Balancing statistics and ecology: lumping experimental data for model selection
Nelly van der Hoeven1*, Lia Hemerik2 and Patrick A. Jansen3§
*: Present address: ECOSTAT, Vondellaan 23, 2332 AA Leiden, The Netherlands
Leiden University, IEES, Department of Theoretical Evolutionary Biology, P.O. Box 9516, 2300 RA Leiden, The Netherlands
- Biometris, Department of mathematical and statistical methods, Wageningen University, P.O.box 100, 6700 AC Wageningen, The Netherlands
- Wageningen University, Forest Ecology and Forest Management group, P.O.Box 342, 6700 AH Wageningen, The Netherlands
§: Present address: Alterra - Wageningen UR, Centre for Ecosystem Studies, P.O. Box 74, 6700 AA Wageningen, The Netherlands.
Ecological experiments often accumulate data by carrying out many replicate trials, each containing a limited number of observations, which are then pooled and analysed in the search for a pattern. Replicating trials may be the only way to obtain sufficient data, yet lumping disregards the possibility of differences in experimental conditions influencing the overall pattern. This paper discusses how to deal with this dilemma in model selection. Three methods of model selection are introduced: likelihood-ratio testing, the AIC with or without small-sample correction and the BIC. Subsequently, we apply the AICc method to an example on size-dependent seed dispersal by scatterhoarding rodents.
The example involves binary data on the selection and removal of Carapa procera (Meliaceae) seeds by scattterharding rodents in replicate trials during years of different ambient seed abundance. The question is whether there is an optimum size for seeds to be removed and dispersed by the rodents. We fit five models, varying from no effect of seed mass to an optimum seed mass. We show that lumping the data produces the expected pattern, but gives a poor fit compared to analyses in which grouping levels are taken into account, either by letting the parameters depend on the group, by assuming a random effect of the group on the parameter values, or by assuming some of the parameters fixed for all groups, whereas others depend on the group. Model fitting with some parameters fixed for all groups, and others depending on the trial give the best fit. The general pattern is, however, rather weak.
We explore how far models must differ in order to be able to discriminate between them, using the minimum Kullback-Leibler distance as a measure for the difference. We then show by simulation that the differences are too small to discriminate at all between the five models tested at the level of replicate trials.
We recommend a combined approach in which the level of lumping trials is chosen by the amount of variation explained in comparison to an analysis at the trial level. It is shown that combining data from different trials only leads to an increase in the probability of identifying the correct model with the AIC criterion if the distance of all simpler (=less extended models) to the simulated model is sufficiently large in each trial. Otherwise, increasing the number of replicate trials might even lead to a decrease in the power of the AIC.
Key words: AIC; Carapa procera; Kullback-Leibler distance; Likelihood-Ratio test; model selection; Myoprocta acouchy; noncentral chi-square distribution; power; Red acouchy; scatterhoarding; seed dispersal; seed size
In: T.A.C. Reydon & L. Hemerik (Eds): Current themes in Theoretical Biology: A Dutch Perspective. pp 233-265. Springer, Dordrecht, The Netherlands, 2004.
Een selectie uit de publikaties van Nelly van der
Is it safe to pool the Blank Control Data with the Solvent Control data? N. van der Hoeven,
Ecotoxicol. Environm. Safety, 73:1480-1483, 2010
Multi-criteria decision analysis of test endpoints for detecting the effects of endocrine active substances in fish full life cycle tests.
M. Crane, M. Gross, P. Matthiessen, G.T. Ankley, S. Axford, P. Bjerregaard, R. Brown, P. Chapman, M. Dorgeloh, M. Galay-Burgos, J. Green, C. Hazlerigg, J. Janssen, K. Lorenzen, J. Parrott, H. Rufli, C. Schäfers, M. Seki, H.C. Stolzenberg, N. van der Hoeven, D. Vethaak, IJ. Winfield, S. Zok & J. Wheeler
Integr Environ Assess Manag., 6: 378-389, 2010
Exposure analysis of bisphenol A in surface water systems in North America and Europe. (PMID:19746705)
G.M. Klecka, C.A. Staples, K.E. Clark, N. van der Hoeven, D.E. Thomas & S.G. Hentges
Environmental Science & Technology, 43: 6145-6150, 2009
The Minimum Significant Difference at the NOEC calculated with a non-parametric test.
