Dynamic simulation models is R powerful enough? - PowerPoint PPT Presentation

Faculty Faculty of of Forest Forest- -, Geo , Geo- - and and Hydrosciences Hydrosciences, Institute of , Institute of Hydrobiology Hydrobiology Faculty Faculty of of Forest Forest - - , Geo , Geo - - and and Hydrosciences Hydrosciences , Institute of , Institute of Hydrobiology Hydrobiology Dynamic simulation models – is R powerful enough? Thomas.Petzoldt@TU-Dresden.de

dN  − N  Dynamic models … 1 = ⋅ ⋅ r N   dt K   • … models that respect time explicitly . • used in many fields: mathematics, physics, chemistry, biology, ecology, engineering, economics… • "What makes using system dynamics different from other approaches to studying complex systems is the use of feedback loops and stocks and flows . These elements help describe how even seemingly simple systems display baffling nonlinearity . http://en.wikipedia.org/wiki/System_dynamics

Example 1: A Lotka-Volterra-type model Substrate Producer Consumer Source Sink P S K Import b c d e f dS = − ⋅ ⋅ import b S P dt dP = ⋅ ⋅ − ⋅ ⋅ c S P d P K dt dK = ⋅ ⋅ − ⋅ e P K f K dt

The LV-type model in R �� !� !� !� !� ! ! ! ! "�� "� �� # # "� "� �� # # "� "� "�# "� # # # �� $ �� $ ��$ ��$�� $�� $�� $�� $�� $�� $�� $�� $�� $�� $�� $��%�� $��%�� $��%�� $��%�� $�� $�� $��%�� $��%�� $��%�� $��%�� &��$�� &��$�� &��$�� &��$�� package deSolve (Soetaert, Petzoldt, Setzer)

Benchmark dS = − ⋅ ⋅ import b S P dt dP = ⋅ ⋅ − ⋅ ⋅ c S P d P K dt dK = ⋅ ⋅ − ⋅ e P K f K dt CPU time 3 equations (ODEs) in R, 1000 (external) timesteps case A: interpolated input (approxfun) • ………… 1.4 s • case B: import <- if (trunc(t) %% 2 == 0) 0 else 0.1 ………… 0.8 s Time is ok for this toy model, but is R suited for more complex simulations? 3 ODEs = 1 s � � � spatial system with 10.000 ODEs > 1 hour? �

Example 2: A stream model Experimentally manipulated small stream of our limnological workgroup � Hamburg 500 km Elbe River Dresden 20 km � Experimental Range 650m � Rennes 1200 km

Downward drift of water insects in the stream (Mayflies) Is buffer stretch sufficiently long? 3) Fish treatment 2) Buffer stretch with fish > drift drift nofish fish 1) Reference Fences Fences Fences Fences no fish v flow up down Water Sediment

Can be described by a basic PDE model ∂ ∂ M M Mobile Organisms = ⋅ − ⋅ − ⋅ up S down M v ∂ ∂ t x dS = − ⋅ + ⋅ up S down M Sessile Organisms dt v flow up down Water Sediment x x x dx 1 2 n

Dynamic simulation models is R powerful enough? - PowerPoint PPT Presentation

Faculty Faculty of of Forest Forest- -, Geo , Geo- - and and Hydrosciences Hydrosciences, Institute of , Institute of Hydrobiology Hydrobiology Faculty Faculty of of Forest Forest - - , Geo , Geo - - and and Hydrosciences

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Dynamic simulation models is R powerful enough? - PowerPoint PPT Presentation

Faculty Faculty of of Forest Forest- -, Geo , Geo- - and and Hydrosciences Hydrosciences, Institute of , Institute of Hydrobiology Hydrobiology Faculty Faculty of of Forest Forest - - , Geo , Geo - - and and Hydrosciences

1 7 8 Types of simulation models Dynamic simulation models Stochastic vs. deterministic.

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A Computationally Practical Simulation Estimation Algorithm for Dynamic Panel Data Models with

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