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Table 1 Elements in a species association matrix. Interaction frequencies (aij) between c animal and r plant species and their respective totals (rows:Ai, columns: Aj, total elements: m).

From: Measuring specialization in species interaction networks

  Animal sp.1 sp. 2 ... sp. c Total
Plant sp. 1 a 11 a 12 ... a1c A i = 1 = j = 1 c a 1 j MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGbbqqdaWgaaWcbaGaemyAaKMaeyypa0JaeGymaedabeaakiabg2da9maaqahabaGaemyyae2aaSbaaSqaaiabigdaXiabdQgaQbqabaaabaGaemOAaOMaeyypa0JaeGymaedabaGaem4yamganiabggHiLdaaaa@3CE1@
sp. 2 a21 a 22 ... a2c A i = 2 = j = 1 c a 2 j MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGbbqqdaWgaaWcbaGaemyAaKMaeyypa0JaeGOmaidabeaakiabg2da9maaqahabaGaemyyae2aaSbaaSqaaiabikdaYiabdQgaQbqabaaabaGaemOAaOMaeyypa0JaeGymaedabaGaem4yamganiabggHiLdaaaa@3CE5@
... ... ... ... ... ...
sp. r a r 1 a r 2 ... a rc A i = r = j = 1 c a r j MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGbbqqdaWgaaWcbaGaemyAaKMaeyypa0JaemOCaihabeaakiabg2da9maaqahabaGaemyyae2aaSbaaSqaaiabdkhaYjabdQgaQbqabaaabaGaemOAaOMaeyypa0JaeGymaedabaGaem4yamganiabggHiLdaaaa@3DDB@
Total A j = 1 = i = 1 r a i 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGbbqqdaWgaaWcbaGaemOAaOMaeyypa0JaeGymaedabeaakiabg2da9maaqahabaGaemyyae2aaSbaaSqaaiabdMgaPjabigdaXaqabaaabaGaemyAaKMaeyypa0JaeGymaedabaGaemOCaihaniabggHiLdaaaa@3CFD@ A j = 2 = i = 1 r a i 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGbbqqdaWgaaWcbaGaemOAaOMaeyypa0JaeGOmaidabeaakiabg2da9maaqahabaGaemyyae2aaSbaaSqaaiabdMgaPjabikdaYaqabaaabaGaemyAaKMaeyypa0JaeGymaedabaGaemOCaihaniabggHiLdaaaa@3D01@ ... A j = c = i = 1 r a i c MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGbbqqdaWgaaWcbaGaemOAaOMaeyypa0Jaem4yamgabeaakiabg2da9maaqahabaGaemyyae2aaSbaaSqaaiabdMgaPjabdogaJbqabaaabaGaemyAaKMaeyypa0JaeGymaedabaGaemOCaihaniabggHiLdaaaa@3DBB@ m = i = 1 r j = 1 c a i j MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGTbqBcqGH9aqpdaaeWbqaamaaqahabaGaemyyae2aaSbaaSqaaiabdMgaPjabdQgaQbqabaaabaGaemOAaOMaeyypa0JaeGymaedabaGaem4yamganiabggHiLdaaleaacqWGPbqAcqGH9aqpcqaIXaqmaeaacqWGYbGCa0GaeyyeIuoaaaa@411D@