Hoeven, N. van der,
In: Proceedings of the 30th Anniversary Meeting of the Netherlands Society of Toxicology, june 2009. p. 122
Calculation of the Minimum Significant Difference at the NOEC using a non-parametric test.
Hoeven, N. van der,
Ecotoxicol. Environm. Safety, 70: 61-66, 2008
Does bisphenol a induce superfeminization in Marisa cornuarietis?
Part I: Intra- and inter-laboratory variability in test endpoints. Forbes, V.E., H. Selck, A. Palmqvist, J. Aufderheide, R. Warbritton, N. Pounds, R. Thompson, N. van der Hoeven & N. Caspers
Ecotoxicol. Environm. Safety, 66: 309-318, 2007
Does bisphenol A induce superfeminization in Marisa cornuarietis?
Part II: Toxicity test results and requirements for statistical
power analyses. Forbes, V.E., J. Aufderheide, R. Warbritton, N. van der Hoeven & N. Caspers
Ecotoxicol. Environm. Safety, 66: 319-325, 2007
Statistical issues in fish life-cycle tests with many endpoints.
Hoeven, N. van der & D.R. Dietrich,
Abstract and poster for SETAC Europe, May 2005, Lille
The probability to select the correct model using likelihood-ratio based criteria in choosing between two nested models of which the more extended one is true.
Hoeven, N. van der,
Journal of Statistical Planning and Inference, 135: 477-486, 2005
Effects of bisphenol A on adult fathead minnow (P. promelas) gonadal histology: a 42-day exposure study.
Dietrich, D.R., J. Wolf, A.R. Brown, J.E. Caunter, N. van der Hoeven & U. Friederich,
Abstract and poster for the Cluster workshop on Ecological relevance of chemically induced endocrine disruption in wildlife. University of Exeter, july 2004.
The Netherlands working group on Statistics and Ecotoxicology: Statistics and Models for Risk Assessment.
Hoeven, N. van der,
In: Proceedings of the Jubilee Annual Meeting of the Netherlands Society of Toxicology, june 2004. p. 114
Current issues in statistics and models for Ecotoxicological Risk Assessment.
Hoeven, N. van der,
Acta Biotheoretica 52: 201-217, 2004
Balancing statistics and ecology: on the lumping of experimental data for model selection.
Hoeven, N. van der, L. Hemerik & P.A. Jansen. In: T.A.C. Reydon & L. Hemerik (Eds): Current themes in Theoretical Biology: A Dutch Perspective. pp 233-265. Springer, Dordrecht, The Netherlands, 2004.
