Aggregation may or may not eliminate reproductive uncertainty.

In matrix population models, there cannot be any ‘reproductive uncertainty’ when the life cycle graph contains only one reproductive stage. Otherwise, it is logical to expect that aggregating all the reproductive stages into a single one would exclude the very basis of uncertainty. However, can the aggregation change principally the model characteristics such as the dominant eigenvalue λ 1 of the projection matrix, thus signifying the aggregation failure? I demonstrate that it can with the data mined in a case study on the dynamics of a local stage-structured population of Eritrichium caucasicum , a short-lived perennial plant species inhabiting an alpine lichen heath. Frobenius Theorem for nonnegative matrices specifies the upper and lower bounds for λ 1 via the row (or column) sums of matrix elements, and the lower bound, when it exceeds the maximal possible λ 1 of the original, disaggregated matrix, does explain why the aggregation may fail to eliminate reproductive uncertainty. [ABSTRACT FROM AUTHOR]