Pathogen transmission modes determine contact network structure, altering other pathogen characteristics

(a) Dataset

We compiled a dataset of animal contact networks where edges represent one of 12 different contact types, using the Animal Social Network Repository (ASNR) [25,26]. The ASNR is an open-source animal behaviour network library in which we have compiled network data from the available literature across eight animal taxonomic classes (Mammalia, Aves, Reptilia, Amphibia, Insecta, Arachnida, Actinopterygii and Cephalapoda). Contact types include group membership, non-physical social interactions, spatial proximity, foraging interactions, trophallaxis (mouth-to-mouth food sharing), synchronous and asynchronous resource sharing, agonistic behaviours, grooming, other physical contact or mating interactions. Our sample size for this study consisted of 232 contact networks from all eight taxonomic classes (electronic supplementary material, figure S1). Of these 232 networks, 181 had weighted edges determined by the duration, frequency or association probability (e.g. half-weight index) of the contact type. We assume that these networks were observed without the presence of a pathogen or active infection.

(b) Defining and characterizing contact networks

For each network in our dataset, nodes represented an individual animal and edges represented a contact type between two animals. Based on the contact type, we divided our dataset into four different transmission mode categories (table 1). We focus on four transmission modes that our sample represents well: fluid-exchange, direct physical, non-physical close and indirect. We define each transmission mode category as follows:

1.	Fluid-exchange contact: host interactions that result in the exchange of bodily fluids. This includes sexual contact such as cloacal transfer, intromission and spermataphore transfer, as well as direct food-sharing interactions such as trophallaxis.
2.	Direct physical contact: interactions of physical touch that include grooming, agonistic host behaviours (e.g. head-butting, fighting), and other physical social contact.
3.	Non-physical close contact: close spatial proximity in which face-to-face contact, or respiratory droplet exchange, could occur. This includes group memberships, or spatial proximity.
4.	Indirect contact: asynchronous resource-sharing interactions. Indirect contact is unique in that individuals do not need to be using the resource at the same time to be connected in the network.

We note that our non-physical, physical and fluid-exchange categories have an inherent nested structure with non-physical the broadest category, and fluid exchange the most selective (electronic supplementary material, figure S2). In other words, pathogens that transmit on non-physical networks (i.e. respiratory droplet pathogens such as SARS-CoV-2) can also transmit on direct physical and fluid-exchange networks, but fluid-exchange transmitted pathogens (e.g. sexually transmitted pathogens such as gonorrhea (Neisseria gonorrhoeae)) can only transmit on fluid-exchange networks. We manage this nested structure by classifying each empirical network into the most specific category possible using the definitions above.

For each network, we calculated the following eight network metrics that are known to influence infection dynamics and social structure, ignoring edge weights (table 2): total network density, degree heterogeneity, degree assortativity, average clustering coefficient, average betweenness centrality, network diameter, fragmentation and subgroup cohesion. Fragmentation (i.e. the number of communities in each network), was estimated using the Louvain method [27] and the remaining network metrics were calculated using the NetworkX package in Python (https://networkx.github.io/).

(c) Identifying how network structure depends on transmission mode

To examine how contact network structure differs depending on its associated transmission mode category, we fitted a multivariate GLMM using the MCMCglmm package in R [28], where the eight network metrics (table 2) made up our multivariate response, and the associated transmission mode category was our predictor variable.

We also controlled for the effect of network size on these metrics by including the number of nodes as a predictor. Edge weight type (weighted versus unweighted) was also included to control for data sampling design and edge weighting criteria. As the spatial scale of data collection has been shown to influence network structure [18], we also included sampling scale as a predictor. Studies that collected data on captive animal populations (where all nodes and interactions are theoretically known) were labelled as captive sampling. Studies that focused data collection on specific social groups were categorized as social sampling, and those that focused data collection on all individuals within a fixed spatial boundary were labelled as spatial sampling. Since the social system of an animal species is also shown to influence network structure [18], we included species social structure (relatively solitary, gregarious and socially hierarchical defined in electronic supplementary material, table S1 based on [18]) as a predictor. Finally, we controlled for repeated measurements within studies by including study ID as a random effect in the analysis. We were unable to include a random effect for taxonomic class or use a phylogenetically controlled model, because there was an unbalanced representation of different taxa across the four transmission mode categories that made these effects difficult to fit successfully (electronic supplementary material, figure S1).