Using marine bioassays to classify the toxicity of Dutch harbour sediments. Stronkhorst, J., C. Schipper, J. Brils, M. Dubbeldam, J. Postma & N. van der Hoeven
Environmental Toxicology and Chemistry, 22: 1535-1547, 2003
What can egg distributions of solitary parasitoids tell us about the information the parasitoid has and uses for its oviposition decisions? Hemerik, L.,N. van der Hoeven &
J. J.M. van Alphen, Acta Biotheoretica, 50: 167-188, 2002
Statistical tests and power analysis for three in-vivo bioassays
to determine the quality of marine sediments. Hoeven, N. van der, B. J. Kater &
J. F. Pieters, Environmetrics 13: 281-293, 2002
Significance tables for the exact variance test for the Poisson
distribution with alternative underdispersion. N. van der Hoeven & L Hemerik,
Environmental and Ecological Statistics 9: 201-213, 2002
Estimating the 5-percentile of the species sensitivity
distribution without any assumptions about the distribution. N. van der Hoeven,
Ecotoxicology 10: 25-34, 2001
Power analysis for the NOEC: What is the probability to detect
small toxic effects on three different species using the appropriate standardized test
protocols? N. van der Hoeven, Ecotoxicology 7: 355-361, 1998
The acute toxicity of selected alkylphenols on young and adult
Daphnia magna. A.A.M. Gerritsen, N. van der Hoeven & A. Pielaat,
Ecotoxicol. Environm. Safety 39: 227-232. 1998
The ecotoxicity and the biodegradability of lactic acid, alkyl
lactate esters and lactic acid salts. C.T. Bowmer, R.N. Hooftman, A.O. Hanstveit,
P.W.M. Venderbosch & N. van der Hoeven, Chemosphere 37:
How to measure no effect? Part I: Towards a new measure of
chronic toxicity in ecotoxicology. Introduction and workshop results. N. van der Hoeven,
F. Noppert & A. Leopold, Environmetrics 8: 241-248, 1997
How to measure no effect? Part III: Statistical aspects of
NOEC, ECx and NEC estimates. N. van der Hoeven, Environmetrics 8: 255-261, 1997
The effect of chlorpyrifos on individuals of Daphnia
pulex in laboratory and field. N. van der Hoeven & A.A.M. Gerritsen,
Environm. Toxicol. Chem. 16: 2438-2447, 1997
A model based on soil structural aspects describing the fate of
genetically modified bacteria in soil. N. van der Hoeven & J.D. van Elsas,
Ecological Modelling 89: 161-173, 1996
Competition between cohorts of juvenile Daphnia
magna. E.L. Enserink, N. van der Hoeven, M. Smith, M. van der Klis & M.A.
van der Gaag, Archiv für Hydrobiologie 136: 433-454, 1996
Reliability of quantitative toxicity test results: from
experimental control to data processing. Enserink, E.L. & N. van der Hoeven,
The Science of the Total Environment, suppl. 1993, Proceedings of the Second
European Conference on Ecotoxicology, eds. W. Slooff & H. de Kruijf, p. 699-704,
LC50 estimates and their confidence intervals. The case that
only one test concentration has partial effect. N. van der Hoeven, Water
Research 25: 401-408, 1991
Effects of toxicants on individuals and populations of Daphnia,
a simulation study. N. van der Hoeven, Comparative Biochemistry and
Physiology 100C: 283-286, 1991
Effect of 3,4-dichloroaniline and metavanadate on Daphnia
populations. N. van der Hoeven, Ecotoxicology and Environmental Safety
20: 53-70, 1990
Salmonella test: Relation between mutagenicity and number of
revertant colonies. N. van der Hoeven, S.A.L.M. Kooijman & W.K. de Raat,
Mutation Research 234: 289-302, 1990
Superparasitism as an ESS: to reject or not to reject, that is
the question. N. van der Hoeven & L. Hemerik, J. of Theoretical Biology
146: 467-482, 1990
Population consequences of a physiological model for individual
development S.A.L.M. Kooijman, N. van der Hoeven & D.C. van der Werf,
Functional Ecology 3: 325-336, 1989
Oscillations in Daphnia populations. N. van der
Hoeven, A.M. de Roos & S.A.L.M. Kooijman, Econieuws 2, 7-8,
The population dynamics of Daphnia at constant food supply: a
review, re-evaluation and analysis of experimental series from the literature. N. van
der Hoeven, Netherlands Journal of Zoology 39: 126-155, 1989
Random elements in a population model based on individual
development. N. van der Hoeven, in: Ecodynamics, Proc. Int. Workshop at Jülich,
FRG, 19-20 Oct. 1987. Eds. W. Wolff, C.J. Soeder & F.R. Drepper, pp 333-342,
Research Notes in Physics, Springer Verlag., 1988