Why are the middle points the most `sensitive' in the sensitivity experiments?

Logofet, Dmitrii O.; Lesnaya, Ekaterina V.

doi:10.1016/s0304-3800(97)00125-7

Cited by 3 publications

(4 citation statements)

References 4 publications

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“…Then, to first order, When calculating C, the derivative of ξ must be evaluated somewhere. Experience suggests that the evaluating it at the midpoint between θ (1) and θ (2) gives good results (Logofet and Lesnaya 1997;Caswell 2001).…”

Section: Ltre Decomposition Of Demographic Differencesmentioning

confidence: 99%

Matrix Calculus and Notation

Caswell

2019

Demographic Research Monographs

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In October of 2005, I scribbled in a notebook, "can it possibly be that simple?" I was referring to the sensitivity of transient dynamics (the eventual results appear in Chap. 7), and had just begun to use matrix calculus as a tool. The answer to my question was yes. It can be that simple. This book relies on this set of mathematical techniques. This chapter introduces the basics, which will be used throughout the text. For more information, I recommend four sources in particular. The most complete treatment, but not the easiest starting point, is the book by Magnus and Neudecker (1988). More accessible introductions can be found in the paper by Magnus and Neudecker (1985) and especially the text by Abadir and Magnus (2005). A review paper by Nel (1980) is helpful in placing the Magnus-Neudecker formulation in the context of other attempts at a calculus of matrices. Sensitivity analysis asks how much change in an outcome variable y is caused by a change in some parameter x. At its most basic level, and with some reasonable assumptions about the continuity and differentiability of the functional relationships involved, the solution is given by differential calculus. If y is a function of x, then the derivative dy dx tells how y responds to a change in x, i.e., the sensitivity of y to a change in x. However, the outcomes of a demographic calculation may be scalar-valued (e.g., the population growth rate λ), vector-valued (e.g., the stable stage distribution), or matrix-valued (e.g., the fundamental matrix). Any of these outcomes may be

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Section: Ltre Decomposition Of Demographic Differencesmentioning

confidence: 99%

Matrix Calculus and Notation

Caswell

2019

Demographic Research Monographs

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“…We determined the degree to which the differences in the population growth rates (λ) between control and laminarin exposed groups were determined by the differences in each parameter (G i , P i , and F 3 ) by means of a life table response experiment (LTRE) analysis (Caswell, 2001). With this technique, the effects of laminarin exposure on λ, measured in respect to water‐only control, was decomposed into contributions from each stage‐specific survival probability and fecundity terms as follow:

\begin{matrix} left λ^{t} \approx λ^{c} + \frac{\partial normalλ}{{∂G}_{1}} ∆ G_{1} + \frac{\partial normalλ}{{∂G}_{2}} ∆ G_{2} + \frac{\partial normalλ}{{∂P}_{1}} ∆ P_{1} + \frac{\partial normalλ}{{∂P}_{2}} ∆ P_{2} + \frac{\partial normalλ}{{∂P}_{3}} ∆ P_{3} + \frac{\partial normalλ}{{∂F}_{3}} ∆ F_{3} \end{matrix}

, where λ t and λ c denote the values of λ for laminarin exposed and water‐only control groups, respectively, ΔG 1 , ΔG 2 , ΔP 1 , ΔP 2 , ΔP 3 , and ΔF 3 are, for each parameter, the differences between laminarin exposed and water‐only control values, and

\partial normalλ

∂G

\partial normalλ

∂P

, and

\partial normalλ

∂F

are the sensitivities to λ calculated halfway between the two parameter sets (laminarin exposed and water‐only control) being compared (Logofet & Lesnaya, 1997).…”

Section: Methodsmentioning

confidence: 99%

“…ΔF 3 , where λ t and λ c denote the values of λ for laminarin exposed and water-only control groups, respectively, ΔG 1 , ΔG 2 , ΔP 1 , ΔP 2 , ΔP 3 , and ΔF 3 are, for each parameter, the differences between laminarin exposed and water-only control values, and λ / G, λ / P, and λ / F are the sensitivities to λ calculated halfway between the two parameter sets (laminarin exposed and water-only control) being compared (Logofet & Lesnaya, 1997).…”

Section: Demographic Analysismentioning

confidence: 99%

Evaluation of lethal and sublethal effects of laminarin on the green peach aphid,Myzus persicae, under extended laboratory conditions

