. Ageing individuals were less social partly because they preferred to inhabit lower-density, lower-quality areas at the edge of the study area that offer fewer social opportunities. They may ultimately inhabit these areas because physiological changes cause ageing individuals to alter their habitat selection. Red deer teeth are worn down as they age 38,39 , reducing their ability to ingest food as efficiently. Older deer may accommodate these physiological changes by moving to areas that allow them to feed on alternative vegetation (for example, if longer grasses are easier to crop with worn incisors), which also contain lower densities of conspecifics. In this way, social declines could arise partly as a by-product of habitat selection based on physiological ageing rather than being related to changes in social preferences itself.
Nevertheless, we found that social senescence was evident even when spatial factors were accounted for: older individuals still had smaller groups even when considering their home range areas, local population density and location on the landscape, implying that alterations in spatial behaviour could not be the only explanation for the deer becoming less social with age. Although we tested six spatial metrics and three social metrics, these behaviours are extremely unlikely to be independent: for example, moving away from the centre of the population, towards areas of lower density, and having fewer social associates are all likely to be part of the same correlated selection of behaviours that are very difficult to discern using observational data. Furthermore, while we fitted spatial behaviours as explanatory variables in our models of social connectedness, social and spatial behaviour are part of a bidirectional process involving a number of feedbacks 36,37,40 . As such, although we formulate spatial behaviours as being explanatory of changes in social connectedness, it is possible that changes in spatial behaviour were themselves influenced by changes in social behaviour. Similarly, our measures of sociality were based on 'gambit of the group' , which ultimately represents spatio-temporal proximity 41 , rather than on observations of between-individual interactions (for example, fights). The spatial component of the gambit of the group metric could drive increased confounding with spatial behaviours such as range area. Future investigations could investigate such behaviours to examine and compare their relationships with age and spatial behaviour. Our results should not necessarily be interpreted as separate evidence for (absence of) changes in each spatial behaviour in isolation, but to indicate that age is associated with generalizable within-individual changes in socio-spatial behavioural syndromes and reduced social connectedness.
Social senescence could be a response to aggressive or competitive interactions with younger individuals that may have greater resource demands: to give an example, reproductive female olive baboons (Papio anubis) are more aggressive to other females for this reason 42 . Older female deer are less likely to reproduce 33 , but reproductive status was included in our models and is therefore unlikely to be directly responsible for the observed social senescence. Alternatively, ageing deer may reduce their connections to individuals with whom they have had more aggressive interactions in favour of more positive interactions, thereby becoming more 'socially selective' as they age 12 . This tendency to avoid aggressive interactions could also cause them to have reduced grazing quality (as we observed) if younger individuals monopolize the higher-quality resources, or if the younger individuals are more competitive and older individuals avoid this competition by moving to less-favoured areas (that is, competitive exclusion). Inferring such competitive or aggressive interactions would probably require high-resolution methods such as direct behavioural observation in combination with telemetry, which provide detailed information on fine-scale movement patterns but often currently come with important restrictive trade-offs in terms of how many individuals are GPS-tagged or observed and for how long 43,44 . Telemetry-or behavioural observation-based approaches may not be feasible to run for the duration necessary to detect the subtle, life-long patterns of social senescence we observed. Crucially, our long-term longitudinal data (complete with high-certainty life history measures) were also able to differentiate selective disappearance and changes in demographic network structure from within-individual declines, which may be important for producing age-related social changes in other populations (for example, ibex 30 ). These findings therefore imply a trade-off between the resolution and breadth of behavioural data, while supporting the value of individual-based long-term studies of wild animals for identifying senescence 9 and behavioural changes 30 .
Older individuals may decrease their social connectedness because of changing motivations as they age-for example, if it is advantageous to be well connected when young (for example, to gain social information) but less so when older (for example, owing to previously accumulated knowledge) [19][20][21] . Alternatively, if older individuals undergo immunosenescence 45 , they may reduce social connections as a compensatory measure to avoid parasite exposure. Identifying these kinds of mechanisms would require investigating the fitness-and disease-related consequences of sociality, asking whether the fitness of younger individuals holds a different relationship to social connectedness than the fitness of older individuals does. Importantly, such sociality-fitness relationships are likely to depend on a species' social system; as the deer exhibit a loose, fission-fusion system, our results may be less applicable to species with tight, consistent social groups that move and forage together. Investigating demographic structuring, selective disappearance and spatial behaviours in primate populations (for example, refs. 12,28,46 ) may shed an important light on the different drivers of age-related changes in sociality across mammals and other taxa. Ultimately, broadening the selection of study organisms for age-sociality interactions to include those with a wider variety of fluid and rigid social systems could help to develop generalizable insights about the causes and consequences of social ageing across the tree of life.
In sum, we provide evidence of social senescence in wild deer, and show that this senescence could be explained partly by altered spatial behaviour. Although experiments might be necessary to fully discern the specific drivers of social senescence, we were able to use long-term observational data to successfully identify a within-individual decline (that is, senescence) in social connectedness that was robust to selective disappearance, demographic changes and changes in spatial behaviours. As such, these findings provide novel insights into the ecology and evolution of social behavioural changes and the ecological role played by ageing individuals, forming a foundation for understanding how age governs the structure of wild animal societies by shaping individual behaviour.

