Modelling Dispersal of Genetic Information in Structured Agricultural Landscapes with Partial Differential Equations

Transcription

1 Modelling Dispersal of Genetic Information in Structured Agricultural Landscapes with artial Differential Equations resented at the COMSOL Conference 2008 Hannover O. Richter and K. Lipsius Institute of Geoecology Braunschweig University of Technology Germany

2 The biosafety problem: outcrossing from GMO crops GM wind? phenology? model output/ threshold value? flowering period? geometry? atmospheric stability? long distance transport? short distance transport? scale? land use? crop rotation? conventional & organic weather? soil? obstacles? landscape sructure?

3 Modelling gene flow in landscapes with partial differential equations Advantages: The processes can be cast into a highly aggregated mathematical form umber of parameters is limited Geometries of heterogeneous landscapes can be linked to finite element nets

4 General approach t i = L[ i ] fi (, 2 space operator L[ ] K ) i 1Ln 1 n = reaction terms: population dynamics, genetics = D( ) r v Diffusion Convection t = D( x, y) r(1 K( x, ) y) Simple example: linear diffusion and logistic growth

5 Conceptual model lants (donators) ollen lants (recipients) Seed ext generation aa aa S aa aa a aa aa S aa aa A AA AA S AA AA ollen dispersal Seed dispersal

6 Equations ollen t i = r ( D ( x, y) u ) f (, t) i i i i ij Seed S t ij = r ( D ( x, y) S vs ) f (,, t) Sij ij ij ij ij i lants t ij = r ij (1 K ij ( x, ) y) α ij S ij S ij K ms i=a, A j=a, A

7 a p aa aa p a f = μ β ) 2 ( A p AA aa p A f = μ β ) 2 ( aa s A a a aa aa s aa S f = μ β ) )( 2 ( aa s A a A AA aa s AA S f = μ β ) )( 2 ( aa s A a a AA aa s A a A aa aa s aa S f = μ β β ) )( 2 ( ) )( 2 ( Interaction terms ollen Seed

8 Imposing spatial and temporal structures The system consists of DE s and ODE S ODE s model plant growth DE s model dispersal of pollen and seed The capacity terms K(x,y,t) and the diffusion coefficients D ij (x,y) are linked to spatial structure Time dependent coefficients e.g. ß s (t),r(t) define temporal patterns

9 rocesses implemented Crop rotation: capacities on fields change in time Crop management: sowing, harvest, and other management practices influencing e.g. seed production, seed survival Transport: Diffusion and convection as Resistance against transport

10 arameter derivation arameter set for each genetic variety Capacity, seed production, pollen production, seed survival, diffusion, convection Describes environmental fitness over time Depends on crop rotation and crop management practices

11 Linking geoinformation and model t = D( x, y) r( x, y, t) (1 ) K( x, y, t) Resistance map Map of environmental Capacity (time dependent)

12 Import of a Landscape to Comsol ArcToolbox: Export to CAD tool Finite element mesh

13 Theoretical biosafety study of a genetically modified crop The crop under study such as oil seed rape has been made tolerant to non-selective systemic herbicides At the phenotype level, resistance affects mortality rates under herbicide applications. Question: how does the management of roadsides influence the propagation of unwanted genetic information?

14 Scenario: Initial allocation of land use and crops Cultivation of GM OSR Cultivation of non GM OSR Set aside and roads

15 Scenario parameters Crop rotation: 3 years: osr, ww, wb Allocation of parameters Capacity: woodland: low, fields: time dependent, lanes: high/low Spatial resistance: woodland: high, fields: middle, lanes: low

16 GM ratio with no herbicides in roads with no isolation distance!

17 GM ratio with herbicides along main road (e.g. railway track) with isolation distance

18 GM ratio with herbicides along all roads with isolation distance

19 GM densities in a non GM field for three scenarios of herbicide applications along roads 20 all roads main road no road GM OSR density time (months)

20 Herbicide application along roads facilitates spread of GM species

21 Summary and Outlook The coupling of DEs and population dynamics with geoinformation provides a model framework for gene flow at landscape scale. It is easliy implemented into COMSOL multiphysics The highly aggregated approach results in only few model parameters, so parameter estimation from field observations is feasible. This is the next step to be taken to endow the model with realistic parameter sets. ossible applications are optimization of crop rotation and crop allocation schemes and evaluation of isolation distances.

22 Thank you for your attention

23 Selected parameter values arameter GM OSR O AA Conv. OSR O aa β S D S road D S field K road K conv field K GM field K WW K WB