Each species must be defined in every compartment it may be found. However, we want to make sure we use the same name in all definitions, because it is really the same species. Note, however, that SBML requires the species id to be unique.

<listOfSpecies>

  <species id="A1"
	          name="A"
	          boundaryCondition="false"
	          compartment="CompartmentOne"
	          hasOnlySubstanceUnits="true"
	          initialAmount="0"
	          substanceUnits="item">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">   
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>
    </annotation>
  </species>

  <species id="A2"
	          name="A"
	          boundaryCondition="false"
	          compartment="CompartmentTwo"
	          hasOnlySubstanceUnits="true"
	          initialAmount="0"
	          substanceUnits="item">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>
    </annotation>
  </species>

  <species id="A3"
	          name="A"
	          boundaryCondition="false"
	          compartment="CompartmentThree"
	          hasOnlySubstanceUnits="true"
	          initialAmount="1"
	          substanceUnits="item">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="0.01e-8" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
     </MesoRD:species_diffusion>
    </annotation>
  </species>

  <species id="B1"
	          name="B"
	          boundaryCondition="false"
	          compartment="CompartmentOne"
	          hasOnlySubstanceUnits="true"
	          initialAmount="0"
	          substanceUnits="item">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="2.0e-8" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="2.0e-8" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne"
                        MesoRD:rate="2.0e-8" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>
    </annotation>
  </species>

  <species id="B2"
	          name="B"
	          boundaryCondition="false"
	          compartment="CompartmentTwo"
	          hasOnlySubstanceUnits="true"
	          initialAmount="0"
	          substanceUnits="item">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="2.0e-8" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="2.0e-8" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="2.0e-8" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>
    </annotation>
  </species>

  <species id="B3"
	          name="B"
	          boundaryCondition="false"
	          compartment="CompartmentThree"
	          hasOnlySubstanceUnits="true"
	          initialAmount="0"
	          substanceUnits="item">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="2.0e-8" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="2.0e-8" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>
    </annotation>
  </species>

  <species id="C1"
	          name="C"
	          boundaryCondition="false"
	          compartment="CompartmentOne"
	          hasOnlySubstanceUnits="false"
	          initialConcentration="0"
	          substanceUnits="mole">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>
    </annotation>
  </species>

  <species id="C2"
	          name="C"
	          boundaryCondition="false"
	          compartment="CompartmentTwo"
	          hasOnlySubstanceUnits="false"
	          initialConcentration="0"
	          substanceUnits="mole">
    
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>
    </annotation>
  </species>

  <species id="C3"
	          name="C"
	          boundaryCondition="false"
	          compartment="CompartmentThree"
	          hasOnlySubstanceUnits="false"
	          initialConcentration="1e-9"
	          substanceUnits="mole">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>                  
    </annotation>
  </species>
  
  <species id="D1"
	          name="D"
	          boundaryCondition="false"
	          compartment="CompartmentOne"
	          hasOnlySubstanceUnits="true"
	          initialAmount="0"
	          substanceUnits="item">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>
    </annotation>
  </species>

  <species id="D2"
	          name="D"
	          boundaryCondition="false"
	          compartment="CompartmentTwo"
	          hasOnlySubstanceUnits="true"
	          initialAmount="0"
	          substanceUnits="item">
    
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="2.0e-8" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>                  
    </annotation>
  </species>
  
  <species id="D3"
	          name="D"
	          boundaryCondition="false"
	          compartment="CompartmentThree"
	          hasOnlySubstanceUnits="true"
	          initialAmount="0"
	          substanceUnits="item">
    <annotation>
     <MesoRD:species_diffusion xmlns:MesoRD="http://www.icm.uu.se">
      <MesoRD:diffusion MesoRD:compartment="CompartmentThree" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentTwo" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      <MesoRD:diffusion MesoRD:compartment="CompartmentOne" 
                        MesoRD:rate="0" 
                        MesoRD:units="cm2ps"/>
      </MesoRD:species_diffusion>
    </annotation>
  </species>

</listOfSpecies>

Here A and C molecules have non-zero initial amounts. A is initialised with one molecule in CompartmentThree. C is initialised with as a concentration in CompartmentThree. Neither A or C and diffuse away from CompartmentThree, but A makes B molecules that can diffuse into CompartmentOne and CompartmenTwo.