Methods
Data collection and study system. The study was carried out on an unpredated long-term study population of red deer on the Isle of Rum, Scotland (57°N, 6°20′W). The natural history of this matrilineal mammalian system has been studied extensively 32 , and we focused on females aged 5+ years, as these females have the most complete associated census data, few males live year round in the study area and nearly all females have bred for the first time at the age of 5. These individuals are known to exhibit age-related declines in a range of behavioural and life history traits 11,33,47 . Individuals are monitored from birth, providing substantial life history and behavioural data, and >90% of calves are caught and tagged, with tissue samples taken 32 . Census data were collected for the years 1974-2019, totalling 201,746 census observations. Deer were censused by field workers five times a month, for 8 months of the year, along one of two alternating routes 32 . Individuals' identities, locations (to the nearest 100 M), and group membership were recorded. Grouping events were estimated by experienced field workers according to a variant of the 'chain rule' (for example, ref. 48 ), where individuals grazing in a contiguous group within close proximity of each other (under ~10 m) were deemed to be associating, with mean 204.5 groups observed per individual across their lifetime (range 1-853). If they breed, female deer on Rum give birth to a single offspring, typically in May, and we therefore consider their annual cycle as running from May in one calendar year to May the next. All individuals are deemed to be age 'zero' in their first year, and all turn 'one' on the first of May the following year, regardless of when they were born. This age assignment continues throughout their lives (for example, in the 2015 deer year, all individuals that were born in 1994 were considered '21 years old'). Accordingly, we summarized individuals' behaviours on the basis of a 'deer year' , which runs from 1 May to 30 April; any female that died in the course of this period was removed. Our full dataset included 4,519 observations of 738 individuals. Previous work shows that gestation and lactation impose costs to subsequent survival and reproduction 49,50 .
To characterize each female's investment in reproduction the previous year, we used three categories based on field observations: none (did not give birth); summer (the female's calf died in the summer, before 1 October); and winter (the female's calf survived past 1 October).
Deriving behavioural metrics. All code and data are available at https:// github.com/gfalbery/Lonely-Old-Deers. Following previous methodology 22 , we constructed a series of 46 annual social networks using 'gambit of the group, ' where individuals in the same grouping event (as described above) were taken to be associating 41 . Dyadic associations were calculated using the 'simple ratio index' 51 derived as a proportion of total sightings (grouping events) in which the focal individuals were seen together: Sightings A,B /(Sightings A + Sightings B − Sightings A,B ). In this dyadic matrix, 0 = never seen together and 1 = never seen apart. Using the annual social networks, we derived three individual-level annual network metrics that are commonly used across animal social networks and have been considered in detail 25,26,52,53 . Our measures included three 'direct' sociality metrics, which only consider an individual's connections with other individuals: (1) Group size: the average number of individuals a deer associated with per sighting; (2) Degree: the number of unique individuals she was observed with over the course of a year, irrespective of how frequently she was observed with them; (3) Strength: the sum of all their weighted social associations to others, also known as 'weighted degree' .
