From theory to application: Elasticity-consistent aggregation of Leslie matrix population models for comparative demography

Abstract Ecology has entered the big data era. This influx of data has now enabled ecologists to address questions about life history and demographic patterns across the tree of life. Supporting this momentum, the COMADRE and COMPADRE databases represent a boon to comparative demography. However, these initiatives also present challenges due to the complexities of the life cycles that they describe. Matrix population models can vary in sampling frequency, life cycle stage width, life cycle complexity, and census type (e.g. pre- or post-reproduction). Complicating this picture is the fact that there are myriad matrix model representations of the same population, and model representation influences key demographic parameters. Thus, a key challenge in exploiting large demographic datasets is fair comparison of models constructed with different projection intervals and complexities. One way to compare models of different complexity is to reduce (‘aggregate’) the larger models to the dimensionality of the smaller models. The commonly used aggregator (i.e. the standard aggregator), although it yields stable growth rate and stable stage distribution consistent with the original demographic model, does not provide consistent reproductive values and elasticities. To address this limitation, we extend and validate an existing elasticity-consistent aggregator, overcoming several of its methodological and biological limitations. Specifically, we derive the aggregator using balancing and interstage flows, which removes the requirement of matrix primitivity, and we restrict aggregation to Leslie-to-Leslie models, thereby preventing biologically infeasible survival probabilities exceeding one. We further introduce explicit metrics of aggregation effectiveness and apply the approach to 12 Leslie matrix population models representing animal populations from diverse taxonomic classes. The elasticity-consistent aggregator returns a Leslie matrix that preserves key properties of the original matrix, including irreducibility and primitivity, and yields consistent estimates of population growth rate, stable age distribution, and reproductive values. Moreover, across all aggregated models from the 12 examined animal populations, the elasticity-consistent aggregator produced more accurate estimates than the standard aggregator for 86% of generation times, 60% of Demetrius’ entropies, and 76% of net reproductive rates. By preserving key properties of the original model, the elasticity-consistent aggregator provides a useful framework for comparing matrix population models of varying complexity in comparative demography. Such a method helps seize the promise of big data in ecology and discover principles across the tree of life, from microbes to fungi, plants, and animals. Competing Interest Statement The authors have declared no competing interest.