The inevitability of surprise in agroecosystems

Model Description

This is a simple model of competition between noxious and benigne weeds in an agroecosystem based on predator-prey dynamics. The interesting aspect of this model is that it demonstrates the inevitability of surprises in system behavior - meaning that for some systems, early warning signals (e.g, increased variance or autocorrelatin) are almost non-existent prior to critical transitions in systems. The reference article, Vandermeer (2011), gives the following overview. "Many critical transformations of ecosystems contain advanced signals of their imminence, but it is also true that many critical transformations can be shown to contain no such signal, at least with the sorts of data normally available to ?eld workers. This paper explores some generalized theoretical structures and distinguishes  between  those  that  may  provide  a  signal that  could  be   used to predict  a  critical transformation and those that, by their very nature, do  not provide such a clue. I argue that it is almost certain that such completely unpredictable structures will sometimes emerge from systems that tend to be   as   complicated  as   agroecosystems,  in   both  their  natural  and  social   sciences  manifestations. Precaution should thus be  taken when designing agroecosystems".

Reference

Vandermeer, J. (2011). The inevitability of surprise in agroecosystems. Ecological Complexity, 8(4), 377–382. doi:10.1016/j.ecocom.2011.10.001

Scenarios

Here, we demonstrate how suddenly the biomass of noxious weeds can rise without any early warning signals. Set the y-axis to the biomass of noxious weeds (N2) and x-axis to the time. Set the parameters as the following: K1=2, K2=0.9, alpha12=0.8, and alpha21=0.8. Now, slowly increase the the carrying capacity of noxious weeds (K2) from 0.9 to 2.5. You will see that N2 rises gradually - meaning that there are early warning signals/trends indicating that the change is under way. To observe the case where there are no clear warning signals, set the competition parameters to 1.1 (alpha12=1.1 and alpha21=1.1). Again, slowly increase the the carrying capacity of noxious weeds (K2) from 0.9 to 2.5. At about K2=2.06~2.07, you will see that there is a sudden jump in N2. This time, there were no early warning signs indicating that the radical change was imminent.

$\Large \frac{dN_{2}}{dt}=N_{2}\left (\frac{K_{2}-N_{2}-\alpha_{21}N_{1}}{K_{2}} \right )$
Rate of change in the biomass of noxious weeds
$\Large \frac{dN_{1}}{dt}=N_{1}\left (\frac{K_{1}-N_{1}-\alpha_{12}N_{2}}{K_{1}} \right )$
Rate of change in the biomass of benign weeds 
#=====define parameters


par K1=2, K2=0.9, alpha12=0.8, alpha21=0.8
#=====define some hidden variables=====



#============economic functions


#==================demographicfunctions



#=====auxiliary quantities=================

#======right hand sides

dN1/dt=N1*((K1-N1-alpha12*N2)/(K1))
dN2/dt=N2*((K2-N2-alpha21*N1)/(K2))



#=============initial data

init N1=0.2, N2=0.1
@ meth=qualrk
@ bounds=500
@ total=500
@ dt=1
@ yp=N2
@ ylo=0,yhi=2


done

Yu JHD,  Arizona State University. 

Bozicevic M,  Arizona State University. 

You can adjust total time of simulation below.
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This model has four parameters. You can set their values below.
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