tool for analyzing the spread of diseases and species distributions. Joaqu´ın Mart´ınez-Minaya. 1. , Antonio Vicent. 2. , Antonio López-Qu´ılez. 1. ,. F. Xavier Picó.
Highly structured spatial models as a tool for analyzing the spread of diseases and species distributions Joaqu´ın Mart´ınez-Minaya1, Antonio Vicent2, Antonio L´ opez-Qu´ılez1, F. Xavier Pic´ o3, Arnald Marcer4,5 and David Conesa1 1Universitat de Val` encia, 2IVIA, 3CSIC, 4CREAF, 5Universitat Aut´onoma de Barcelona.
THREE DATASETS CIRCULAR LEAF SPOT (CLS)
ARABIDOPSIS THALIANA
OLIVE DECLINE SYNDROME (ODS)
• CLS is a persimmon disease caused by the fungus Mycosphaerella nawae, which induces necrotic lesions on leaves, defoliation and fruit drop. The disease was detected in 2008 in Spain (Vicent et al., 2011).
• A. thaliana is a small flowering plant considered a weed. It is important for molecular biology and for ecological and evolutionary genetics. The Iberian Peninsula (IP) has received some attention in several A. thaliana genetic structure studies (Marcer et al., 2016).
• ODS is a lethal plant disease caused by the bacterium Xylella fastidiosa, and affecting not only olive but also grapes, citrus, stone fruits and almonds.
• Cumulative percent of ascospores released (Y ) and cumulative degree days (CDD) are avaliable in the location L’Alcudia since 2010 until 2015. • Aim: modelling the dynamics of the ascospores formed in persimmon leaf litter, to implement weather-based spray programs.
• Proportion of specie’s presence of four spatially separated Iberian genetic clusters, climate variables and geographic coordinates are avaliable in the IP. • Aim: revealing the geographical structure of its genetic variation and study climatic factors related with A. thaliana presence.
• The affected areas are in the southem region of Apulia in Italy, Corsica and continental France, as well as outbreaks in Germany and Spain (White et al., 2017). • Presence/absence of the disease, climate variables and coordinates are avalaible in Apulia • Aim: to study climatic and spatial factors related with the presence/absence of the disease.
THE RESPONSE VARIABLE Cumulative % ascospores released
1.00 ● ● ● ●
0.75
● ●
2010 2011 2012 2013 2014 2015
● ● ● ●
0.50 ● ●
● ●
0.25
● ●
● ●
0.00
● ●●●
● ● ● ●
● ●
● ● ● ● ● ●● ● ●● ● ●
● ●
● ●
● ●
● ● ● ● ●● ● ● ● ● ●
● ●
● ● ● ● ● ● ● ● ● ●
●
● ●
● ●
●
●
● ●
● ● ●
●
●
● ●
●
● ● ●● ●● ● ●
● ●
d
●
●
● ● ●
● ●
c
●
●●
●
●
d
●
●
●
c
●
● ●
●
● ●●
●
●
●
●
●
●
● ● ●
● ●
●
● ●
● ● ● ●
● ●
●
●
●
●
● ●
b
●●
● ●
● ● ●
● ● ● ●
●
●
a
● ●
● ●
●
●● ●● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●●
b
●
● ●
●
●● ● ● ● ● ●● ● ●
● ● ● ●
● ● ●
●
●
●
●
●● ● ●
●
●
●
●
● ●●
● ●
●● ● ● ● ● ● ● ●
● ● ● ● ●●
a
● ●
●
●
●
10
20
30
40
Cumulative degree−days (x100)
• Proportion of cumulative ascospores released vs Cumulative degreedays (x100) for years from 2010 to 2015 in the location of L’Alcdia (Generalitat Valenciana, Spain).
• Proportion of specie’s presence for the four different genetic clusters: GC1, GC2, GC3 and GC4 corresponding to a,b,c and d respectively.
• a,b and c represents the different sampling campaigns done in 2014, 2015 and 2016. d represents the data corresponding to the first sampling campaign in Lecce province analyzed in this poster.
