Scavenger birds
=======================

Description
-----------

This example presents a PDP system to study the evolution of the bearded vulture in the Pyrenees (NE Spain). It overcomes some limitations of a previous work incorporating other scavenger species and additional prey species that provide food for the scavenger intraguild and interact with the Bearded Vulture in the ecosystem. After the validation, the new model can be a useful tool for the study of the evolution and management of the ecosystem. P systems provide a high level computational modelling framework which integrates the structural and dynamical aspects of ecosystems in a compressive and relevant way. The inherent randomness and uncertainty in ecosystems is captured by using probabilistic strategies.

Model
-----

The corresponding P-Lingua file is the following::

        @model<probabilistic>
        
        def main()
        {
                call init_membrane_structure();
                call init_multisets();
                call init_rules();
        }
        
        def init_membrane_structure()
        {
           @mu= [[[ [  ]'2 ]'1]'101,101]'global;
        }
        
        def init_multisets()
        {
                @ms(1) += X{i,j}*q{i,j} : 0<=j<=g{i,7},1<=i<=n;
                @ms(1) += b{0,i} : 1<=i<=n;
                @ms(2) = C;
        }
        
        def init_rules()
        {
             /******************************/
                 /*The set R of evolution rules*/
             /******************************/
                 /*r0*/ [C --> Gp*Beta,Cp]'2 :: 1;
                 /*r1*/ [b{0,i} --> b{i}]'1 :: 1 : 1<=i<=n;
          
             /********************/
             /*Reproduction-Rules*/
             /********************/
                 /*Adult males*/
             /*r2*/ [X{i,j} --> Y{i,j}]'1 :: (1-k{i,1})*(1-k{i,4}) : g{i,5}<=j<=g{i,7},1<=i<=n;
             
             /*Adult females that reproduce*/
             /*r3*/ [X{i,j} --> Y{i,j},Y{i,0}*k{i,3}]'1 :: k{i,2}*k{i,1}*(1-k{i,4}) : i<>5,g{i,5}<=j<g{i,6},1<=i<=n;
             /*r4*/	[X{5,j} --> Y{5,j},Y{5,0}*k{5,3}]'1 :: 0.5*k{5,1}*k{5,2}: g{5,5}<=j<g{5,6}; 
                 /*r5*/	[X{5,j} --> Y{5,j},Y{6,0}*k{5,3}]'1 :: 0.5*k{5,1}*k{5,2}: g{5,5}<=j<g{5,6};
        
                 /*Adult females that do not reproduce*/ 
                 /*r6*/ [X{i,j} --> Y{i,j}]'1 :: (1-k{i,2})*k{i,1}*(1-k{i,4}) : g{i,5}<=j<g{i,6},1<=i<=n;
                 /*r7*/ [X{i,j} --> Y{i,j}]'1 :: k{i,1}*(1-k{i,4}) : g{i,6}<=j<=g{i,7},1<=i<=n;
        
                 /*************************************/
             /*Young animals that do not reproduce*/
             /*************************************/
                 /*r8*/ [X{i,j} --> Y{i,j}]'1 :: 1-k{i,4} : 1<=j<g{i,5},1<=i<=n;
        
                 /**************/
             /*Growth rules*/
             /**************/
                 /*r9*/ [X{i,j} --> Y{i,g{i,5}-1},Y{i,j}]'1 :: k{i,5}*k{i,4} : g{i,5}<=j<=g{i,7},1<=i<=n;
                 /*r10*/ [X{i,j} --> Y{i,j}]'1 :: (1-k{i,5})*k{i,4} : g{i,5}<=j<=g{i,7},1<=i<=n;
        
                 /*****************/
             /*Mortality rules*/
             /*****************/
             /*r11*/ b{i}[]'2 --> +[b{i},a{i}*g{i,8}]'2 :: 1 : 1<=i<=n;
        
                 /*Young animals that survive*/
                 /*r12*/ Y{i,j}[]'2 --> +[V{i,j},T{i}]'2 :: 1-m{i,1}-m{i,3} : 0<=j<g{i,4},1<=i<=n;
        
                 /*Young animals that die*/
                 /*r13*/ Y{i,j}[]'2 --> +[Hp{i}*(f{i,1}*g{i,3}),Fp{i}*(f{i,2}*g{i,3}),Bp*(f{i,1}*g{i,3}),Mp*(f{i,2}*g{i,3})]'2 :: m{i,1} : 0<=j<g{i,4},1<=i<=n;
        
                 /*Young animals that are retired from the ecosystem*/
                 /*r14*/ [Y{i,j} --> #]'1 :: m{i,3} : 0<=j<g{i,4},1<=i<=n;
        
                 /*Adult animals that do not reach an average life expectancy and survive*/
                 /*r15*/ Y{i,j}[]'2 --> +[V{i,j},T{i}]'2 :: 1-m{i,2} : g{i,4}<=j<g{i,7},1<=i<=n;
        
                 /*Adult animals that do not reach an average life expectancy and die*/
                 /*r16*/ Y{i,j}[]'2 --> +[Hp{i}*(f{i,3}*g{i,3}),Fp{i}*(f{i,4}*g{i,3}),Bp*(f{i,3}*g{i,3}),Mp*(f{i,4}*g{i,3}),V{i,g{i,5}-1}*k{i,4},T{i}*k{i,4}]'2 :: m{i,2} : g{i,4}<=j<g{i,7},1<=i<=n;
        
