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Pearson r coefficients show the strength of relationship between network duration and carrying capacity at each disaster frequency.

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The right-hand column shows the remaining population at the end of a run, averaged from the results of 20 simulation runs at each carrying capacity. Households only died off at capacities of 15, and below. These results show that more household deaths at lower carrying capacities are not confounding the relationship between increasing carrying capacity and network size. For more detailed analysis of death rates, including time series analyses of household deaths, see Section G in S1 File.

Pearson r coefficients show the strength of relationship with carrying capacity for network size, duration, and population. Fig 5 shows an experiment where whenever a network of 20 or more clients formed during runs at a capacity of 10,, carrying capacity would be raised to 50, while that network remained in existence. Now a much larger and longer-lasting network formed in every run, and in 13 out of 20 runs this network incorporated more than 80 households. This experiment indicates that if available biomass increases during key moments when burgeoning networks are still small but beginning to form, the likelihood that a large network will develop is much increased.

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Network size, duration, and end population at a fixed carrying capacity of 10,, and during an experiment raising carrying capacity to 50, if a large network developed. Averaged over 20 runs for each carrying capacity. To perform general sensitivity analysis on our ABM, we employ the commonly used method of multiple regressions [ 32 ], with results reported in Table 1. The dependent variables are size of the largest network, duration of the largest network, and population size. To perform multiple regressions we use the SPSS statistics package, inputting runs of results for each dependent variable at each disaster frequency, repeated at every carrying capacity.

This gives run results for every combination of carrying capacity and disaster frequency, totalling 4, runs. SPSS then calculates R-squared and R values, expressing the degree to which our two independent variables are correlated with each dependent variable. The Beta coefficients provide the direction of the relationship positive or negative correlations.

These results show the dependent variables are highly sensitive to the employed variation in carrying capacity and disaster frequency.

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  7. There is a strong positive relationship between carrying capacity and network size and duration, and a negative relationship between disaster frequency and network duration. To expound further on model dynamics, we explain here how the independent variable of carrying capacity results in wealth inequality and changing network size and duration. Development of wealth inequality requires 1 disasters that strike agents differentially, and 2 some level of carrying capacity. Without disasters, agents would grow their herds equally each time step, resulting in Gini indices of 0.

    As previously discussed, disasters must not be so high as to cause average losses to exceed average growth—in this case wealth inequality cannot develop, as agents cannot accumulate wealth. However, disasters alone are insufficient to result in high wealth inequality. Instituting any carrying capacity however, results in uniformly high wealth inequality Fig 1. This is likely the result of two factors. Firstly, once carrying capacity is reached growth ceases, and thus the current level of inequality due to stochastic timing of disasters affecting agents differentially does not continue to average itself out over time.

    Furthermore, while the order in which agents grow their herds each time step when total herd falls below capacity is random, once a wealthy agent grows their herd, remaining agents may not have the opportunity for growth, as capacity may already have been reached. In terms of fit with the empirical record, we feel this dynamic is realistic when dealing with a finite resource pool common pasture with limited total biomass.

    In this context, wealthy agents have higher absolute growth potential despite equal relative growth potential—e. While growth is relative, the lower patron threshold animals is absolute. This means that at higher carrying capacities, a wealthy patron requires a larger number of successive disasters before their herd decreases below this threshold and their network is dissolved.

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    Furthermore, redistributing 60 animals to clients represents a significant burden on patron herd size, better absorbed by the proportionally larger patron herd at higher carrying capacities. For example, a patron with 89 clients will, at a minimum, have distributed 60 animals to each client once, representing 5, animals. While agent herds will more frequently dip below the poverty threshold 60 animals at lower carrying capacities as wealth distribution is the same as at higher capacities, but total system animals are fewer , this is more than counterbalanced by the lower probability that a patron is able to support so many clients without collapsing.

    At higher capacities, not only do patrons have a larger buffer before collapse, but also their clients will require less redistribution to maintain. In other words, at the highest carrying capacities, after initial redistribution of animals to a new client, a patron is less likely to have to support that client again. We also discuss common confounding variables that may act upon our simulation dynamics in empirical cases, and how our type of simulation can be applied to empirical analysis. We stress that by examining multiple case studies we are not implying a necessary or exclusive correlation between positive climatic change and nomadic empire creation.