MODELS USING INLA AND SPDE (Rue et al., 2009; Lindgren et al., 2011) Likelihood Yi ∼ Bernoulli(πi), logit(πi) = X iβ + W i,
Likelihood
Likelihood
Yij ∼ Beta(pij , qij ), pij = µij φi, qij = φi(1 − µij ), logit(µij ) = β0 + β1 · CDDi + anyoj , φi = exp(θ),
Yi ∼ Beta(pi, qi), pi = µiφi, qi = φi(1 − µi), logit(µi) = X iβ + W i, φi = exp(θ),
Latent Gaussian field −4 β0, β1 ∼ N(0; 10 ), anyoj ∼ N(0; τa),
Latent Gaussian field −4 β0, . . . , βM ∼ N(0; 10 ), W ∼ N(0; Q(r, σW )),
Hyperparameters
Hyperparameters
θ ∼ LogGamma(1; 0.01), −5 θa = log(τa), τa ∼ LogGamma(1; 5 · 10 ).
θ ∼ LogGamma(1; 0.01), log(r) ∼ N(µr ; 0.25), log(σW ) ∼ N(µσW ; 0.25).
Latent Gaussian field −4 β0, . . . , βM ∼ N(0; 10 ), W ∼ N(0; Q(r, σW )), Hyperparameters log(r) ∼ N(µr ; 0.1), log(σW ) ∼ N(µσW ; 0.1). • W is the spatial effect with Mat´ern covariance function, r is referred to the range of the spatial effect and σW to the standard deviation of the spatial effect. µr has been chosen as the logarithm of the twenty percent of the total diameter of the region and µσW as the logarithm of 1.
RESULTS a
b 1
Cumulative % ascospores released
1.00 ● ● ● ●
0.75
● ●
2010 2011 2012 2013 2014 2015
● ● ● ● ● ●
●
● ●
●
● ● ● ●
● ●
●
0.50
●
●
●●
1
● ●
●
b
a
●● ●
● ●
0.75
● ● ● ● ● ●
●
●
●
●● ●
●
●●
c
● ● ●
d
0.50
●
●
● ●
0.25
● ●
● ● ●
●
●
● ● ● ●
● ●
●●
● ●
●
● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ●● ● ● ●
10
●
●
●
● ●
● ●
●●
●
●
● ●
● ● ● ●
● ●
●●
●
●
●
●
●
● ● ●
● ● ●
● ● ● ●
●
●
● ●
●
0
●
●
●
0.00
● ●●
● ● ● ● ●●
●● ● ● ● ●● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ●● ●
● ● ●● ● ●● ●
● ●
●
●
● ● ● ● ●
● ● ●
●
1
0.4
0.5
0.2
0
0
●
● ● ●
0.25
●
●
●
●
20
30
40
Cumulative degree−days (x100)
• Mean and 95 % credible interval of the predictive posterior distribution for the mean is represented in the graph. Hence, Infection periods can be determined.
0
• Mean of the predictive posterior distribution for the mean of the four different genetic clusters: GC1, GC2, GC3 and GC4, corresponding to a,b,c and d respectively and using a model without spatial effect for GC3. Both, spatial and climatic factors have been relevant in the study of the genetic clusters GC1, GC2 and GC4.
• Mean (a) and standard deviation (b) of the predictive posterior distribution for the mean of the probability of X. fastidiosa presence πi in Lecce province. Both, spatial and climatic factors have been relevant in the study of this disease.
Lindgren, F., Rue, H., and Lindstr¨om, J. (2011). An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(4):423–498. Marcer, A., M´endez-Vigo, B., Alonso-Blanco, C., and Pic´o, F. X. (2016). Tackling intraspecific genetic structure in distribution models better reflects species geographical range. Ecology and evolution, 6(7):2084–2097. Rue, H., Martino, S., and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series b (statistical methodology), 71(2):319–392. Vicent, A., Bassimba, D., and Intrigliolo, D. (2011). Effects of temperature, water regime and irrigation system on the release of ascospores of Mycosphaerella nawae, causal agent of circular leaf spot of persimmon. Plant Pathology, 60(5):890–908. White, S. M., Bullock, J. M., Hooftman, D. A., and Chapman, D. S. (2017). Modelling the spread and control of Xylella fastidiosa in the early stages of invasion in Apulia, Italy. Biological Invasions, 19(6):1825–1837.
This work has been partially supported by research grants MTM2016 - 77501 - P and CGL2016 - 77720 - P from the Spanish Ministry of Economy and Competitiveness, INIA RTA2013 - 00004 - C03 - 02 FEDER, VALi+d grant from Generalitat Valenciana and grant 2014 - SGR - 913 from Generalitat de Catalunya.
