I NTUITIONISTIC FUZZY ESTIMATIONS OF BIOLOGICAL INTERACTIONS Hristo Aladjov, IBPBME-BAS
Human dominated Earth � More than 75% ice-free Attached algae and estuaries 37.332 1.892 Net energy return Soybean Earth surface is altered Swamps and marshes 37.332 Output energy 5.558 Tropical forest 37.332 Maize as a result of human Input energy Temperate forest 24.266 5.9326 Wheat activities Coniferous forest 14.933 4.3536 Rice Savanna 13.066 � Only 11% of terrestrial � Only 11% of terrestrial 8.0365 Agricultural land Agricultural land 11.718 11.718 Soybean-wheat Soybean-wheat net primary production Semi-arid woodland and shrubland 11.200 8.0934 Pigeonpea -wheat Temperate grassland 9.333 comes from wilderness. 9.287 Maize-veg. pea-wheat Lakes and streams 9.333 8.487 Continental shelf 6.533 � Biodiversity Rice-veg. pea-wheat-greengram Tundra and alpine 2.613 10.2789 Rice-mustard-greengram � Soil quality Open ocean 2.335 10.2862 Rice-wheat Desert scrub 1.307 � Forestation Extreme desert 0.058 0 5 10 15 20 25 30 35 40 Energy input/output MJ/sq.m/year 0 5 10 15 20 25 30 35 40 � Climate Net Primary Productivity [MJ/sq.m/year] Adapted from Kormondy 1976;
The Natural Solution � Agricultural land accounts for 20% of ice-free land use � Cooperate rather than compete with nature – less energy/work better productivity � Use ecosystem inspired techniques for agriculture (polyculture, forest gardening, companion planting, plant guilds, cover crops, intercropping, no tilt) � Increased biodiversity, stability, productivity, sustainability � The key factor to build and maintain such ecosystem inspired biomes is to understand the interactions between organisms
IF Estimation of Biological Interaction Interaction between two objects �, � ∈ ℵ at least one of which is a living organism could be described as the intuitionistic fuzzy number: � ��,�� = �����, ���, ����, ���� , � ��,�� = �����, ���, ����, ���� , where: ��, �� is the ordered tuple of the two interacting objects, ��, �� �: ℵ 2 → �0,1� is the positive effect of y over x, �: ℵ 2 → �0,1� is the negative effect of y over x, and 0 ≤ ����, ��� + ����, ��� ≤ 1 . Level of uncertainty �: ℵ 2 → �0,1� can be defined as ����, ��� = 1 − ����, ��� − ����, ��� .
Neutralism � Neutralism describes the relationship between two objects which interact but do not affect each other. Effect Effect Intuitionistic Fuzzy Extreme crisp case ����, ��� = 0, ����, ��� = 0, on x on y Definition ����, ��� = 0 ����, ��� = 0 �����, ��� = 0.5 �����, ��� = ����, ��� 0 0 � ����, ��� = ����, ��� ����, ��� = 0.5 � ����, ��� = 0.5 � ����, ��� = 0.5 �
Amensalism � Amensalism between two objects x, y involves y impeding the success of x while the x has no effect on y Effect Effect Effect Effect Intuitionistic Fuzzy Intuitionistic Fuzzy Extreme crisp case Extreme crisp case ����, ��� = 0, ����, ��� = 0, on x on y Definition ����, ��� = 0 ����, ��� = 0 �μ��x, y�� < ���x, y�� � μ��x, y�� = 0 - 0 � ϑ��x, y�� = 1 μ��y, x�� = ϑ��y, x�� � μ��y, x�� = 0.5 � � ϑ��y, x�� = 0.5
Commensalism � Commensalism between two objects x, y occurs when x benefits from y, while x has no effect on y Effect Effect Effect Effect Intuitionistic Fuzzy Intuitionistic Fuzzy Extreme crisp case Extreme crisp case ����, ��� = 0, ����, ��� = 0, on x on y Definition ����, ��� = 0 ����, ��� = 0 �μ��x, y�� > ���x, y�� � μ��x, y�� = 1 + 0 � ϑ��x, y�� = 0 μ��y, x�� = ϑ��y, x�� � μ��y, x�� = 0.5 � � ϑ��y, x�� = 0.5