    This latter is a multivariate process, and the effects of climate may be confounded or outweighed by any number of political, social, and cultural variables emerging from a long causal chain of historical particulars. Nonetheless, our approach is to use simple, abstract simulations involving as few variables as possible.

    This builds up an understanding of relationships that allows for a better appreciation of the ultimate effect of additional variables.

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    Additionally, the more abstracted a model, the more potential it has to be applied and analyzed in a variety of particularistic scenarios. In applying our model, we are primarily interested in cases where empirical evidence has already suggested enhanced environmental productivity did correlate with documented moments of nomadic empire creation, hierarchy, and centralization.

    Comparing model processes with empirical data is a great challenge, since the archaeological and historical record on the particulars of the emergence of these empires is so scarce.

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    In the case of the creation of the Mongol Empire, Di Cosmo [ 33 ] notes that the only early historical source, the Secret History of the Mongols , is of unknown reliability. This is compounded by its overwhelming focus on lauding the military exploits of Genghis Khan and his allies, at the expense of elucidating critical background factors involved in the economics and logistics of network creation and maintenance.

    In cases such as these, we feel simulation is an ideal tool to experiment with mechanisms that can connect the dots between a an empirically observed environmental context, and b an empirically observed socio-political phenomenon. Two of these correlations between climate and empire the Mongol and Xiongnu periods happen to be the two largest and longest lasting nomadic empires in the historical record.

    As such, they are our primary case studies.

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    We are also interested in evidence for the adoption of strategies designed to mitigate the effect of climatic downturns on hierarchical networks and polities among nomads, and cases where the effects of climate have been confounded by other political, social, or cultural variables. According to recent dendroclimatology research, Mongolia experienced drought from to CE, and an unprecedented pluvial from to CE, along with above-average temperatures [ 5 ].

    Pederson et al. Putnam et al. In Mongolia, they argue this led to a southward push of snow lines, grasslands, and concomitant wetting of Inner Asian deserts, substantially increasing available biomass. Climate data suggesting a warmer and wetter period in the early years of the Mongol Empire fits well with our model predictions, as these are the conditions characterized by increased rangeland productivity that increase the probability of large stable network formation Fig 4.

    In the present, Khentii is known as one of the most productive regions in Mongolia; in it had households with over 1, head of livestock, placing it second in Mongolia, at double the national average [ 27 ]. The relatively high carrying capacity of Khentii pastures is borne out by NDVI satellite imagery, reflecting photosynthesis capacity per unit land, shown in Fig 6. Darker green indicates higher biomass. While we experiment with poor climatic conditions followed by positive climate change and enhanced productivity Fig 5 , the preceding period of negative productivity drought observed by Pederson et al.

    Even in simulations run exclusively in high productivity, low risk environments, network duration shows regular turnover in patrons, such that roughly ten different large networks could be expected per 2, time cycles under these parameters Fig 3. The actual process simulated in our model, of differential success of herding agents followed by redistribution of animals from rich to poor households, is extremely difficult to identify in historical sources, and particularly in archaeological data.

    The aforementioned Secret History of the Mongols SHM may be an embellishment of military valour, but social and cultural references would probably have been recognizable to contemporary readers, and provide indirect evidence for processes seen in simulation. Chapters covering the reign of Ogedei Khan — CE make passing reference to Ogedei mandating the collection and redistribution of sheep from aristocratic and military leaders to poorer households SHM — Aristocratic characters in the Secret History also make occasional references to the camp locations and movements of specialist herders of horse, sheep, and other animals working for them, implying contractual herding agreements e.

    SHM , , Wright [ 34 ] has recently argued that the characteristic empty walled enclosures of the Mongol Empire period functioned as animal collection centres, in an early example of nomadic pastoral taxation and surplus. Regular taxation of livestock at these enclosures during seasonal migratory movements indicates one way a centralized power, or patron, could redistribute wealth where it was needed to maintain followers and authority.

    While the Secret History of the Mongols is equivocal regarding exactly how Genghis Khan provisioned and maintained his growing network of followers [ 33 ], Pederson et al. Taken in isolation, this sparse data would be difficult to form into a coherent theory of empire creation, but coupled with simulation experiments, a pattern of network formation based on redistribution of unequal herding surplus seems plausible.

    This is further supported by data from the ethnographic era on the development of patron-client contract herding relations in a variety of nomadic pastoral societies [ 9 , 31 ]. Other elements of the Mongol Empire and its rise provide an opportunity to understand the complex interplay between the simple relationship our model demonstrates, and its interaction with socio-political variables.

