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Abstract Population ecology and biogeography applications often necessitate the transfer of models across spatial and/or temporal dimensions to make predictions outside the bounds of the data used for model fitting. However, ecological data are often spatiotemporally unbalanced such that the spatial or the temporal dimension tends to contain more data than the other. This unbalance frequently leads model transfers to become substitutions, which are predictions to a different dimension than the predictive model was built on. Despite the prevalence of substitutions in ecology, studies validating their performance and their underlying assumptions are scarce.Here, we present a case study demonstrating both space‐for‐time and time‐for‐space substitutions (TFSS) using emperor penguins (Aptenodytes forsteri) as the focal species. Using an abundance‐based species distribution model (aSDM) of adult emperor penguins in attendance during spring across 50 colonies, we predict long‐term annual fluctuations in fledgling abundance and breeding success at a single colony, Pointe Géologie. Subsequently, we construct statistical models from time series of extended counts on Pointe Géologie to predict average colony abundance distribution across 50 colonies.Our analysis reveals that the distance to nearest open water (NOW) exhibits the strongest association with both temporal and spatial data. Space‐for‐time substitution performance of the aSDM, as measured by the Pearson correlation coefficient, was 0.63 and 0.56 when predicting breeding success and fledgling abundance time series, respectively. Linear regression of fledgling abundance on NOW yields similar TFSS performance when predicting the abundance distribution of emperor penguin colonies with a correlation coefficient of 0.58.We posit that such space–time equivalence arises because: (1) emperor penguin colonies conform to their existing fundamental niche; (2) there is not yet any environmental novelty when comparing the spatial versus temporal variation of distance to the nearest open water; and (3) models of more specific components of life histories, such as fledgling abundance, rather than total population abundance, are more transferable. Identifying these conditions empirically can enhance the qualitative validation of substitutions in cases where direct validation data are lacking.
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Allotaxonometry and rank-turbulence divergence: a universal instrument for comparing complex systems
Abstract Complex systems often comprise many kinds of components which vary over many orders of magnitude in size: Populations of cities in countries, individual and corporate wealth in economies, species abundance in ecologies, word frequency in natural language, and node degree in complex networks. Here, we introduce ‘allotaxonometry’ along with ‘rank-turbulence divergence’ (RTD), a tunable instrument for comparing any two ranked lists of components. We analytically develop our rank-based divergence in a series of steps, and then establish a rank-based allotaxonograph which pairs a map-like histogram for rank-rank pairs with an ordered list of components according to divergence contribution. We explore the performance of rank-turbulence divergence, which we view as an instrument of ‘type calculus’, for a series of distinct settings including: Language use on Twitter and in books, species abundance, baby name popularity, market capitalization, performance in sports, mortality causes, and job titles. We provide a series of supplementary flipbooks which demonstrate the tunability and storytelling power of rank-based allotaxonometry.
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- Award ID(s):
- 2242829
- PAR ID:
- 10514102
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- EPJ Data Science
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2193-1127
- Page Range / eLocation ID:
- 37
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1140/epjds/s13688-023-00400-x
