Novel challenges and opportunities in the theory and practice of matrix population modelling: An editorial for the special feature

Logofet, Dmitrii O.; Salguero‐Gómez, Roberto

doi:10.1016/j.ecolmodel.2021.109457

Cited by 7 publications

(3 citation statements)

References 77 publications

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“…Being nonnegative, the PPM becomes a legal target for the Perron-Frobenius Theorem [5,6], whereby a rich repertoire of model properties and population characteristics can be obtained after the PPM has been calibrated from data [4,7]. In particular, the dominant eigenvalue, λ 1 > 0, of matrix L(t) serves as a "measure of how the local population is adapted to the environment where and when the data have been mined to calibrate the PPM" [8] (p. 1).…”

Section: Introductionmentioning

confidence: 99%

Pattern-Multiplicative Average of Nonnegative Matrices Revisited: Eigenvalue Approximation Is the Best of Versatile Optimization Tools

Logofet

2023

Mathematics

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Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern, too. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative (or geometric) nature of averaging. The original concept of PMA was motivated by the practice of matrix population models as a tool to assess the population viability from long-term monitoring data. The task has reduced to searching for an approximate solution to an overdetermined system of polynomial equations for unknown elements of the average matrix (G), and hence to a nonlinear constrained minimization problem for the matrix norm. Former practical solutions faced certain technical problems, which required sophisticated algorithms but returned acceptable estimates. Now, we formulate (for the first time in ecological modeling and nonnegative matrix theory) the PMA problem as an eigenvalue approximation one and reduce it to a standard problem of linear programing (LP). The basic equation of averaging also determines the exact value of λ1(G), the dominant eigenvalue of matrix G, and the corresponding eigenvector. These are bound by the well-known linear equations, which enable an LP formulation of the former nonlinear problem. The LP approach is realized for 13 fixed-pattern matrices gained in a case study of Androsace albana, an alpine short-lived perennial, monitored on permanent plots over 14 years. A standard software routine reveals the unique exact solution, rather than an approximate one, to the PMA problem, which turns the LP approach into ‘’the best of versatile optimization tools”. The exact solution turns out to be peculiar in reaching zero bounds for certain nonnegative entries of G, which deserves modified problem formulation separating the lower bounds from zero.

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Section: Introductionmentioning

confidence: 99%

Pattern-Multiplicative Average of Nonnegative Matrices Revisited: Eigenvalue Approximation Is the Best of Versatile Optimization Tools

Logofet

2023

Mathematics

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“…In addition to age-specific population models, stage-specific models have also been developed. Since we would like to dedicate another study to the monitoring in stage-structured models (using observer design), in addition to the classical model of Lefkovitch [28], here we only refer to the very recent surveys by Logofet and Salguero-Gómez [29] and Logofet and Ulanova [30] (see also Logofet and Klochkova [31]). Stage-specific models, however, may display structural properties needing different constructions for observer design.…”

Section: Introductionmentioning

confidence: 99%

Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment

et al. 2022

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This paper is a contribution to the modeling–methodological development of the application of mathematical systems theory in population biology. A discrete-time nonlinear Leslie-type model is considered, where both the reproduction and survival rates decrease as the total population size increases. In this context, the monitoring problem means that, from the observation of the size of certain age classes as a function of time, we want to recover (estimate) the whole state process (i.e., the time-dependent size of the rest of the classes). First, for the linearization approach, conditions for the existence and asymptotic stability of a positive equilibrium are obtained, then the discrete-time observer design method is applied to estimate an unknown state trajectory near the equilibrium, where we could observe a single age class. It is also shown how the observer design can be used to detect an unknown change in the environment that affects the population dynamics. The environmental change is supposed to be generated by additional dynamics (exosystem). Now, the Leslie-type model is extended with this exosystem, and the observer design is applied to this extended system. In this way, an estimation can be obtained for different (constant or periodic) environmental changes as well.

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“…We focused on the vital rates required to parameterize matrix population models (MPMs), which are used widely by population ecologists and conservation biologists to project population dynamics over time (Caswell, 2001; Logofet & Salguero‐Gómez, 2021). MPMs streamline this process by representing stage‐structured life histories in a mathematical format facilitating neat ‘book‐keeping’ of vital rates (Caswell, 1997; Mills, 2012).…”

Section: Introductionmentioning

confidence: 99%

Vital rate estimates for the common eiderSomateria mollissima, a data‐rich exemplar of the seaduck tribe

Nicol‐Harper

Wood

Diamond

et al. 2021

Ecol Sol and Evidence

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This database collates vital rate estimates for the common eider (Somateria mollissima), providing a complete demographic parameterization for this slow life‐history species. Monitored across its circumpolar range, the common eider represents a data‐rich exemplar species for the less‐studied seaducks, many of which are under threat. The database contains estimates of the following vital rates: first‐year survival; second‐year survival; adult annual survival; first breeding (both age‐specific recruitment probability, and breeding propensity across potential recruitment ages); breeding propensity of established female breeders; clutch size; hatching success; and fledging success. These estimates are drawn from 134 studies, across the scientific and grey literature, including three previously inaccessible datasets on clutch size that were contributed in response to a call for data through the IUCN Species Survival Commission's Duck Specialist Group. Although clutch size has been much studied, the contributed datasets have enhanced coverage of studies reported in non‐English languages, which were otherwise only represented when cited in English‐language publications. Breeding propensity has been little studied, perhaps because adult females are often assumed to attempt breeding every year; we obtained a mean breeding propensity of 0.72. Our synthesis highlights the following gaps in data availability: juvenile and male survival; population change; and studies from Russia (at least accessible in English). The database is intended to serve population modellers and scientists involved in the policy and practice of seaduck conservation and management.

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Novel challenges and opportunities in the theory and practice of matrix population modelling: An editorial for the special feature

Cited by 7 publications

References 77 publications

Pattern-Multiplicative Average of Nonnegative Matrices Revisited: Eigenvalue Approximation Is the Best of Versatile Optimization Tools

Pattern-Multiplicative Average of Nonnegative Matrices Revisited: Eigenvalue Approximation Is the Best of Versatile Optimization Tools

Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment

Vital rate estimates for the common eiderSomateria mollissima, a data‐rich exemplar of the seaduck tribe

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