    While a climatic upturn at the end of the twelfth century increased the probability of a nomadic polity, political occurrences external to the Mongolian herding landscape were also critical. From the tenth to twelfth centuries, Mongolia was a territory within the Khitan Liao Empire, a status severely curtailing any indigenous polity creation. The collapse of the Liao after military defeat at the hands of the Jurchen Jin Empire subsequently created a relative power vacuum on the Mongolian steppe, which grew larger following Jin withdrawal in the mid twelfth century [ 36 ].

    External political and military events played a critical role in creating an environment of relative freedom from confounding external variables, in which network dynamics among herders could play out against the backdrop of an enhanced climate. Likewise, socio-political structures, whether by design or by accident, may sometimes function to mitigate effects that emerge in our model, such as the rapid breakdown of large networks during climatic downturns.

    A noteworthy feature of the later Mongol Empire, in comparison to earlier nomadic polities, was its adaption of sedentary features such as fixed urban centres. These included the capital city of Karakorum, and the later capital of Dadu present-day Beijing.

    These cities could be supplied with and store grain from conquered Chinese agricultural areas [ 37 ]. Official documentation from the Mongol Yuan Dynasty makes repeated mention of large numbers of Mongolian herders, made destitute by environmental disasters such as winter snow storms, entering these centres and being granted grain or cash [ 38 , 39 ]. An adaptation of our present simulation model includes externally provisioned urban centres that poor agents can migrate to instead of seeking herding patrons [ 40 ]. Results indicate these centres substantially increase the resilience and duration of remaining herding networks during short-term climatic downturns, by providing a runoff zone for agents that would otherwise drain the energy resources of their patrons.

    Mongol Empire urban centres are a useful example of how an additional variable may confound the relationship between climate and networks expressed in our model. However, understanding of the effect of this new variable is substantially enhanced by prior knowledge of the simple relationship between climate and networks we report here.

    Given that our results indicate relative probabilities of large network creation, it does not surprise us to find that the largest of all nomadic empires 1 originated in a part of the pastoral world that is relatively lush [ 25 ], 2 centered on a sub region of Mongolia that is arguably its most productive, and 3 arose during a time period with an uncharacteristically favourable climate for herding.

    While these correlations may seem fairly obvious in hindsight, this is not the case, given longstanding negative climate theories of nomadic empire creation. This has been coupled with the longstanding viewpoint of sedentary societies concerning the relatively primitive character of nomadic social organization and its dependency on sedentary neighbours for surplus energy.

    The Xiongnu Empire is the first historically documented empire created by nomads in present-day Mongolian territory, and the longest lasting, presenting a useful comparison with the later Mongol period. Likewise, precipitation research indicates this warm period was also wet [ 42 , 43 ]. More specific to the Xiongnu, Houle [ 44 ] has collected relevant environmental, archaeological, and faunal data from multiple regions of Mongolia to test the Mongol Empire model of climate and empire creation developed by Pederson et al.

    Faunal analysis in the Khanuy Valley indicates this led to expanded rangeland productivity, with an estimated threefold increase in the large domestic mammal population, and a doubling of the human population during the initial Xiongnu period. This region is associated archaeologically with elite Xiongnu burials and is generally taken as the heartland of the Xiongnu polity.

    In contrast to the Mongol Empire climate model developed by Pederson et al. Each empire is a multivariate phenomenon with different particulars governing emergence. Even in our model, which tests the effect of environmental productivity on network formation, climate change is not the sole driver, as we observe the formation of large networks albeit at differing rates of probability under a wide variety of environmental parameters.

    Rather, wealth inequality, or more precisely the ability of some agents to gather, store, and redistribute surplus energy, is ultimately the driver of hierarchical network formation in our model. What our simulation shows is that a rise in environmental productivity increases the probability of large network formation. In this context, our findings provide interesting insights into the Xiongnu, who were able to maintain an uncharacteristically large and long lasting nomadic polity during a period of documented warmth, wetness, and increased rangeland productivity.

    As Houle [ 44 ] notes, archaeological evidence on the degree of centralization in the Xiongnu polity is unclear in comparison to the Mongols, whose politics have greater historical documentation, and whose material remains include capital cities.

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    However, nomadic empires before the adaption of sedentary features such as fixed capitals may present little to no material evidence of centralization or hierarchy for future archaeologists.