All response variables were continuous; to encourage proper model fitting we log-transformed then centred them (by subtracting the mean) and then scaled to unit variances (by dividing by the standard deviation). We ran one MCMC chain for 10 500 iterations, with a thinning interval of 10 after burn-in of 500 with uninformative priors. Non-physical contact transmission was the intercept factor level for the transmission mode category fixed effect. For each response variable, if the effect sizes of the three remaining transmission mode categories overlapped with zero then it was considered not different from non-physical contact. To examine differences between the remaining three modes, we observed the proportional overlap between their effect sizes across all 1000 iterations, multiplied by 2 per a two-tailed test; if it was less than 0.05, then the response variables were considered different between the transmission mode categories.

Within the ASNR, several studies provided more than one network for the study species or population. To avoid biasing our sample towards these studies, we randomly selected a maximum of 15 networks from each study (n = 232). To ensure that our results were not affected by this random subsampling, we reran our model 1000 times, each time choosing a different sample of networks from each study with more than 15 networks. We then chose a random estimate from each model run and computed an average of model estimates across the 1000 different subsamples.

(d) Characterizing critical transmission thresholds

We assume that our dataset consists of contact networks constructed in the absence of pathogens or active infections. Therefore, to examine how network structure affects a pathogen's ability to persist on a network, we must model the way a pathogen spreads on these networks using mathematical models.

We sought to identify a pathogen's critical transmissibility (T_c) on contact networks based on transmission mode. For a pathogen to persist in a network, its basic reproduction number (R₀) must be greater than 1, and R₀ depends on both a pathogen's T and the contact patterns of the network it travels on. Therefore, for each network, we sought T_c for which $T_{\mathrm{c}}(\mathrm{contact})=\hspace{0.17em}{R}_0>1$. To estimate T_c, we considered the impact of contact network structure by calculating R₀ using Monte Carlo simulations of a susceptible–infected–recovered (SIR) model of infection spread through each network. We ignored edge weights because the impact of interaction weight (e.g. contact duration or frequency) on infection spread is not well understood generally. We used an SIR percolation simulation model [29], where each outbreak was initiated by infecting a randomly chosen individual in the network. For the first generation of the simulation, the individual is given an opportunity to infect all its contacts, with transmissibility T, and then recover. This process is then repeated for each infected node, until no infections remain in the network. For each network, we simulated 250 disease outbreaks and of those classified large-scale epidemics as those where at least 10% of the population is infected. We repeated this for each T value in the range (0.01–0.8), and recorded the first T value for which at least 10% of the outbreaks were large-scale epidemics. Percolation theory suggests that our expectation for the probability of having a large-scale epidemic should match the expected size of a large-scale epidemic [29]. This reported T value is our estimate of the network's critical transmissibility T_c.

Past studies suggest that degree (i.e. density) and degree heterogeneity are the most important aspects of network structure affecting how a pathogen will transmit across a network [30]. In order to test this, we considered two control scenarios where we (1) isolated the effect of homogeneous degree (i.e. all individuals have the same number of contacts) on T_c and (2) isolated the effect of heterogeneous degree (i.e. on average, individuals have the number of contacts as scenario 1, but individual degree varies around this mean) on T_c. Therefore, we sought T_c for which $T_{\mathrm{c}}⟨k_{\mathrm{e}}⟩=\hspace{0.17em}{R}_0>1$, where $⟨k_{\mathrm{e}}⟩$ is the average excess degree of the network. The excess degree is the potential number of contacts an individual can infect after they have been infected by one of their contacts, and on average this value is larger for networks with degree heterogeneity than for homogeneous degree networks [22].

