Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demography
Abstract Keyfitz' entropy is a widely used metric to quantify the shape of the survivorship curve of populations, from plants to animals and microbes. Keyfitz' entropy values <1 correspond to life histories with an increasing mortality rate with age (i.e. actuarial senescence), whereas...
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| Format: | Article |
| Language: | English |
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Wiley
2023-05-01
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| Series: | Methods in Ecology and Evolution |
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| Online Access: | https://doi.org/10.1111/2041-210X.14083 |
| _version_ | 1797766999588208640 |
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| author | Charlotte deVries Connor Bernard Roberto Salguero‐Gómez |
| author_facet | Charlotte deVries Connor Bernard Roberto Salguero‐Gómez |
| author_sort | Charlotte deVries |
| collection | DOAJ |
| description | Abstract Keyfitz' entropy is a widely used metric to quantify the shape of the survivorship curve of populations, from plants to animals and microbes. Keyfitz' entropy values <1 correspond to life histories with an increasing mortality rate with age (i.e. actuarial senescence), whereas values >1 correspond to species with a decreasing mortality rate with age (negative senescence), and a Keyfitz entropy of exactly 1 corresponds to a constant mortality rate with age. Keyfitz' entropy was originally defined using a continuous‐time model, and has since been discretised to facilitate its calculation from discrete‐time demographic data. Here, we show that the previously used discretisation of the continuous‐time metric does not preserve the relationship with increasing, decreasing or constant mortality rates. To resolve this discrepancy, we propose a new discrete‐time formula for Keyfitz' entropy for age‐classified life histories. We show that this new method of discretisation preserves the relationship with increasing, decreasing, or constant mortality rates. We analyse the relationship between the original and the new discretisation, and we find that the existing metric tends to underestimate Keyfitz' entropy for both short‐lived species and long‐lived species, thereby introducing a consistent bias. To conclude, to avoid biases when classifying life histories as (non‐)senescent, we suggest researchers use either the new metric proposed here, or one of the many previously suggested survivorship shape metrics applicable to discrete‐time demographic data such as Gini coefficient or Hayley's median. |
| first_indexed | 2024-03-12T20:33:22Z |
| format | Article |
| id | doaj.art-8a1370f065d348acb89f263192b73353 |
| institution | Directory Open Access Journal |
| issn | 2041-210X |
| language | English |
| last_indexed | 2024-03-12T20:33:22Z |
| publishDate | 2023-05-01 |
| publisher | Wiley |
| record_format | Article |
| series | Methods in Ecology and Evolution |
| spelling | doaj.art-8a1370f065d348acb89f263192b733532023-08-01T18:55:36ZengWileyMethods in Ecology and Evolution2041-210X2023-05-011451312131910.1111/2041-210X.14083Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demographyCharlotte deVries0Connor Bernard1Roberto Salguero‐Gómez2Institute for Biodiversity and Ecosystem Dynamics University of Amsterdam Amsterdam The NetherlandsDepartment of Biology University of Oxford Oxford UKDepartment of Biology University of Oxford Oxford UKAbstract Keyfitz' entropy is a widely used metric to quantify the shape of the survivorship curve of populations, from plants to animals and microbes. Keyfitz' entropy values <1 correspond to life histories with an increasing mortality rate with age (i.e. actuarial senescence), whereas values >1 correspond to species with a decreasing mortality rate with age (negative senescence), and a Keyfitz entropy of exactly 1 corresponds to a constant mortality rate with age. Keyfitz' entropy was originally defined using a continuous‐time model, and has since been discretised to facilitate its calculation from discrete‐time demographic data. Here, we show that the previously used discretisation of the continuous‐time metric does not preserve the relationship with increasing, decreasing or constant mortality rates. To resolve this discrepancy, we propose a new discrete‐time formula for Keyfitz' entropy for age‐classified life histories. We show that this new method of discretisation preserves the relationship with increasing, decreasing, or constant mortality rates. We analyse the relationship between the original and the new discretisation, and we find that the existing metric tends to underestimate Keyfitz' entropy for both short‐lived species and long‐lived species, thereby introducing a consistent bias. To conclude, to avoid biases when classifying life histories as (non‐)senescent, we suggest researchers use either the new metric proposed here, or one of the many previously suggested survivorship shape metrics applicable to discrete‐time demographic data such as Gini coefficient or Hayley's median.https://doi.org/10.1111/2041-210X.14083demographyKeyfitz entropymortalitysenescenceshape of life measures |
| spellingShingle | Charlotte deVries Connor Bernard Roberto Salguero‐Gómez Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demography Methods in Ecology and Evolution demography Keyfitz entropy mortality senescence shape of life measures |
| title | Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demography |
| title_full | Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demography |
| title_fullStr | Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demography |
| title_full_unstemmed | Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demography |
| title_short | Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demography |
| title_sort | discretising keyfitz entropy for studies of actuarial senescence and comparative demography |
| topic | demography Keyfitz entropy mortality senescence shape of life measures |
| url | https://doi.org/10.1111/2041-210X.14083 |
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