Amelie Fritz, Angelina Makeyeva, Kaspar Staub, Detlef Groth

• Background: Recent research reported height biased migration of taller individuals and a Monte Carlo simulation showed that such preferential migration of taller individuals into network hubs can induce a secular trend of height. In the simulation model taller agents in the hubs raise the overall height of all individuals in the network by a community effect. However, it could be seen that the actual network structure influences the strength of this effect. In this paper the background and the influence of the network structure on the strength of the secular trend by migration is investigated. Material and methods: Three principal network types are analyzed: networks derived from street connections in Switzerland, more regular fishing net like networks and randomly generated ones. Our networks have between 10 and 152 nodes and between 20 and 307 edges connecting the nodes. Depending on the network size between 5.000 and 90.000 agents with an average height of 170 cm (SD 6.5 cm) are initially released into the network. In eachBackground: Recent research reported height biased migration of taller individuals and a Monte Carlo simulation showed that such preferential migration of taller individuals into network hubs can induce a secular trend of height. In the simulation model taller agents in the hubs raise the overall height of all individuals in the network by a community effect. However, it could be seen that the actual network structure influences the strength of this effect. In this paper the background and the influence of the network structure on the strength of the secular trend by migration is investigated. Material and methods: Three principal network types are analyzed: networks derived from street connections in Switzerland, more regular fishing net like networks and randomly generated ones. Our networks have between 10 and 152 nodes and between 20 and 307 edges connecting the nodes. Depending on the network size between 5.000 and 90.000 agents with an average height of 170 cm (SD 6.5 cm) are initially released into the network. In each iteration new agents are regenerated based on the actual average body height of the previous iteration and, to a certain proportion, corrected by body heights in the neighboring nodes. After generating new agents, a certain number of them migrated into neighbor nodes, the model let preferentially taller agents migrate into network hubs. Migration is balanced by back migration of the same number of agents from nodes with high centrality measures to less connected nodes. The latter is random as well, but not biased by the agents height. Furthermore the distribution of agents per node and their correlation to the centrality of the nodes is varied in a systematic manner. After 100 iterations, the secular trend, i.e. the gain in body height for the different networks, is investigated in relation to the network properties. Results: We observe an increase of average agent body height after 100 iterations if height biased migration is enabled. The increase rate depends on the height of the neighboring factor, the population distribution, the relationship between population in the nodes and their centrality as well as on the network topology. Networks with uniform like distributions of the agents in the nodes, uncorrelated associations between node centrality and agent number per node, as well as very heterogeneous networks with very different node centralities lead to biggest gains in average body height. Conclusion: Our simulations show, that height biased migration into network hubs can possibly contribute to the secular trend of height increase in the human population. The strength of this "tall by migration" event depends on the actual properties of the underlying network. There is a possible significance of this mechanism for social networks, when hubs are represented by individuals and edges as their personal relationships. However, the required high number of iterations to achieve significant effects in more natural network structures in our models requires further studies to test the relevance and real effect sizes in real world scenarios.…