For the first control scenario, we considered a pathogen's T_c in a homogeneous degree network, in which the average excess degree, $⟨k_{\mathrm{e}}⟩$, is:

where $⟨k⟩$ is the average degree of the network. For the second control scenario, we considered a network with degree heterogeneity, thus the average excess degree is:

We consider these to be ‘control’ scenarios because equations (2.1) and (2.2) allow us to consider only the two network metrics of interest (density and degree heterogeneity), while our simulation method will inherently take in to account all aspects of network structure (centrality, clustering, etc.). By isolating how homogeneous and heterogeneous degree effects T_c, and comparing these results to our full network structure simulation method, we can elucidate how much of the variation in T_c may be attributed to the degree (density) and degree heterogeneity of a network.

We compared the T_c values for each transmission mode category of contact networks (non-physical close, direct physical, fluid-exchange, indirect) within each scenario using a one-way ANOVA, and pairwise t-tests with a Tukey HSD family-wise error-rate correction.

(e) Examining diversity of empirical pathogen characteristics

To examine how our results are reflected in known pathogen traits, we considered the transmissibility of a pathogen (T) as a function of its infectious duration (G) and its probability of infection (β) [21,22]:

To provide context for the covarying characteristics of known pathogens, we examine known β and G values (infection characteristics) for a small set of well-characterized pathogens to see how they compare to our findings. Because data on pathogen traits in non-human animals is limited, we instead focus on these traits in common human pathogens. We use two systematic reviews on the natural histories of pathogens for common diseases in preschools [31,32] to summarize data on pathogens that use each transmission mode. We only included the pathogens in our summary if the source of the data was from a well-designed study, using the levels of evidence of I and II provided in the first review [31] (electronic supplementary material, table S2). If there were no data, or the source of the data was poor (levels of evidence of III or IV) for the pathogen's infectious period (G), we instead used the shedding periods, defined as the period of time during which an individual excretes the pathogen; the shedding period can be used to estimate the duration of infectiousness when there is lack of direct evidence [31]. If there were no or poor data for the shedding period, then it was not included in this summary. We then verified the data for these pathogens using the second review [32].

Since these reviews did not contain any sexually transmitted pathogens, we took the 10 sexually transmitted pathogens listed on the CDC website (www.cdc.gov/std) and examined the literature for their natural histories. We found studies that estimated both the probability of infection (β) and infectious period (G) of four of the 10 pathogens (syphilis [33,34], gonorrhea [35,36], chlamydia [37,38] and trichomoniasis [39,40]).

(a) Network structure is dependent on host behaviour type

We examined how network structure was predicted by the pathogen transmission mode represented by specific contact types using a multivariate GLMM. We summarized network structure with eight topological characteristics (table 2), and all the metrics except subgroup cohesion and fragmentation differed among transmission mode categories. The predicted distributions for the six remaining network metrics by transmission mode category are summarized in figure 1 and all other effect sizes from our model are in electronic supplementary material, tables S3–S6.

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Fluid-exchange contact networks differed from physical and non-physical contact networks in all six network metrics and differed from indirect contact networks for clustering and network diameter. Indirect contact networks only differed from physical and non-physical networks in their degree heterogeneity. Physical and non-physical networks could not be differentiated by the network metrics we tested. This suggests that fluid-exchange contact types create the most unique contact patterns.

Physical and non-physical contact networks had higher density values and shorter network diameters than fluid-exchange networks, and lower degree heterogeneity than both fluid-exchange and indirect contact networks. This indicates that physical and non-physical contact types create networks that are more connected, with less variation in each individual's number of contacts.

Fluid-exchange contact networks also had lower degree assortativity than physical and non-physical contact networks. That is, high-degree individuals in fluid-exchange contact networks tend to be connected to low-degree individuals, whereas high-degree individuals in physical and non-physical contact networks are more likely to be connected to other high degree individuals. Indirect contact networks did not differ in their degree assortativity from any other contact network. Fluid-exchange contact networks also had lower average clustering values than all other contact networks.

