Group size and modularity interact to shape the spread of infection and information through animal societies

Abstract

Social interactions between animals can provide many benefits, including the ability to gain useful environmental information through social learning. However, these social contacts can also facilitate the transmission of infectious diseases through a population. Animals engaging in social interactions therefore face a trade-off between the potential informational benefits and the risk of acquiring disease. Theoretical models have suggested that modular social networks, associated with the formation of groups or sub-groups, can slow spread of infection by trapping it within particular groups. However, these social structures will not necessarily impact the spread of information in the same way if its transmission follows a "complex contagion", e.g. through individuals disproportionally copying the majority (conformist learning). Here we use simulation models to demonstrate that modular networks can promote the spread of information relative to the spread of infection, but only when the network is fragmented and group sizes are small. We show that the difference in transmission between information and disease is maximised for more well-connected social networks when the likelihood of transmission is intermediate. Our results have important implications for understanding the selective pressures operating on the social structure of animal societies, revealing that highly fragmented networks such as those formed in fission-fusion social groups and multilevel societies can be effective in modulating the infection-information trade-off for individuals within them.

Supplementary information: The online version contains supplementary material available at 10.1007/s00265-021-03102-4.

Keywords: Conformist learning; Infectious disease; Social learning rule; Social network; Transmission.

Fig. 1

Summary of simulations for a single parameter set

Fig. 2

Visualisation of transmission probabilities for a) disease and b) information, depending on the number or proportion of infected/informed contacts, at different values of R₀

Fig. 3

Examples of the networks at different levels of network density (row), rewired to different values of network modularity (column) and two different group sizes (5 and 40) for the same population size (200)

Fig. 4

Overview of mean time taken for disease (red) and information (blue) to infect 75% of nodes in modular networks of 200 nodes. Smaller datapoints are results for each of the 20 repeats, while large datapoints are the mean for that parameter combination. Results are shown for different levels of network modularity (column), density (row) and R₀ (symbol and colour). Note that for illustrative purposes, we include only a subset of group sizes and other parameter values in this figure, while the full dataset is visualised in Supplementary Fig. 4. Note also that for infection spread, some runs of the simulation with a group size of five and network density of 0.1 did not complete before the time cut-off of our simulations and are not shown on this plot

Fig. 5

Overview of the difference between modular and random networks in mean time taken for disease (red) and information (blue) to infect 75% of nodes in a network of 200 nodes. The Y-axis shows the mean time taken for a transmission process to reach 75% of nodes in a random network subtracted from the mean time taken for a transmission process to reach 75% of nodes in a modular network derived from that random network. Positive values therefore indicate slower spreading in modular networks, negative values faster spreading. Smaller datapoints are results from each of the 20 repeats, while large datapoints are the means for that parameter combination. Results are shown for different levels of network modularity (column), density (row), and R₀ (symbol and colour). Note that we include only a subset of group sizes and other parameter values in this figure; for a figure showing the full dataset, see supplementary Fig. 5. Note also that for infection spread, some runs of the simulation with a group size of five and network density of 0.1 did not complete before the time cut-off of our simulations and are not shown on this plot

Fig. 6

Effect of network density on the difference in time taken for disease and information to infect 75% of 200 nodes in a modular network consisting of small groups of 5 individuals. The Y-axis shows the time taken for disease to infect 75% of nodes subtracted from the time taken for information to inform 75% of nodes. Positive values on the Y-axis therefore indicate information taking longer to reach this level of infection than disease, while negative values on the Y-axis indicate disease taking longer. Smaller datapoints are raw data, while large datapoints are means. Results are shown for different levels of R₀, network modularity and density. Means for parameter combinations where 75% of individuals were not infected by our cut-off of 3500 time steps are excluded

Fig. 7

Effect of transmissibility on the difference in time taken for disease and information to infect 75% of nodes in a 200-node network of density 0.05 with small groups of 5 individuals. The Y-axis shows the time taken for disease to infect 75% of nodes subtracted from the time taken for information to inform 75% of nodes. Positive values on the Y-axis therefore indicate information taking longer to reach this level of infection than disease, while negative values on the Y-axis indicate disease taking longer. Smaller datapoints are raw data, while large datapoints are means. Results are shown for different levels of network modularity