Details
| Original language | English |
|---|---|
| Article number | 221326 |
| Journal | Royal Society Open Science |
| Volume | 9 |
| Issue number | 11 |
| Publication status | Published - 30 Nov 2022 |
Abstract
Nutrition is one of the underlying factors necessary for the expression of life-histories and fitness across the tree of life. In recent decades, the geometric framework (GF) has become a powerful framework to obtain biological insights through the construction of multidimensional performance landscapes. However, to date, many properties of these multidimensional landscapes have remained inaccessible due to our lack of mathematical and statistical frameworks for GF analysis. This has limited our ability to understand, describe and estimate parameters which may contain useful biological information from GF multidimensional performance landscapes. Here, we propose a new model to investigate the curvature of GF multidimensional landscapes by calculating the parameters from differential geometry known as Gaussian and mean curvatures. We also estimate the surface area of multidimensional performance landscapes as a way to measure landscape deviations from flat. We applied the models to a landmark dataset in the field, where we also validate the assumptions required for the calculations of curvature. In particular, we showed that linear models perform as well as other models used in GF data, enabling landscapes to be approximated by quadratic polynomials. We then introduced the Hausdorff distance as a metric to compare the similarity of multidimensional landscapes.
Keywords
- climate change, diet, ecological specialization, Grinnellian niche, persistence homology
ASJC Scopus subject areas
Sustainable Development Goals
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In: Royal Society Open Science, Vol. 9, No. 11, 221326, 30.11.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Nutrigonometry III
T2 - Curvature, area and differences between performance landscapes
AU - Morimoto, Juliano
AU - Conceição, Pedro
AU - Smoczyk, Knut
N1 - Funding Information: J.M. is supported by the BBSRC (BB/V015249/1), a Royal Society Research grant no. (RGS-R2-202220), a SULSA Saltire Emerging Research Award (20253009) and a Riemann Fellowship. P.C. is supported by the EPSRC (EP/P025072/) and the Ecole Polytechnique Federale de Lausanne via a collaboration agreement with the University of Aberdeen. Acknowledgements
PY - 2022/11/30
Y1 - 2022/11/30
N2 - Nutrition is one of the underlying factors necessary for the expression of life-histories and fitness across the tree of life. In recent decades, the geometric framework (GF) has become a powerful framework to obtain biological insights through the construction of multidimensional performance landscapes. However, to date, many properties of these multidimensional landscapes have remained inaccessible due to our lack of mathematical and statistical frameworks for GF analysis. This has limited our ability to understand, describe and estimate parameters which may contain useful biological information from GF multidimensional performance landscapes. Here, we propose a new model to investigate the curvature of GF multidimensional landscapes by calculating the parameters from differential geometry known as Gaussian and mean curvatures. We also estimate the surface area of multidimensional performance landscapes as a way to measure landscape deviations from flat. We applied the models to a landmark dataset in the field, where we also validate the assumptions required for the calculations of curvature. In particular, we showed that linear models perform as well as other models used in GF data, enabling landscapes to be approximated by quadratic polynomials. We then introduced the Hausdorff distance as a metric to compare the similarity of multidimensional landscapes.
AB - Nutrition is one of the underlying factors necessary for the expression of life-histories and fitness across the tree of life. In recent decades, the geometric framework (GF) has become a powerful framework to obtain biological insights through the construction of multidimensional performance landscapes. However, to date, many properties of these multidimensional landscapes have remained inaccessible due to our lack of mathematical and statistical frameworks for GF analysis. This has limited our ability to understand, describe and estimate parameters which may contain useful biological information from GF multidimensional performance landscapes. Here, we propose a new model to investigate the curvature of GF multidimensional landscapes by calculating the parameters from differential geometry known as Gaussian and mean curvatures. We also estimate the surface area of multidimensional performance landscapes as a way to measure landscape deviations from flat. We applied the models to a landmark dataset in the field, where we also validate the assumptions required for the calculations of curvature. In particular, we showed that linear models perform as well as other models used in GF data, enabling landscapes to be approximated by quadratic polynomials. We then introduced the Hausdorff distance as a metric to compare the similarity of multidimensional landscapes.
KW - climate change
KW - diet
KW - ecological specialization
KW - Grinnellian niche
KW - persistence homology
UR - http://www.scopus.com/inward/record.url?scp=85143722916&partnerID=8YFLogxK
U2 - 10.1098/rsos.221326
DO - 10.1098/rsos.221326
M3 - Article
AN - SCOPUS:85143722916
VL - 9
JO - Royal Society Open Science
JF - Royal Society Open Science
SN - 2054-5703
IS - 11
M1 - 221326
ER -