scholarly journals Stage-structured matrix models for organisms with non-geometric development times

Ecology ◽  
2009 ◽  
Vol 90 (1) ◽  
pp. 57-68 ◽  
Author(s):  
Andrew Birt ◽  
Richard M. Feldman ◽  
David M. Cairns ◽  
Robert N. Coulson ◽  
Maria Tchakerian ◽  
...  
Keyword(s):  
Matrix Models ◽  
Structured Matrix ◽  
Development Times

scholarly journals Demonstrating the Effect of Height Variation on Stand-Level Optimization with Diameter-Structured Matrix Model

Forests ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 226
Author(s):  
Johanna Pyy ◽  
Erkki Laitinen ◽  
Anssi Ahtikoski
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Net Present Value ◽  
Rotation Period ◽  
Present Value ◽  
Height Variation ◽  
Structured Matrix ◽  
The Matrix ◽  
Log Price ◽  
Financial Outcome

The weakness of the population matrix models is that they do not take into account the variation inside the class. In this study, we introduce an approach to add height variation of the trees to the diameter-structured matrix models. In this approach, a new sub-model that describes the height growth of the trees is included in the diameter-structured model. We used this height- and diameter-structured matrix model to maximize the net present value (NPV) for the remaining part of the ongoing rotation for Scots pine (Pinus sylvestris L.) stand and studied how the height variation affects to the results obtained through stand-level optimization. In the optimization, the height variation was taken into account by setting the lower saw-log price for the short trees. The results show that including the height variation into the optimization reduced the financial outcome by 16–18% and considerably changed the structure of optimal management (e.g., timings for thinnings, rotation period and intensity of thinnings). We introduced an approach that can be applied to include not only height variation but also variation of other tree properties (such as branchiness or the amount of heartwood and sapwood) into the matrix models.

Sensitivity and elasticity analysis of Tetranychus urticae Koch population parameters: Consequences for pest management 

2020 ◽  
Vol 25 (2) ◽  
pp. 268-284
Author(s):  
Alireza Nemati ◽  
Elham Riahi ◽  
Saadollah Houshmand
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Matrix Models ◽  
Survival Rates ◽  
Demographic Variables ◽  
Adult Survival ◽  
Egg Survival ◽  
Horticultural Crops ◽  
Structured Matrix ◽  
Different Temperatures

Sensitivity and elasticity analyses quantify the effect of an absolute and proportional change in demographic variables on population growth rate (λ), respectively. The methods are used to identify the variable(s) that have the largest influence on λ. Tetranychus urticae Koch is one of the most polyphagous tetranychid mites which has been collected from plenty plant species including agricultural and horticultural crops. In this study, sensitivity and elasticity analyses were used to investigate the effects of various demographic variables on λ at five different temperatures (15, 20, 25, 30 and 35 °C), using both age- and stage-structured matrix models. Considering the sensitivity of λ to age-dependent fecundity rates (fx), it was found that starting oviposition one day earlier was associated with the highest sensitivity compared to the other age classes, irrespective of temperature. Besides, results from both age- and stage-structured matrix models indicated that λ is more sensitive to changes in survival rates than in fecundity rates at all temperatures. Furthermore, female individuals at the ages of 46, 23, 14, 11 and 7 days had the highest contribution to population growth in comparison with other ages, when reared at the above-mentioned temperatures, respectively. Also, the sensitivity of λ to the changes in survival of adults was higher than in other stages. Besides, the elasticity to fecundity rate at the age of first reproduction was considerably higher than those associated with the age of last reproduction. The survival rates (si) generally exhibited a higher elasticity than the transition rates (gi). Overall, adult survival had the highest influence on λ followed by immature survival, egg survival, and female fecundity. Consequently, management efforts that aim at decreasing adult survival are likely to yield the best results with regard to reducing the growth rate of T. urticae.

scholarly journals Time-invariant and stochastic disperser-structured matrix models: Invasion rates of fleshy-fruited exotic shrubs

2015 ◽  
Vol 20 (6) ◽  
pp. 1639-1662 ◽  
Author(s):  
Carol C. Horvitz ◽  
◽  
Anthony L. Koop ◽  
Kelley D. Erickson ◽  
Keyword(s):  
Matrix Models ◽  
Structured Matrix ◽  
Time Invariant

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

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