The time distribution of biological phenomena – illustrated with the London marathon

School of Biological and Marine Sciences, University of Plymouth, Plymouth, United Kingdom
DOI
10.7287/peerj.preprints.27175v1
Subject Areas
Mathematical Biology, Population Biology
Keywords
phenology, senescence, time distribution, gender differences, endurance sports
Copyright
© 2018 Franco
Licence
This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
Cite this article
Franco M. 2018. The time distribution of biological phenomena – illustrated with the London marathon. PeerJ Preprints 6:e27175v1

Abstract

Background. The time distribution of biological phenomena (phenology) is a subject of wide interest, but a general statistical distribution to describe and quantify its essential properties is lacking. Existing distributions are limiting, if not entirely inappropriate, because their parameters do not in general correlate with biologically relevant attributes of the organism and the conditions under which they find themselves. Methods. A distribution function that allows quantification of three essential properties of a biological dynamic process occurring over a continuous timescale was derived from first principles. The distribution turned out to have three parameters with clear meanings and units: (i) a scaled rate of completion (dimensionless), (ii) a measure of temporal concentration of the process (units: time-1), and (iii) an overall measure of temporal delay (units: time). Its performance as an accurate description of the process was tested with completion data for the London Marathon employing non-linear regression. Results. The parameters of the distribution correlated with biological attributes of the runners (gender and age) and with the maximum temperature on the day of the race. These relationships mirrored known differences in morphology and physiology of participants and the deterioration of these biological attributes with age (senescence), as well as the known effects of hypo- and hyperthermia. Discussion. By relating the variation in parameter values to possible biological and environmental variables, the marathon example demonstrates the ability of the distribution to help identify possible triggers and drivers of the duration, shape and temporal shift of its temporal distribution. This more detailed account of the effect of biological and environmental variables would provide a deeper insight into the drivers of a wide variety of phenological phenomena of high current interest, such as the shifting patterns of leafing, flowering, growth, migration, etc. of many organisms worldwide.

Author Comment

This is a submission to PeerJ for review.

Supplemental Information

Supplementary Material 1

Statistical properties of the distribution

DOI: 10.7287/peerj.preprints.27175v1/supp-1

Supplementary Material 2

Maple code to calculate statistical moments

DOI: 10.7287/peerj.preprints.27175v1/supp-2

Supplementary Material 3

Summary statistics

DOI: 10.7287/peerj.preprints.27175v1/supp-3

Maple code

Maple code to estimate the distribution's statistical moments.

DOI: 10.7287/peerj.preprints.27175v1/supp-4

London Marathon 2001

Dataset of completion times for the London Marathon 2001

DOI: 10.7287/peerj.preprints.27175v1/supp-5

London Marathon 2002

Dataset of completion times for the London Marathon 2002

DOI: 10.7287/peerj.preprints.27175v1/supp-6

London Marathon 2003

Dataset of completion times for the London Marathon 2003

DOI: 10.7287/peerj.preprints.27175v1/supp-7

London Marathon 2004

Dataset of completion times for the London Marathon 2004

DOI: 10.7287/peerj.preprints.27175v1/supp-8

London Marathon 2005

Dataset of completion times for the London Marathon 2005

DOI: 10.7287/peerj.preprints.27175v1/supp-9

London Marathon 2006

Dataset of completion times for the London Marathon 2006

DOI: 10.7287/peerj.preprints.27175v1/supp-10

London Marathon 2007

Dataset of completion times for the London Marathon 2007

DOI: 10.7287/peerj.preprints.27175v1/supp-11

London Marathon 2008

Dataset of completion times for the London Marathon 2008

DOI: 10.7287/peerj.preprints.27175v1/supp-12

London Marathon 2009

Dataset of completion times for the London Marathon 2009

DOI: 10.7287/peerj.preprints.27175v1/supp-13

London Marathon 2010

Dataset of completion times for the London Marathon 2010

DOI: 10.7287/peerj.preprints.27175v1/supp-14

London Marathon 2011

Dataset of completion times for the London Marathon 2011

DOI: 10.7287/peerj.preprints.27175v1/supp-15

London Marathon 2016

Dataset of completion times for the London Marathon 2016.

DOI: 10.7287/peerj.preprints.27175v1/supp-16

London Marathon 2016 by gender and age

Dataset of completion times for the London Marathon 2016. Individuals have been classified by gender and age class.

DOI: 10.7287/peerj.preprints.27175v1/supp-17