Finally, fluid-exchange contact networks have higher betweenness centrality values than physical and non-physical contact networks. This means that these networks tend to have more ‘bridge nodes’, or nodes that connect different communities together: this is despite the fact that the number of communities (fragmentation) and the cohesiveness of those communities do not differ among contact networks.

(b) Pathogen transmissibility must be higher for contact networks with lower connectivity

We demonstrated the effect of full contact structure on critical transmissibility values (T_c) in networks for each of our four transmission mode categories. We then specifically examined the effect of network density (average number of contacts) and degree heterogeneity (variation in number of contacts) on T_c in two different control scenarios.

We find that generally pathogens needed significantly higher critical transmissibility values on fluid-exchange contact networks than on physical, non-physical, and indirect transmission contact networks (figure 2). By comparing our empirical simulation scenario to the two control scenarios, we find that fluid-exchange and indirect contact networks are more vulnerable to disease invasion (i.e. lower T_c) than expected based on their average connectivity (figure 2). This result is consistent with network epidemiology theory, which predicts that higher degree heterogeneity (as we find in fluid-exchange and indirect contact networks) make disease invasion more likely. For physical and non-physical contact networks, on the other hand, the critical transmissibility is comparable in all three scenarios, suggesting that the average network connectivity (or network density) is sufficient to predict disease invasion in such networks.

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(c) The structure of a contact network can influence the infection characteristics of associated pathogens

We compiled peer-reviewed data from common human pathogens as life-history data on pathogens in non-human animals was extremely limited. We visualized two of the characteristics that define a pathogen's transmissibility: its infectious period and its infection probability (figure 3).

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First, we showed that pathogens that transmit on indirect contact networks (e.g. food/waterborne, faecal–oral) have relatively short infectious periods, and varied between low to moderate infection probability. Next, we found pathogens that transmit on fluid-exchange contact networks (e.g. sex, saliva) have the longest infectious periods. Of those, the two pathogens (herpes, syphilis) that tend to have shorter infectious periods (despite intermittent infectivity over long periods) but alternatively have moderate to high infectivity. These results suggest that fluid-exchange pathogens do in fact have higher T_c values than other pathogens, and they tend to increase their T_c by extending their infectious periods over increasing their infection probability. Finally, we see that pathogens that transmit on physical and non-physical contact networks have some of the shortest infectious periods and a range of infection probabilities, but most pathogens with high infectivity are associated with these transmission modes.

(a) Differences among contact networks and their implications for pathogen spread

Most notably, compared to physical and non-physical contact networks, fluid-exchange networks were less dense and had more heterogeneous degree values, with greater diameters, reduced clustering and greater disassortativity by degree. They also had more bridge nodes than all other network types. That is, these networks tend to be more poorly connected, and with greater skew in nodes’ importance in the network. This selection of network traits likely arises through a combination of mechanisms, linked to the fact that many of these networks were based on sexual interactions.

First, the infrequency of copulation events will drive low network density, with correlated increases in the diameter of the network and the prevalence of bridge connections; second, the fact that all networks solely included male–female copulation events likely increases clustering and reduces the tendency for assortative mating; and finally, the common nature of polygyny and overdispersed mating events (i.e. few individuals monopolizing sexual resources) will drive greater degree heterogeneity, as well as driving disassortativity. These latter traits agree with our understanding of the overdispersed nature of sexual interaction networks [41–43]. The fluid-exchange category also included trophallaxis networks, which are also generally highly heterogeneous; in ants, more than 50% of trophallaxis interactions may come from less than 25% of individuals [44]. While the majority of the trophallaxis networks represented in our dataset are indeed in ants, many other species such as birds and mammals also partake in trophallaxis, usually in the form of parental care [45]; these unique parent–offspring interactions would also likely result in sparse, heterogeneous and highly fragmented networks.

