Integrated paleoecological modeling of Pleistocene vegetation and megafauna

During the last glacial, large grazers — among others, woolly mammoths, steppe bison, and horses — inhabited Eurasia’s so-called mammoth steppe. This cold steppe was evidently productive enough to sustain a diverse assembly of large mammals, but it remains controversial which population densities it could support. In sufficient densities, large herbivores can act as ecosystem engineers: creating and maintaining grassland habitat by means of disturbance and nutrient cycling. Estimating carrying capacity (i.e., long-term mean megafauna densities) of the Pleistocene mammoth steppe is therefore pivotal for understanding this paleoecosystem. In order to estimate mammoth steppe carrying capacity I developed a dynamic mechanistic grazer population model and coupled it with an existing dynamic vegetation model. Large herbivore population densities emerge from the bottom up from physiological and demographic processes. This kind of predictive mechanistic modeling faces two particular epistemic obstacles: scarcity of observational data and confirmation bias. I argue that a model’s predictions can, to varying degree, count as evidence, but their credibility rests upon arguments justifying that the model stands in for the target system. With little or no independent data for model evaluation, this epistemic justification of the model hinges on its underlying theory. This link between theory and predictions is rife with uncertainty. Therefore I propose to place uncertainty quantification at the heart and center of mechanistic model development and application. Confirmation bias, the second obstacle, can arise from (inadvertently) tuning the model to match one’s expectations. Using a Bayesian framework I lay out how the risk of confirmation bias calls for a blinding veil to the outcome of the final predictive simulation: so that the posterior does not influence the prior. For practical implementation I advocate preregistration as a tool to separate exploratory model development from predictive model application. Together, uncertainty analysis and preregistration strengthen our confidence in model predictions. Bottom-up modeling should derive conceptual choices from theory and parameter values from observations. Physiological mechanisms and parameters of the grazer model are transparently linked to theory and observations. Modeling challenges lie in modeling thermoregulation and seasonally adapting metabolic rates. In test simulations, I analyzed seasonality in forage and body fat, population stability, and coexistence of different herbivore types. In the model, carrying capacity is limited by forage availability in winter. For estimating carrying capacity for the mammoth steppe I chose the eponymous woolly mammoth (Mammuthus primigenius) to represent biomass of the whole grazer guild. Reviewing the literature I identified plausible ranges for parameter values. In order to account for parameter uncertainties I chose a Bayesian approach, taking the parameter ranges as priors. To define the likelihood function I selected a sample of modern-day locations with climate conditions that span the supposed climatic envelope of the glacial mammoth steppe. The likelihood of seeing the data under the model is then the proportion of locations where the model predicts viable mammoth populations. This kind of model fitting made no assumption about mammoth densities but only about their presence under certain environmental conditions. Subsequently I analyzed parameter sensitivity by fitting boosted regression trees on the output of all calibration simulations, which produced a ranking of parameters by their influence on mean population density. The posterior credibility interval of simulated mammoth mean densities spans 13–85 kg/ha (95% quantile). This falls between the lower and the higher estimates of mammoth steppe herbivore density from previous modeling and fossil-based studies. However, I discuss reasons why the model results are probably an overestimation. Notwithstanding uncertainties in primary production, my results call for a more nuanced view on potential natural baselines. Potential large herbivore biomass densities of over 100 kg/ha, which a number of recent publications assume, might be an overestimation. Parameter posterior densities of my Bayesian simulations reveal that mammoths were unable to suffer any annual adult background mortality above 5%. This figure confirms other published estimates and underlines the high susceptibility of mammoth populations to predation on adults, particularly by humans. Notably, juvenile background mortality rate plays an insignificant role for long-term population densities. Simulated carrying capacity strongly depends on net primary production. Therefore, future modeling efforts should focus on improving quantitative understanding of graminoid productivity and plant–herbivore interactions under glacial conditions.