Each metric was fitted as a response variable in separate model sets. These metrics were well correlated (Extended Data Fig. 4) and therefore should not be considered substantially different phenotypes; instead, we present all three metrics under the expectation that they would all change in similar directions, being highly correlated.
We derived six correlated metrics related to population structure and spatial behaviour, hereafter referred to collectively as 'spatial metrics' . These metrics were to be used first as response variables to identify the drivers of spatial behaviours (model sets 4 and 5), and as explanatory variables to identify how spatial behaviours affect social metrics (model set 6).
(1) Local population density (hereafter 'density') was calculated on the basis of an annual population-level space use kernel derived in AdeHabitatHR 54 and using each individual's annual centroids (that is, mean X and Y coordinates), following previous methodology 22 . Briefly, for each year, we took each individual's annual centroid and calculated the spatial density of these centroids (that is, individuals per km 2 ). Each individual was then assigned a local density value based on their location on this annual kernel. (2) Distance between an individual's annual centroids was taken to indicate shifting in average location from year to year, to identify whether individuals' locations move more in their later years ('annual centroid distance'). (3) To detect long-term patterns of an individual's space use on the two-dimensional landscape, and to identify whether ageing individuals move gradually outwards, we took distance from the overall centre of the population, calculated by taking the mean of all annual centroids' easting and northing ('population centroid distance').
(4) To examine changes in range size over the course of an individual's lifespan, we used the 70% isocline of an individual's space use kernel ('home range area'). On the basis of each individual's annual sighting locations and using the AdeHabitatHR package 54 , this was calculated using a density kernel estimator based on previous methodology 11,22 . (5) To investigate the degree to which an individual's annual home range fell within its previous home range, we used an asymmetrical measure of home range overlap from year to year, using the space use kernels ('home range overlap'). A value of 1 for this variable would indicate that an individual's home range in year t fell entirely within its home range in year t − 1; a value of 0.5 indicates that half of its home range lay within its previous home range; and a value of 0 indicates no overlap with its previous annual home range. Combined with the 'annual centroid distance' metric, this home range overlap metric aimed to test whether an individual's range generally shrunk to smaller areas within its known range, consistent with physiological decline, rather than an active movement to areas outside its previous range. (6) To investigate changes in grazing quality, for each individual we calculated the proportion of sightings that occurred on high-quality short or long greens each year ('grazing quality'). A value of 1 denoted that an individual was only ever present on these high-quality grasses, while a value of 0 denoted an individual was never seen grazing on them and was instead always seen on other land types such as rock, sand or lower-quality grazing like heather or Molinia.
For metrics that represented year-to-year changes ('annual centroid distance' and 'home range overlap'), we included only observations that occurred in sequential years (year t and year t + 1, year t + 1 and year t + 2, and so on). For example, if a female was only observed in two non-sequential years (year t and year t + 2), both timepoints were coded as missing. Importantly, because these variables were well correlated (Extended Data Fig. 4), we choose not to interpret these results independently, but to paint a general picture of age-related changes in spatial behaviours, with the caveat that the results of these models are probably non-independent.