These traits could have a selection of important consequences for transmission of pathogens through fluid-exchange networks. First, less dense networks are likely to provide fewer transmission opportunities for fluid-borne pathogens [46], while larger diameters will inhibit the spread of an outbreak. Second, degree heterogeneity is known to be a key driver of sexually transmitted pathogen risk in human contact networks [16,47]. Where contact numbers are highly heterogeneous, superspreaders can lead to rapid, explosive outbreaks, allowing pathogens to persist [21]. Indeed, past work has shown that HIV, a sexually transmitted pathogen, can exploit this contact heterogeneity to attain sufficient transmissibility, and other sexually transmitted pathogens likely do the same [48]. However, previous work on contact networks has shown that network density and individual variation in contact are negatively correlated [49]. Our results support these findings, as we found fluid-exchange and indirect contact networks have lower densities and higher-degree heterogeneity compared to physical and non-physical contact networks. This suggests that while having high-degree heterogeneity might make a network more vulnerable to explosive outbreaks [18,21], this may trade off with lower overall transmission probabilities [49]. Third, low clustering values might be beneficial for pathogens, especially given the low densities, as a pathogen may be less likely to get stuck in cliques that might form among individuals [50]. Fourth, the common nature of bridge nodes in fluid-exchange networks might be especially important when considering control measures for pathogens on these networks. Previous work has shown that pathogens with high transmissibility are able to persist in socially fragmented networks because bridge nodes allow for transmission among communities [30]. Therefore, the removal of these nodes will prevent or slow pathogen spread through a population [47]. While both physical and fluid-exchange transmission require relatively close contact, controlling disease spread by identifying bridge nodes might be more powerful for fluid-exchange pathogens than for others.

Notably, indirect contact networks had a more heterogeneous degree distribution than physical and non-physical contact networks, meaning there is more between-individual variation in asynchronous resource sharing compared to that in close proximity or physical touch. Past research has demonstrated this phenomenon in many solitary desert species that share burrows asynchronously, and while there are many ecological factors that might drive these individual preferences for resource-use patterns (such as differences in sex, age and environment) [30,51], we still do not have a full mechanistic understanding of them. It is possible that this pattern will drive greater heterogeneity in infection with indirectly transmitted pathogens.

(b) Network structure and the pressures on pathogen characteristics

Pathogens that transmit on indirect contact networks (e.g. food/waterborne, faecal–oral) seem to have relatively short infectious periods, and vary between low to moderate infection probabilities (figure 3). However, we found many aspects of indirect contact network structure were not different from fluid-exchange networks (i.e. low network densities and high degree heterogeneity) (figure 1). These results contradict expectations that these indirect networks should be highly connected since individuals need to have only used the same space at some point in time to be connected. For example, many individuals sharing the same sanitation facilities through time such as on airplanes [52], cruise ships [53] and hotels [54] can cause recurring outbreaks of Norwalk virus, a common faecal–oral pathogen; as there is no need to physically contact an individual to be infected by them, these contact networks are known to be extremely highly connected [55]. There are several possible explanations for our surprising finding: first, our results may be driven by the fact that relatively solitary species (which have low connectivity due to their social structure [30]) are highly represented in our indirect networks sample. Additionally, these networks often involve territorial species; resource sharing (both synchronous and asynchronous) is likely minimized in species that hold territories (e.g. [56]). Moreover, territoriality can be sex specific in that males very rarely use the same space and resources even asynchronously but females can move freely between male territories, which can result in a sex-specific degree heterogeneity in some species (e.g. [57,58]). Indeed, our GLMM showed a high amount of variation in the effect sizes of indirect contact networks and we found that pathogens using indirect contact networks do not need high T_c values to persist on these networks. This suggests that a species’ social system strongly influences the structure of indirect contact networks. Including additional species with other social systems may increase the average connectivity of indirect contact networks, which would be more representative of their associated pathogen characteristics. This paucity of variation in social systems is a common problem in meta-analyses of social network structure, and ongoing data collection may help to ameliorate this difficulty in the future.

