Soledad CASTANO
(1,2), Hélène GUIS
(1), Jean VAILLANT
(3), Thomas BALENGHIEN
(1), Jean-Claude DELECOLLE
(4), Thierry BALDET
(1)and David PLEYDELL
(1,2)(1)French Agricultural Research Center for International Development (CIRAD), CMAEE, Baillarguet Campus, Montpellier, France (2)Agricultural Research National Institute (INRA), CMAEE, Duclos Campus, Guadeloupe, France (3)Mathematics and Computation Department, University of Antilles and Guyane, Pointe-à-Pitre, Guadeloupe (4)Strasbourg Institute for Parasitology and Tropical Diseases, Strasbourg, France
Towards the analysis of ecological time series
using state-space models
References
1 - M.R. Easterling, S.P. Ellner and P.M. Dixon. Size-specific sensitivity: Applying a new structured population model. Ecology 81, 694–708, 2000. 2 - C. Andrieu, A. Doucet, and R. Holenstein. Particle Markov chain Monte Carlo methods. J. Royal Statistical Society B, 72(2):1–33, 2010.
3 - R. Venail, T. Balenghien, H. Guis, A. Tran, et al. Assessing diversity and abundance of vector populations at a national scale: example of Culicoides surveillance in France after Bluetongue virus emergence. Arthropods as Vectors of Emerging Diseases: Springer Berlin Heidelberg. 77–102, 2012.
European Conference on Mathematical and Theoretical Biology, 15-19 Juin 2014, Gothenburg, Sweden
Introduction & Framework
Results
THE METHODOLOGICAL CHALLENGE
• Identify a model structure that can minimise prediction error. • Quantify uncertainty via Bayesian methods.
• Generate priors from laboratory data.
• Calibrate models to surveillance network time series.
• Obtain efficient Markov Chain Monte Carlo mixing for SSMs.
MATRIX POPULATION MODELS
• Between-individual heterogeneity in a physical characteristic is repressented by splitting components of matrix M in a discretised IPM approach.
• This approach accounts for heterogeneity in degree-day accummulation & represents the metabolic status of individuals.
• Kernel parameters were estimated to reproduce development time distributions of each stage at various fixed temperatures T.
MODELLING THE LIFE CYCLE OF CULICOIDES
DATA FOR KERNEL ESTIMATION
Ecological time series provide incomplete snapshots of a system. Using such data to predicting population level responses to global change is the holy grail of population dynamics.
State-space models (SSM), which couple stochastic dynamic models of the “state-space” with models accounting for imperfect observation, offer an attractive solution.
INTEGRAL PROJECTION MODELS
(1)(IPM)
• Mathematical and computational simplicity possible. e.g. constant scalar elements & linear dynamics • But, ignore between-individual heterogeneity in developmental response to environmental variation.
Example adult
abundance time series
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pop. vec. at t+1 KERNEL pop. vec. at t survival-growth fertility
Midges of the genre Culicoides transmit several animal
diseases (i.e. Bluetongue, Schmallenberg, AHS).
Modelling Culicoides’ life cycles is crucial for predicting epidemic outcomes & quantifying control efficacy.
The French National Culicoides Surveillance Network provides a rich source for confronting models with data.
EGGS
PUPAE
t t A A P P L E A E t t Mn A P L E P T P T P T F P A P L E n 0 0 0 0 0 0 0 0 1 1 between-stagestransition probabilities per capita fertility
Proportion of completed development, T=20ºC
from Venail et al.(3) (2012)
Life stage Eggs, Larvae & Pupae Adults
Data source Various published studies Unpublished laboratory data
Comments Imputation of missing sample sizes required estimating p(survival) from a similar study
Provides distributions for egg
production & gonotrophic cycle length
Survival probability estimates permitted Bayesian imputation
of missing sample sizes.
Imputed sample sizes helped quantify uncertainty in kernel
parameters (mean & standard deviation).
Truncated Gaussian kernels were estimated with a fifty
developmental sub-unit resolution at fixed temperatures.
Development times were shortest at T=30°C, greatest at
T=17°C & most variable at T=17°C.
Kernel link to temperature clearly non-linear.
No. collected individuals (by catch)
No. collected individuals (monthly mean) Monthly rainfall (mm)
Monthly min temperature (ºC) Monthly max temperature (ºC)