Statistical analysis.
To investigate phenotypic associations with social behaviour, we fitted GLMMs using the integrated nested Laplace approximation (INLA) in the R package R-INLA 55,56 . This method allows fitting of an SPDE random effect to control for and quantify spatial autocorrelation 57,58 . The SPDE effect models spatial autocorrelation by estimating to what degree points that are closer to each other in space are more similar than points that are further away 35 . The model then accounts for this similarity, finding sources of variation that occur over and above that expected given the spatial patterns of the response variable. It does so using Matérn covariance, approximating the continuous Gaussian field of the response variable using a triangulated mesh of connected discrete locations 55 . The fits of equivalent models with and without the SPDE effect were compared using the DIC to investigate the importance of spatial autocorrelation. All P values are derived from estimating the proportion of the marginal distribution for a given effect that overlapped with zero, and multiplying it by 2. This can be thought of as being the probability of drawing a value greater than or lower than zero (depending on the direction of the effect), per a two-tailed test.
All GLMMs used a Gaussian family specification. For all models, we used non-informative priors for the SPDE effects; we assessed covariance of our explanatory variables and their variance inflation factor (VIF) to ensure models fit well and without being overwhelmed by correlations among our predictors (all VIF values <2). We checked model fit by assessing correlations between predicted and observed values and by ensuring even distributions of the model residuals.
We constructed six sets of models designed to test different mechanisms driving age-related changes in sociality (see model set details below). All models included the following 'base' fixed effects: year (continuous); annual population size (continuous, log-transformed); number of observations per individual (continuous); reproductive status (three categories: no calf; calf summer death; calf survived to 1 October); age in years (continuous). All continuous explanatory and response variables were scaled (mean 0, standard deviation 1) to help model fitting. All models included random effects of individual ID and observation year.
Before beginning the behavioural analysis, to investigate the spatial autocorrelation of age and to examine its spatial distribution visually, we fitted a model with age as a response variable and with only the SPDE effect as an explanatory variable.
Social metrics and age. Model set 1: Our first model set examined whether our sociality metrics changed over individuals' lifespans, using mean annual measures (N = 4,203 female-years), and including only the base covariates outlined above. We then added a spatial autocorrelation term using an SPDE random effect in INLA, to investigate whether the models were robust to spatial structuring. Comparing the effect of the base model with the spatial model would indicate whether the response variable is spatially structured, and comparing the effect estimates would reveal whether this changed our conclusions. We used the DIC as a measure of model fit; we chose a ΔDIC of 10 to identify whether the spatial autocorrelation effect improved the model. Social metrics and selective disappearance. Model set 2: To investigate whether selective disappearance of individuals may influence estimates of age-related social changes (for example, if more social individuals were selectively lost), we sequentially added a selection of variables into the models. As these models used only individuals with a known death year, they used a slightly smaller dataset (N = 3,873 female-years). We first fitted a base model without individual identity as a random effect, and we then sequentially added individual identity as a random effect, and then longevity as a fixed effect (that is, age at death). An explanation of the test for selective disappearance can be found in Van de Pol and Verhulst 10 . Briefly, fitting both longevity and age in the model isolates the effect of within-individual ageing from that of between-individual selective disappearance. If fitting longevity as a covariate altered the size of the age effects, particularly by rendering them insignificant, it would imply important selective disappearance effects (that is, between-individual differences) rather than within-individual changes 10,11 . Finally, we included the SPDE effect to examine whether longevity effects were robust to spatial structuring.
Investigating demographic associations. Model set 3: As the social phenotype of any individual is dependent upon not just itself but also on the other individuals within the population, demographic processes, particularly the loss of an individual's social associates over time, may passively contribute to age-related changes in remaining individuals' sociality (for example, through reducing the potential for encounters with previous associates). To investigate whether these loss processes could drive age-related declines, we tested whether social network positions were predicted by the death of the female's connections the previous year. We fitted this value as an explanatory variable in the models from model set 1, using either (1) connections to individuals that were shot, or (2) those that died for any reason. A negative estimate for this effect would imply that age-related declines could be explained by the death of a deer's previous connections, rather than solely individual-level change.
Spatial metrics. Model set 4: We investigated how age altered spatial behaviour, using our six spatial metrics as response variables (described above). These models included the same covariates as the social behaviour models (model set 1). For annual movement and the home range area and overlap metrics, we also fitted the SPDE effect; for density and population centroid distance, the response variables were explicitly spatially distributed on the landscape, so fitting the SPDE effect would be misleading.