Competition � Competition is an interaction between two objects that is mutually detrimental. Effect Effect Effect Effect Intuitionistic Fuzzy Intuitionistic Fuzzy Extreme crisp case Extreme crisp case ����, ��� = 0, ����, ��� = 0, on x on y Definition ����, ��� = 0 ����, ��� = 0 �μ��x, y�� < ���x, y�� �μ��x, y�� = 0 - - � μ��y, x�� < ���y, x�� ϑ��x, y�� = 1 � μ��y, x�� = 0 � ϑ��y, x�� = 1 �
Mutualism � Mutualism is an interaction between two objects, which is mutually beneficial. Effect Effect Effect Effect Intuitionistic Fuzzy Intuitionistic Fuzzy Extreme crisp case Extreme crisp case ����, ��� = 0, ����, ��� = 0, on x on y Definition ����, ��� = 0 ����, ��� = 0 �μ��x, y�� = 1 �μ��x, y�� > ���x, y�� + + � μ��y, x�� > ���y, x�� ϑ��x, y�� = 0 � μ��y, x�� = 1 � ϑ��y, x�� = 0 �
Predation / Parasitism � Predation or Parasitism between two x,y organisms is when x benefits at the expense of the y Effect Effect Intuitionistic Fuzzy Extreme crisp case ����, ��� = 0, ����, ��� = 0, on x on x on y on y Definition Definition ����, ��� = 0 ����, ��� = 0 �μ��x, y�� = 1 �μ��x, y�� > ���x, y�� + - � μ��y, x�� < ���y, x�� ϑ��x, y�� = 0 � μ��y, x�� = 0 � ϑ��y, x�� = 1 �
Interaction matrix � We can construct the following Indexed matrix ' 1 ' 2 ⋯ ' ) ' 1 � �1,1� � �2,1� ⋯ � �),1� ' 2 � �1,2� � �2,2� ⋯ � �),2� ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱ ⋱ ⋮ ⋮ � �1,)� � �2,)� � �),)� ' ) ⋯ where ' 1 ,' 2 , ⋯ ' ) are the interacting objects and � �,,-� are the intuitionistic fuzzy estimations of the interactions between object ' , and ' - , where ,, - = 1,2, … )
Initialization � Initially all interactions are unknown and � �,,-� = � �-,,� = 1 ' 1 ' 1 ' 2 ' 2 ⋯ ⋯ ' ) ' ) ' 1 �0,0� �0,0� ⋯ �0,0� ' 2 �0,0� �0,0� ⋯ �0,0� ⋮ ⋮ ⋮ ⋱ ⋮ �0,0� �0,0� �0,0� ' ) ⋯
Update Rule 0 Let / �,,-� be the k-th observation of the effect of object j on object i 0 = �� / 0 ��,, -��, � / 0 ��,, -��� , / �,,-� where ,, - ∈ ℵ & 0 ≤ � / 0 ���, ��� + � / 0 ���, ��� ≤ 1 ,, - ∈ ℵ & 0 ≤ � / 0 ���, ��� + � / 0 ���, ��� ≤ 1 then the k-th intuitionistic fuzzy interaction estimation for the objects I, j can be obtained as a weighted combination of the 0−1 and the observation / �,,-� 0 2 �,,-�
Update rule 0 = �� � 0 ��,, -��, � � 0 ��,, -��� 2 �,,-� � � 0 ��,, -�� = �0 − 1�� � 0−1 ��,, -��+� / 0 ��,, -�� 0 � � 0 ��,, -�� = �0 − 1�� � 0−1 ��,, -��+� / 0 ��,, -�� 0
Challenges Natural interactions are � Dynamic and � in short term depend on the state and needs of the organism (like life stage , deficiencies, stresses…) � and evolve in long term � and evolve in long term � Interconnected and occur between multitude of species. � Multidimensional and can be beneficial in certain aspects while detrimental in others � The hole is greater than the sum of it’s components � Lost traditional knowledge and scarcity of modern experimental data
Next steps � Using species taxonomy we can use the above algorithm to update the information for related species or apply it for different taxonomic rank like family, genus or class. � Scale and magnitude – if we have two relations that are positive which one will have bigger impact positive which one will have bigger impact � Extract information form multispecies interaction � apply the above algorithm for one versus the rest � use existing knowledge to guide the reduction of uncertainty: if current knowledge can explain the interaction use it otherwise search for examples that might provide the explanation � Make a simulation and verify it against experimental data
Thank you! and Escher…
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