The collective vs individual nature of mountaineering: a network and simplicial approach

Mountaineering is a sport of contrary forces: teamwork plays a large role in mental fortitude and skills, but the actual act of climbing, and indeed survival, is largely individualistic. This work studies the effects of the structure and topology of relationships within climbers on the level of cooperation and success. It does so using simplicial complexes, where relationships between climbers are captured through simplexes that correspond to joint previous expeditions with dimension given by the number of climbers minus one and weight given by the number of occurrences of the simplex. First, this analysis establishes the importance of relationships and shows that chances of failure to summit reduce drastically when climbing with repeat partners. From a climber-centric perspective, climbers that belong to simplexes with large dimension were more likely to be successful, across experience levels. From an expedition-centric perspective, the distribution of relationships within a group is explored to identify collective human behavior: from polarized to cooperative. Expeditions containing simplices with large dimension, and usually low weight, i.e., a large number of people had a small number of previous joint expeditions, tended to be more cooperative, with more homogeneity in success amongst climbers. On the other hand, the existence of small, usually strong, subgroups lead to a polarized style where climbers that were not a part of the subgroup were less likely to succeed. Lastly, this work examines the effects of individual features and expedition-wide factors that may play different roles in individualistic and cooperative expeditions. Centrality indicates that individual traits of youth and oxygen use while ascending are strong drivers of success. Of expedition-wide factors, the expedition size and number of expedition days are found to be strongly correlated with success rate.