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Abstract Phenology is one of the most immediate responses to global climate change, but data limitations have made examining phenology patterns across greater taxonomic, spatial and temporal scales challenging. One significant opportunity is leveraging rapidly increasing data resources from digitized museum specimens and community science platforms, but this assumes reliable statistical methods are available to estimate phenology using presence‐only data. Estimating the onset or offset of key events is especially difficult with incidental data, as lower data densities occur towards the tails of an abundance distribution.The Weibull distribution has been recognized as an appropriate distribution to estimate phenology based on presence‐only data, but Weibull‐informed estimators are only available for onset and offset. We describe the mathematical framework for a new Weibull‐parameterized estimator of phenology appropriate for any percentile of a distribution and make it available in anrpackage,phenesse. We use simulations and empirical data on open flower timing and first arrival of monarch butterflies to quantify the accuracy of our estimator and other commonly used phenological estimators for 10 phenological metrics: onset, mean and offset dates, as well as the 1st, 5th, 10th, 50th, 90th, 95th and 99th percentile dates. Root mean squared errors and mean bias of the phenological estimators were calculated for different patterns of abundance and observation processes.Results show a general pattern of decay in performance of estimates when moving from mean estimates towards the tails of the seasonal abundance curve, suggesting that onset and offset continue to be the most difficult phenometrics to estimate. However, with simple phenologies and enough observations, our newly developed estimator can provide useful onset and offset estimates. This is especially true for the start of the season, when incidental observations may be more common.Our simulation demonstrates the potential of generating accurate phenological estimates from presence‐only data and guides the best use of estimators. The estimator that we developed, phenesse, is the least biased and has the lowest estimation error for onset estimates under most simulated and empirical conditions examined, improving the robustness of these estimates for phenological research.
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Phenological patterns in ecology: Problems using circular statistics and solutions based on simulations
Abstract Quantification of phenological patterns (e.g. migration, hibernation or reproduction) should involve statistical assessments of non‐uniform temporal patterns. Circular statistics (e.g. Rayleigh test or Hermans‐Rasson test) provide useful approaches for doing so based on the number of individuals that exhibit particular activities during a number of time intervals.This study used monthly reproductive activity as an example to illustrate problems in applying circular statistics to data when marginal totals characterize experimental designs (e.g. the number of reproductively active individuals per time interval depends on sampling effort or sampling success). We illustrate the nature of this problem by crafting four exemplar data sets and developing a bootstrapping simulation procedure to overcome complications that arise from the existence of marginal totals. In addition, we apply circular statistics and our bootstrapping simulation to empirical data on the reproductive phenology of six species of Neotropical bats from the Amazon.Because sampling effort or success can differ among time intervals, circular statistics can produce misleading results of two types: those suggesting uniform phenologies when empirical patterns are markedly modal, and those suggesting non‐uniform phenologies when empirical patterns are uniform. The bootstrapping simulation overcomes these limitations: the exemplar phenology in which the percentage of reproductively active individuals is modal is appropriately identified as non‐uniform based on the bootstrapping approach, and the exemplar phenology in which the percentage of reproductively active individuals is invariant is appropriately identified as uniform based on the bootstrapping approach. The reproductive phenology of each of the six empirical examples is non‐uniform based on the bootstrapping approach, and this is true for bats species with unimodal peaks or bimodal peaks.In addition to problems with marginal totals, a review of analyses of phenological patterns in ecology identified two other frequent issues in the application of circular statistics: sampling bias and pseudoreplication. Each of these issues and potential solutions are also discussed. By providing source code for the execution of the Rayleigh test and Hermans‐Rasson test, along with the code for the bootstrapping simulation, we offer a useful tool for assessing non‐random phenologies when marginal totals characterize experimental designs.
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- Award ID(s):
- 1950643
- PAR ID:
- 10499191
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Methods in Ecology and Evolution
- Volume:
- 15
- Issue:
- 5
- ISSN:
- 2041-210X
- Format(s):
- Medium: X Size: p. 868-885
- Size(s):
- p. 868-885
- Sponsoring Org:
- National Science Foundation
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