Lanzoni,

Staiano,

Masetti

et al. 2024

Entomologia Exp Applicata

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Recent studies have opened the way for using elicitor‐induced resistance in plants as a method to control arthropod pests. In this study, 1,3‐β‐glucan laminarin, an elicitor of disease resistance in plants, was tested on the green peach aphid, Myzus persicae (Sulzer) (Hemiptera: Aphididae), on peach [Prunus persica (L.) Batsch, Rosaceae] plantlets and evaluated its effects on short‐term mortality and population growth. Laminarin exposure did not affect aphid survival in the short term; however, laminarin‐treated peach plants sustained fewer nymphs and adults in comparison with the control. Aphid populations on plants treated with laminarin declined significantly over the sampling period compared to the control. Moreover, the demographic parameters net reproductive rate (R0), finite rate of increase (λ), and intrinsic rate of increase (rm), all showed decreasing trends in aphid populations reared on laminarin‐treated plants. The decline in aphid populations exposed to laminarin seemed to mainly be linked to reduced adult survival, slower nymph development, and lower nymph survival and only marginally to changes in reproduction outcome. Changes in gene expression causing the final production of defence chemicals by peach plants may contribute to explaining the results. However, potential direct effects of laminarin on M. persicae feeding activity and probing behaviour cannot be ruled out. This study provides evidence that, although laminarin did not display insecticidal activity in the short term, this elicitor caused sublethal effects, significantly reducing aphid populations.

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“…The treatment effects were estimated using the following formulas:and decomposed into contributions from each matrix entries as followsEach equation approximates an observed change in λ with respect to λ (⋅⋅) , and each term in the summation represents the contribution of the difference in the matrix element a kl (age-specific fecundity or survival probability) to the effect of treatment, on the population growth rate. That contribution is the product of the difference between overall mean and treatment-specific vital rate and the sensitivity of that vital rate calculated from a matrix halfway between the matrices being compared (Logofet and Lesnaya, 1997). The interaction term in equation 10 represents the deviation between the observed contribution of a kl to λ ( ij ) of the treatment combination and that predicted on the basis of an additive model (Caswell, 2001).…”

Section: Methodsmentioning

confidence: 99%

Assessing the effects of Bt maize on the non-target pest Rhopalosiphum maidis by demographic and life-history measurement endpoints

Lanzoni

Bosi

Bregola

et al. 2021

Bull. Entomol. Res.

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The most commercialized Bt maize plants in Europe were transformed with genes which express a truncated form of the insecticidal delta-endotoxin (Cry1Ab) from the soil bacterium Bacillus thuringiensis (Bt) specifically against Lepidoptera. Studies on the effect of transgenic maize on non-target arthropods have mainly converged on beneficial insects. However, considering the worldwide extensive cultivation of Bt maize, an increased availability of information on their possible impact on non-target pests is also required. In this study, the impact of Bt-maize on the non-target corn leaf aphid, Rhopalosiphum maidis, was examined by comparing biological traits and demographic parameters of two generations of aphids reared on transgenic maize with those on untransformed near-isogenic plants. Furthermore, free and bound phenolics content on transgenic and near-isogenic plants were measured. Here we show an increased performance of the second generation of R. maidis on Bt-maize that could be attributable to indirect effects, such as the reduction of defense against pests due to unintended changes in plant characteristics caused by the insertion of the transgene. Indeed, the comparison of Bt-maize with its corresponding near-isogenic line strongly suggests that the transformation could have induced adverse effects on the biosynthesis and accumulation of free phenolic compounds. In conclusion, even though there is adequate evidence that aphids performed better on Bt-maize than on non-Bt plants, aphid economic damage has not been reported in commercial Bt corn fields in comparison to non-Bt corn fields. Nevertheless, Bt-maize plants can be more easily exploited by R. maidis, possibly due to a lower level of secondary metabolites present in their leaves. The recognition of this mechanism increases our knowledge concerning how insect-resistant genetically modified plants impact on non-target arthropods communities, including tritrophic web interactions, and can help support a sustainable use of genetically modified crops.

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Why are the middle points the most `sensitive' in the sensitivity experiments?

Cited by 3 publications

References 4 publications

Matrix Calculus and Notation

Matrix Calculus and Notation

Evaluation of lethal and sublethal effects of laminarin on the green peach aphid,Myzus persicae, under extended laboratory conditions

Assessing the effects of Bt maize on the non-target pest Rhopalosiphum maidis by demographic and life-history measurement endpoints

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