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Aggregation may or may not eliminate reproductive uncertainty

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  • Logofet, Dmitrii O.

Abstract

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 λ1 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 λ1 via the row (or column) sums of matrix elements, and the lower bound, when it exceeds the maximal possible λ1 of the original, disaggregated matrix, does explain why the aggregation may fail to eliminate reproductive uncertainty.

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  • Logofet, Dmitrii O., 2017. "Aggregation may or may not eliminate reproductive uncertainty," Ecological Modelling, Elsevier, vol. 363(C), pages 187-191.
    • Handle: RePEc:eee:ecomod:v:363:y:2017:i:c:p:187-191
    DOI: 10.1016/j.ecolmodel.2017.08.004
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    References listed on IDEAS

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    1. Logofet, Dmitrii O., 2013. "Projection matrices in variable environments: λ1 in theory and practice," Ecological Modelling, Elsevier, vol. 251(C), pages 307-311.
    2. Logofet, Dmitrii O., 2008. "Convexity in projection matrices: Projection to a calibration problem," Ecological Modelling, Elsevier, vol. 216(2), pages 217-228.
    3. Oborny, B. & Mony, C. & Herben, T., 2012. "From virtual plants to real communities: A review of modelling clonal growth," Ecological Modelling, Elsevier, vol. 234(C), pages 3-19.
    4. Logofet, Dmitrii O., 2013. "Calamagrostis model revisited: Matrix calibration as a constraint maximization problem," Ecological Modelling, Elsevier, vol. 254(C), pages 71-79.
    5. Logofet, Dmitrii O., 2016. "Estimating the fitness of a local discrete-structured population: From uncertainty to an exact number," Ecological Modelling, Elsevier, vol. 329(C), pages 112-120.
    6. Marescot, Lucile & Gimenez, Olivier & Duchamp, Christophe & Marboutin, Eric & Chapron, Guillaume, 2012. "Reducing matrix population models with application to social animal species," Ecological Modelling, Elsevier, vol. 232(C), pages 91-96.
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    1. Dmitrii O. Logofet & Leonid L. Golubyatnikov & Elena S. Kazantseva & Nina G. Ulanova, 2021. "“Realistic Choice of Annual Matrices Contracts the Range of λ S Estimates” under Reproductive Uncertainty Too," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    2. Dmitrii O. Logofet & Valerii N. Razzhevaikin, 2021. "Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication," Mathematics, MDPI, vol. 9(14), pages 1-15, July.
    3. Logofet, Dmitrii O., 2019. "Does averaging overestimate or underestimate population growth? It depends," Ecological Modelling, Elsevier, vol. 411(C).

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