Bulletin of Mathematical Biology

, Volume 80, Issue 3, pp 687–700 | Cite as

Estimating Intermittent Individual Spawning Behavior via Disaggregating Group Data

  • Joel Nishimura
  • Rebecca Smith
  • Kathleen Jensen
  • Gerald Ankley
  • Karen Watanabe
Research Methods Article


In order to understand fish biology and reproduction, it is important to know the fecundity patterns of individual fish, as frequently established by recording the output of mixed-sex groups of fish in a laboratory setting. However, for understanding individual reproductive health and modeling purposes it is important to estimate individual fecundity from group fecundity. We created a multistage method that disaggregates group-level data into estimates for individual-level clutch size and spawning interval distributions. The first stage of the method develops estimates of the daily spawning probability of fish. Daily spawning probabilities are then used to calculate the log likelihood of candidate distributions of clutch size. Selecting the best candidate distribution for clutch size allows for a Monte Carlo resampling of annotations of the original data which state how many fish spawned on which day. We verify this disaggregation technique by combining data from fathead minnow pairs, and checking that the disaggregation method reproduced the original clutch sizes and spawning intervals. This method will allow scientists to estimate individual clutch size and spawning interval distributions from group spawning data without specialized or elaborate experimental designs.


Disaggregation Maximum likelihood Deconvolution Inverse problems 



The authors would like to thank Drs. Diane Nacci, Bryan Clark and Denise Champlin from the U.S. Environmental Protection Agency, as well as Dr. Thijs Bosker from Leiden University for initiating conversations leading to the development of this method.

Supplementary material

11538_2017_379_MOESM1_ESM.xlsx (19 kb)
Supplementary material 1 (xlsx 18 KB)


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.School of Mathematical and Naturals SciencesArizona State UniversityGlendaleUSA
  2. 2.U.S. Environmental Protection Agency, Mid-Continent Ecology DivisionDuluthUSA

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