Stochastic models and statistical inference for plant pollen dispersal

Catherine Laredo; Agnès Grimaud

Journal de la société française de statistique (2007)

  • Volume: 148, Issue: 1, page 77-105
  • ISSN: 1962-5197

Abstract

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Modelling pollen dispersal is essential to make predictions of cross-pollination rates in various environmental conditions between plants of a cultivated species. An important tool for studying this problem is the “individual pollen dispersal function” or “kernel dispersal”. Various models for airborne pollen dispersal are developed. These models are based on assumptions about wind directionality, gravity, settling velocity and may integrate other biological or external parameters. Some previous approaches have used brownian Motions with drift for modelling pollen trajectories. However, models for pollen transport used in aerobiology are often based on the lagrangian Stochastic approach: velocities of pollen grains satisfy stochastic differential equations or Langevin equations and pollen trajectories are obtained by integrating these velocities. New models based on this approach are introduced. A model where the vertical component is driven by an integrated Ornstein-Uhlenbeck process is studied here. Cross-pollination rates data were obtained from large field experiments of maize using the colour of grains as a phenotypic marker of pollen dispersal. We first studied the various individual dispersal functions associated with these models. Second, a thorough statistical framework was developed in order to estimate and compare their performances on data sets. This framework is quite general and can be used to study many other cross-pollination data. Previous and new models were successively analysed using this framework. This new statistical analysis improved significantly former results which had been obtained on the previous models with other statistical methods. The statistical analyses showed that the performances of Lagrange Stochastic models were good, but not better than the previous mechanistic models analysed using this new statistical framework. These results however might be due to some specific environmental conditions in this experiment. Comparisons with the external parameters were quite good, proving that these models can be used in other environmental conditions. All these results show that mechanistic models are good models for predicting short or medium range pollen dispersal and cross-pollination rates.

How to cite

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Laredo, Catherine, and Grimaud, Agnès. "Stochastic models and statistical inference for plant pollen dispersal." Journal de la société française de statistique 148.1 (2007): 77-105. <http://eudml.org/doc/93458>.

@article{Laredo2007,
abstract = {Modelling pollen dispersal is essential to make predictions of cross-pollination rates in various environmental conditions between plants of a cultivated species. An important tool for studying this problem is the “individual pollen dispersal function” or “kernel dispersal”. Various models for airborne pollen dispersal are developed. These models are based on assumptions about wind directionality, gravity, settling velocity and may integrate other biological or external parameters. Some previous approaches have used brownian Motions with drift for modelling pollen trajectories. However, models for pollen transport used in aerobiology are often based on the lagrangian Stochastic approach: velocities of pollen grains satisfy stochastic differential equations or Langevin equations and pollen trajectories are obtained by integrating these velocities. New models based on this approach are introduced. A model where the vertical component is driven by an integrated Ornstein-Uhlenbeck process is studied here. Cross-pollination rates data were obtained from large field experiments of maize using the colour of grains as a phenotypic marker of pollen dispersal. We first studied the various individual dispersal functions associated with these models. Second, a thorough statistical framework was developed in order to estimate and compare their performances on data sets. This framework is quite general and can be used to study many other cross-pollination data. Previous and new models were successively analysed using this framework. This new statistical analysis improved significantly former results which had been obtained on the previous models with other statistical methods. The statistical analyses showed that the performances of Lagrange Stochastic models were good, but not better than the previous mechanistic models analysed using this new statistical framework. These results however might be due to some specific environmental conditions in this experiment. Comparisons with the external parameters were quite good, proving that these models can be used in other environmental conditions. All these results show that mechanistic models are good models for predicting short or medium range pollen dispersal and cross-pollination rates.},
author = {Laredo, Catherine, Grimaud, Agnès},
journal = {Journal de la société française de statistique},
keywords = {pollen dispersal; field experiment; cross-pollination rates; maize; airborne pollen; meteorological parameters; deconvolution; parametric inference; quasilikelihood; hypothesis testing; ; individual pollen dispersal function; mechanistic models; lagrangian stochastic models; Langevin equations; hitting times},
language = {eng},
number = {1},
pages = {77-105},
publisher = {Société française de statistique},
title = {Stochastic models and statistical inference for plant pollen dispersal},
url = {http://eudml.org/doc/93458},
volume = {148},
year = {2007},
}

TY - JOUR
AU - Laredo, Catherine
AU - Grimaud, Agnès
TI - Stochastic models and statistical inference for plant pollen dispersal
JO - Journal de la société française de statistique
PY - 2007
PB - Société française de statistique
VL - 148
IS - 1
SP - 77
EP - 105
AB - Modelling pollen dispersal is essential to make predictions of cross-pollination rates in various environmental conditions between plants of a cultivated species. An important tool for studying this problem is the “individual pollen dispersal function” or “kernel dispersal”. Various models for airborne pollen dispersal are developed. These models are based on assumptions about wind directionality, gravity, settling velocity and may integrate other biological or external parameters. Some previous approaches have used brownian Motions with drift for modelling pollen trajectories. However, models for pollen transport used in aerobiology are often based on the lagrangian Stochastic approach: velocities of pollen grains satisfy stochastic differential equations or Langevin equations and pollen trajectories are obtained by integrating these velocities. New models based on this approach are introduced. A model where the vertical component is driven by an integrated Ornstein-Uhlenbeck process is studied here. Cross-pollination rates data were obtained from large field experiments of maize using the colour of grains as a phenotypic marker of pollen dispersal. We first studied the various individual dispersal functions associated with these models. Second, a thorough statistical framework was developed in order to estimate and compare their performances on data sets. This framework is quite general and can be used to study many other cross-pollination data. Previous and new models were successively analysed using this framework. This new statistical analysis improved significantly former results which had been obtained on the previous models with other statistical methods. The statistical analyses showed that the performances of Lagrange Stochastic models were good, but not better than the previous mechanistic models analysed using this new statistical framework. These results however might be due to some specific environmental conditions in this experiment. Comparisons with the external parameters were quite good, proving that these models can be used in other environmental conditions. All these results show that mechanistic models are good models for predicting short or medium range pollen dispersal and cross-pollination rates.
LA - eng
KW - pollen dispersal; field experiment; cross-pollination rates; maize; airborne pollen; meteorological parameters; deconvolution; parametric inference; quasilikelihood; hypothesis testing; ; individual pollen dispersal function; mechanistic models; lagrangian stochastic models; Langevin equations; hitting times
UR - http://eudml.org/doc/93458
ER -

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