Spatial metrics and selective disappearance. Model set 5:
We then repeated the selective disappearance protocol used for social metrics (model set 2) on our spatial metrics, to investigate whether any estimated age-related changes in spatial behaviour were altered by selective disappearance of certain individuals.
Investigating how spatial behaviour affects the ageing of sociality. Model set 6: Finally, we investigated whether social metrics were driven by variation in spatial behaviour, and whether age-related declines were robust to these spatial drivers. As several of our spatial measures were well correlated, we used a model addition procedure to identify which spatial measures best explained social network metrics. We used the DIC as a measure of model fit. Beginning with the base model, we sequentially added each spatial metric and then compared the DIC of these models. The best-fitting variable (that is, the one that reduced DIC by the most) was kept, and then the process was repeated, until all variables were fitted or no remaining variables improved the model. We used a change in DIC of 10 to identify variables that improved model fit.
Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

March 2021
Corresponding author(s): Gregory Albery Last updated by author(s): 25 May 2022 Reporting Summary Nature Portfolio wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Portfolio policies, see our Editorial Policies and the Editorial Policy Checklist.

Statistics
For all statistical analyses, confirm that the following items are present in the figure legend, table legend, main text, or Methods section.

n/a Confirmed
The exact sample size (n) for each experimental group/condition, given as a discrete number and unit of measurement A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedly The statistical test(s) used AND whether they are one-or two-sided Only common tests should be described solely by name; describe more complex techniques in the Methods section.
A description of all covariates tested A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals) For null hypothesis testing, the test statistic (e.g. F, t, r) with confidence intervals, effect sizes, degrees of freedom and P value noted

Software and code
Policy information about availability of computer code Data collection NA Data analysis R For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors and reviewers. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Portfolio guidelines for submitting code & software for further information.

Data
Policy information about availability of data All manuscripts must include a data availability statement. This statement should provide the following information, where applicable: -Accession codes, unique identifiers, or web links for publicly available datasets -A description of any restrictions on data availability -For clinical datasets or third party data, please ensure that the statement adheres to our policy All code and data are available at https://github.com/gfalbery/Lonely-Old-Deers Policy information about studies involving human research participants and Sex and Gender in Research.

Reporting on sex and gender
Use the terms sex (biological attribute) and gender (shaped by social and cultural circumstances) carefully in order to avoid confusing both terms. Indicate if findings apply to only one sex or gender; describe whether sex and gender were considered in study design whether sex and/or gender was determined based on self-reporting or assigned and methods used. Provide in the source data disaggregated sex and gender data where this information has been collected, and consent has been obtained for sharing of individual-level data; provide overall numbers in this Reporting Summary. Please state if this information has not been collected. Report sex-and gender-based analyses where performed, justify reasons for lack of sex-and gender-based analysis.

Population characteristics
Describe the covariate-relevant population characteristics of the human research participants (e.g. age, genotypic information, past and current diagnosis and treatment categories). If you filled out the behavioural & social sciences study design questions and have nothing to add here, write "See above."

Recruitment
Describe how participants were recruited. Outline any potential self-selection bias or other biases that may be present and how these are likely to impact results.

Ethics oversight
Identify the organization(s) that approved the study protocol.
Note that full information on the approval of the study protocol must also be provided in the manuscript.

Field-specific reporting
Please select the one below that is the best fit for your research. If you are not sure, read the appropriate sections before making your selection.

Life sciences Behavioural & social sciences Ecological, evolutionary & environmental sciences
For a reference copy of the document with all sections, see nature.com/documents/nr-reporting-summary-flat.pdf

Ecological, evolutionary & environmental sciences study design
All studies must disclose on these points even when the disclosure is negative.

Study description
A study of age-related changes in behaviour in wild red deer. We examined a selection of hypotheses for mechanisms driving social declines with age, using a series of spatial and social network analyses.

Research sample
The full 46-year census dataset available on the deer, using all possible observations and life history measurements.

Sampling strategy
Censuses are conducted 40 times a year, with predetermined routes walked by experienced field workers adept at identifying the deer based on their tags, collars, and markings.

Data collection
The censuses are written by hand, digitised, and uploaded to a central database on an annual basis.
Timing and spatial scale The full 46-year census dataset, using all possible observations and life history measurements.

Data exclusions
We used all individuals aged 5+ with available behavioural and life history data. For the longevity analyses, individuals without a known or approximatable death date were excluded.

Reproducibility
The analyses are all fully reproducible using the provided R scripts.

Randomization
There was no randomisation.

Blinding
There was no blinding.
Did the study involve field work?

Yes No
Field work, collection and transport

Field conditions
THe Isle of Rum red deer study system