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
  • 31 Downloads

Abstract

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.

Keywords

Disaggregation Maximum likelihood Deconvolution Inverse problems 

Notes

Acknowledgements

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)

References

  1. Ankley GT, Jensen KM, Durhan EJ, Makynen EA, Butterworth BC, Kahl MD, Villeneuve DL, Linnum A, Gray LE, Cardon M et al (2005) Effects of two fungicides with multiple modes of action on reproductive endocrine function in the fathead minnow (Pimephales promelas). Toxicol Sci 86(2):300–308CrossRefGoogle Scholar
  2. Ankley GT, Jensen KM, Kahl MD, Korte JJ, Makynen EA (2001) Description and evaluation of a short-term reproduction test with the fathead minnow (Pimephales promelas). Environ Toxicol Chem 20(6):1276–1290CrossRefGoogle Scholar
  3. Ankley GT, Kuehl DW, Kahl MD, Jensen KM, Linnum A, Leino RL, Villeneuve DA (2005) Reproductive and developmental toxicity and bioconcentration of perfluorooctanesulfonate in a partial life-cycle test with the fathead minnow (Pimephales promelas). Environ Toxicol Chem 24(9):2316–2324CrossRefGoogle Scholar
  4. Bosker T, Munkittrick KR, Nacci DE, MacLatchy DL (2013) Laboratory spawning patterns of mummichogs, fundulus heteroclitus (cyprinodontiformes: Fundulidae). Copeia 2013(3):527–538CrossRefGoogle Scholar
  5. Jensen KM, Makynen EA, Kahl MD, Ankley GT (2006) Effects of the feedlot contaminant 17\(\alpha \)-trenbolone on reproductive endocrinology of the fathead minnow. Environ Sci Technol 40(9):3112–3117CrossRefGoogle Scholar
  6. Kauppinen JK, Moffatt DJ, Mantsch HH, Cameron DG (1981) Fourier self-deconvolution: a method for resolving intrinsically overlapped bands. Appl Spectrosc 35(3):271–276CrossRefGoogle Scholar
  7. LaLone CA, Villeneuve DL, Cavallin JE, Kahl MD, Durhan EJ, Makynen EA, Jensen KM, Stevens KE, Severson MN, Blanksma CA et al (2013) Cross-species sensitivity to a novel androgen receptor agonist of potential environmental concern, spironolactone. Environ Toxicol Chem 32(11):2528–2541Google Scholar
  8. Lange A, Paull GC, Hamilton PB, Iguchi T, Tyler CR (2011) Implications of persistent exposure to treated wastewater effluent for breeding in wild roach (Rutilus rutilus) populations. Environ Sci Technol 45(4):1673–1679CrossRefGoogle Scholar
  9. Li Z, Villeneuve DL, Jensen KM, Ankley GT, Watanabe KH (2011) A computational model for asynchronous oocyte growth dynamics in a batch-spawning fish. Can J Fish Aquat Sci 68(9):1528–1538CrossRefGoogle Scholar
  10. Martinez V (1979) Global methods in the inversion of a self-convolution. J Electron Spectrosc Relat Phenom 17(1):33–43CrossRefGoogle Scholar
  11. Maudsley A (1995) Spectral lineshape determination by self-deconvolution. J Magn Reson Ser B 106(1):47–57CrossRefGoogle Scholar
  12. Mendel JM (2012) Maximum-likelihood deconvolution: a journey into model-based signal processing. Springer Science & Business Media, New YorkGoogle Scholar
  13. Park JW, Rinchard J, Liu F, Anderson TA, Kendall RJ, Theodorakis CW (2006) The thyroid endocrine disruptor perchlorate affects reproduction, growth, and survival of mosquitofish. Ecotoxicol Environ Saf 63(3):343–352CrossRefGoogle Scholar
  14. Paull GC, Filby AL, Giddins HG, Coe TS, Hamilton PB, Tyler CR (2010) Dominance hierarchies in zebrafish (Danio rerio) and their relationship with reproductive success. Zebrafish 7(1):109–117CrossRefGoogle Scholar
  15. Villeneuve DL, Blake LS, Brodin JD, Cavallin JE, Durhan EJ, Jensen KM, Kahl MD, Makynen EA, Martinović D, Mueller ND et al (2008) Effects of a 3\(\beta \)-hydroxysteroid dehydrogenase inhibitor, trilostane, on the fathead minnow reproductive axis. Toxicol Sci 104(1):113–123CrossRefGoogle Scholar
  16. Villeneuve DL, Murphy MB, Kahl MD, Jensen KM, Butterworth BC, Makynen EA, Durhan EJ, Linnum A, Leino RL, Curtis LR et al (2006) Evaluation of the methoxytriazine herbicide prometon using a short-term fathead minnow reproduction test and a suite of in vitro bioassays. Environ Toxicol Chem 25(8):2143–2153CrossRefGoogle Scholar

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

Personalised recommendations