             /*Animals that reach an average life expectancy and die in the ecosystem*/
                 /*r17*/ Y{i,g{i,7}}[]'2 --> +[Hp{i}*(f{i,3}*g{i,3}),Fp{i}*(f{i,4}*g{i,3}),Bp*(f{i,3}*g{i,3}),Mp*(f{i,4}*g{i,3}),V{i,g{i,5}-1}*k{i,4},T{i}*k{i,4}]'2 :: k{i,4}+(1-k{i,4})*(m{i,4}+(1-m{i,4})*m{i,2}) : 1<=i<=n;
        
                 /*Animals that reach an average life expectancy and retire from the ecosystem*/
                 /*r18*/ [Y{i,g{i,7}} --> #]'1 :: (1-k{i,4})*(1-m{i,4})*(1-m{i,2}) : 1<=i<=n;
        
                 /******************/
                 /*Regulation rules*/
                 /******************/
             /*r19*/ +[Gp --> G]'2 :: 1;
             /*r20*/ +[Bp --> B]'2 :: 1;
             /*r21*/ +[Mp --> M]'2 :: 1;
             /*r22*/ +[Cp --> C]'2 :: 1;
             /*r23*/ +[Hp{i} --> H{i}]'2 :: 1 : 1<=i<=n;
             /*r24*/ +[Fp{i} --> F{i}]'2 :: 1 : 1<=i<=n;
        
             /*********************************************************************/
             /*Evaluation of the density of the different species in the ecosystem*/
                 /*********************************************************************/
                 /*r25*/ +[T{i}*g{i,8},a{i}*(g{i,8}-g{i,9}) --> #]'2 :: 1 : 1<=i<=n;
             /*r26*/ +[V{i,j} --> Z{i,j}]'2 :: 1 : 0<=j<g{i,7},1<=i<=n;
         
             /***************/
             /*Feeding rules*/ 
             /***************/	 
             /*r27*/ /* +[Z{i,j},a{i},B*(f{i,5}*g{i,3}),G*(f{i,6}*g{i,3}),M*(f{i,7}*g{i,3})]'2 --> X{i,j+1}[]'2 :: 1 : 0<=j<=g{i,7},1<=i<=n; */
        
                 /* We set fix this rule so we don't take into account feeding of herbvibores */
                 /*r27*/ +[Z{i,j},a{i},B*(f{i,5}*g{i,3}),M*(f{i,7}*g{i,3})]'2 --> X{i,j+1}[]'2 :: 1 : 0<=j<=g{i,7},1<=i<=n;
        
                 /***************/
             /*Balance rules*/
             /***************/
                 /*Elimination of the remaining bones, meet and grass*/
                 /*r28*/ [B --> #]'2 :: 1;
                 /*r29*/ [G --> #]'2 :: 1;
                 /*r30*/ [M --> #]'2 :: 1;
                 /*r31*/ [T{i} --> #]'2 :: 1 : 1<=i<=n;
             /*r32*/ [a{i} --> #]'2 :: 1 : 1<=i<=n;
                 /*r33*/ [b{i}]'2 --> b{i}[]'2 :: 1 : 1<=i<=n;
                 /*r34*/ [H{i}]'2 --> H{i}[]'2 :: 1 : 1<=i<=n;
                 /*r35*/ [F{i}]'2 --> F{i}[]'2 :: 1 : 1<=i<=n;
        
                 /*Young animals mortality*/
                 /*r36*/ [Z{i,j} --> Hp{i}*f{i,1},Fp{i}*f{i,2},Bp{i}*f{i,1},Mp{i}*f{i,2}]'2 :: g{i,1} : 0<=j<g{i,4},1<=i<=n;
                 /*r37*/ [Z{i,j}]'2 --> d{i}[]'2 :: 1-g{i,1} : 0<=j<g{i,4},1<=i<=n;
        
                 /*Adult animals mortality*/
                 /*r38*/ [Z{i,j} --> Hp{i}*f{i,3},Fp{i}*f{i,4},Bp{i}*f{i,3},Mp{i}*f{i,4}]'2 :: g{i,1} : g{i,4}<=j<=g{i,7},1<=i<=n;
                 /*r39*/ [Z{i,j} --> #]'2 :: 1-g{i,1} : g{i,4}<=j<=g{i,7},1<=i<=n;
                 /*r40*/ [H{i} --> #]'1 :: 1 : 1<=i<=n;
                 /*r41*/ [F{i} --> #]'1 :: 1 : 1<=i<=n;
         
        }

Files
-----

.. container:: boldlink

    * `Custom application <https://github.com/luivalcab/MeCoSim-public-models/blob/master/010%20-%20Scavengers/The%20Scavenger%20Birds.xls>`_.
    * `Model file <https://github.com/luivalcab/MeCoSim-public-models/blob/master/010%20-%20Scavengers/The%20Scavenger%20Birds.pli>`_.
    * `Scenario file <https://github.com/luivalcab/MeCoSim-public-models/blob/master/010%20-%20Scavengers/The%20Scavenger%20Birds.ec2>`_.

References
----------

.. container:: boldlink

    * `P System Based Model of an Ecosystem of Some Scavenger Birds <http://www.gcn.us.es/7BWMC/volume/12_vultures.pdf>`_, 7th Brainstorming Week on Membrane Computing (detailed `here <http://www.gcn.us.es/?q=node/457>`_).
    * `A P System Based Model of an Ecosystem of Some Scavenger Birds <http://link.springer.com/chapter/10.1007%2F978-3-642-11467-0_14>`_, Lecture Notes on Computer Science (detailed `here <http://www.gcn.us.es/?q=node/512>`_).
    * `A computational modeling for real ecosystems based on P systems <http://link.springer.com/article/10.1007%2Fs11047-010-9191-3>`_, Natural Computing (detailed `here <http://www.gcn.us.es/?q=node/655>`_).