Our simulations revealed that contact network structure should motivate the evolution of higher transmissibility for fluid-exchange pathogens to persist (figure 2); a prediction that was supported by our literature review (figure 3). This supports what we know about the host behaviours involved in bodily fluid exchange; individuals usually have long temporal gaps in between fluid-exchange events compared to other potential disease transmission host behaviours [1]. Therefore, pathogens would benefit more from longer infectious periods giving them more time to spread.

(c) The role of weak ties in defining relevant disease-spreading contact

Previous studies have shown that structural differences between networks are primarily driven by ‘weak ties’ that are disproportionately lower in intensity, frequency, or duration than other contacts [18]. When we eliminated weak ties, we found that differences between transmission mode categories persisted for some structural features (e.g. average clustering and degree assortativity), but others (density and degree heterogeneity) were lost; in other words, removing the weak ties from contact networks makes them more similar to each other in their number and variation of contacts. Given that the structural features of density and degree heterogeneity were most different among fluid-exchange networks, this finding suggests that not only do individuals tend to vary in the number of fluid-exchange contacts they have compared to their other types of contacts, but individuals also vary more in the strength of connections between their different fluid-exchange contacts, compared to their other types of contacts. We hypothesize that this might be the crucial difference between pathogens that spread via fluid exchange and others, but additional data would be required to confirm this hypothesis.

This heterogeneity in how individuals distribute their contact effort is known as ‘social fluidity’, where higher social fluidity suggests a higher prevalence of weak ties [9]. Past work has shown that non-physical contact networks (e.g. spatial association) have smaller values of social fluidity than fluid-exchange networks (e.g. trophallaxis), suggesting that social fluidity and weak ties are especially relevant when considering disease transmission potential in these networks [9]. In some instances, not considering a very brief or infrequent contact as ‘relevant’ for disease transmission might make sense, such as for pathogens that propagate on networks with low social fluidity (e.g. flu). However, for pathogens that are spread via fluid exchange, we found that the density and degree heterogeneity of contact networks are important predictors for determining their transmissibility and traits. This suggests it is imperative to include short or infrequent fluid-exchange interactions when considering the definition of relevant contact for modelling the transmission of these pathogens. By not including these ‘weak’ contacts, it is likely that estimates of fluid-exchange pathogen spread would be inaccurate, and proposed control measures based on these estimates could be unreliable.

(d) Study limitations

Our study has some important limitations. First, we investigated non-human animal networks, while using pathogen traits in humans to understand the implications of network structure on infection characteristics. We would expect some aspects of human contact networks to differ from animal contact networks, particularly with fluid-exchange transmission. For example, human sexual networks have much higher clustering values than what we observed in our animal networks [59]. However, this could be due to the lack of recorded same-sex sexual host behaviours in non-human animal species; same-sex host behaviours including fluid exchange do occur in many non-human animals and are therefore likely underrepresented in our sample [60]. Regardless, even if true clustering values are higher than observed, we would expect this to reduce the R₀ of a pathogen in a network; this might further increase the transmissibility needed to persist [59], further supporting our current results. Overall, we found that network density and degree heterogeneity were the most important metrics when considering a pathogen's ability to persist on a network; we show that fluid-exchange contact networks have low densities and high degree of variation which holds true in human networks [1,16,47]. Future studies could further validate this work by exploring the contact structures of available human contact networks. Alternatively, future work could provide a better overview of the natural histories of pathogens in wildlife. While we would expect infection characteristics to be similar based on our network analysis, we suggest a more thorough review of these characteristics across different taxa.

Our available network datasets likewise restricted our ability to test and untangle some factors. First, because we had a lack of data on indirect contact networks in wildlife species, we were unable to investigate the evolution of traits of environmentally transmitted pathogens. We also did not have good representation of contact networks representative of each transmission mode category across all taxonomic classes, which reduced our ability to control for host taxonomy in our model. Future work may be able to ameliorate these difficulties by measuring indirect contact networks from species with gregarious and hierarchical social makeups, as well increasing the taxonomic sample size of each transmission mode category, for a better representation of contact networks across species and social systems.

Lastly, our work does not consider the impacts of pathogen-mediated changes to contact structure as caused by sickness behavioural changes due to host immune response or pathogen virulence, nor due to pathogen manipulation of host behaviour [15]. For example, rabies can cause increased aggression and biting in hosts, which could increase the number of edges in some physical contact networks [61]. By contrast, some pathogens cause ‘sickness behaviours’ in their hosts, such as bacterial pneumonia in kudu antelope (Tragelaphus strepsiceros), where individuals have been shown to develop fevers and reduce their daily activities by 60% [62]. In cases where infected individuals exhibit sickness behaviours like these, they may reduce their contact rates such that the subsequent contact networks will have fewer edges. We assume the networks in our dataset represent host behaviour in the absence of active infections, but recognize that such disease-mediated behaviour change can alter both network structure and realized pathogen characteristics (e.g. infectious periods can be effectively reduced via sickness behaviours). Future work must consider this critical feedback loop between contact structure and pathogen characteristics, in light of different pathogen transmission modes.

(e) Broader disease ecology implications

It is widely accepted in disease ecology that host behaviour drives pathogen spread, and we have demonstrated how this relationship is affected by the type of contact necessary for transmission. For epidemic dynamics, understanding transmission routes are also necessary as they determine how the density and structure of the population affect the rate at which the disease will spread. Typically, if disease spreads indirectly or through co-incident contact then the transmission rate is assumed to scale proportionally with population density (density-dependence), whereas if transmission requires close, intentional contacts then we expect social connectivity to determine the outcome (frequency-dependence). Classically, this scaling of transmission with population density has been based on the transmission route of the pathogen, with sexually transmitted diseases generally assumed to be transmitted in a frequency-dependent manner [59,63], and respiratory-transmitted disease expected to spread in a density-dependent manner. However, past work has demonstrated that the scaling relationship depends more explicitly on heterogeneity in contacts [9,64], with higher heterogeneity being associated with less density-dependence, rather than pathogen biology. Our work empirically links these two concepts by demonstrating that pathogen transmission mode is associated with contact structure, e.g. contact networks relevant to sexually transmitted diseases are more heterogeneous in contacts and thus are expected to be frequency-dependent. However, our a priori classification of behaviours by transmission mode may be obscuring structural variability that exists within modes. For example, Colman et al. [9] demonstrate that networks with aggressive contacts (e.g. head-butting) have low heterogeneity (thus suggesting density-dependence), while networks with bonding contacts (e.g. grooming) have high heterogeneity (thus suggesting frequency-dependence). In our work, we classified both of these contact types in the physical transmission category, thus limiting the ability to detect this variation in scaling within transmission modes. Future work would benefit from a characterization of transmission scaling based on contact network structure, rather than assumptions about pathogen transmission modes.

Additional variation in host behaviour can be attributed to social differences among and within species [18]. For example, the pace-of-life-history can explain variation in social relationships and across taxonomic scales. While we control for different social systems in our model, there is also potential for further network variation within these social systems and within species. For example, mating system dynamics and patterns of sexual promiscuity can vary widely within groups and populations of the same species, as a function of ecological variation and population sex ratios [43,65,66]. Moreover, two ungulate species Grevy's zebra (Equus grevyi) and onagers (Equus hemionus khur), which both have gregarious social systems, have been shown to have significantly different network structures, likely due to species traits that have evolved from inhabiting different environments [67]. Additionally, recent work has shown the importance of considering spatial components of individual behaviour (e.g. home ranges, landscape use) when modelling social networks and disease transmission [68] as they allow for more accurate model estimates, including a better inference of pathogen transmission modes [69]. We do expect there to be variation in host contact network structure related to traits and spatial behaviours, and suggest that future meta-analytic work that captures host heterogeneities and spatial structure will be necessary to better address this problem empirically.