SLIDE 1 INTUITIONISTIC FUZZY ESTIMATIONS OF BIOLOGICAL INTERACTIONS
Hristo Aladjov, IBPBME-BAS
SLIDE 2 More than 75% ice-free Earth surface is altered as a result of human activities Only 11% of terrestrial
11.718 13.066 14.933 24.266 37.332 37.332 37.332 Agricultural land Savanna Coniferous forest Temperate forest Tropical forest Swamps and marshes Attached algae and estuaries
8.0365 4.3536 5.9326 5.558 1.892
Soybean-wheat Rice Wheat Maize Soybean Net energy return Output energy Input energy
Human dominated Earth
Only 11% of terrestrial net primary production comes from wilderness. Biodiversity Soil quality Forestation Climate
0.058 1.307 2.335 2.613 6.533 9.333 9.333 11.200 11.718 5 10 15 20 25 30 35 40 Extreme desert Desert scrub Open ocean Tundra and alpine Continental shelf Lakes and streams Temperate grassland Semi-arid woodland and shrubland Agricultural land
Net Primary Productivity [MJ/sq.m/year]
10.2862 10.2789 8.487 9.287 8.0934
5 10 15 20 25 30 35 40 Rice-wheat Rice-mustard-greengram Rice-veg. pea-wheat-greengram Maize-veg. pea-wheat Pigeonpea -wheat Soybean-wheat
Energy input/output MJ/sq.m/year Adapted from Kormondy 1976;
SLIDE 3
Agricultural land accounts for 20% of ice-free land use Cooperate rather than compete with nature – less energy/work better productivity
The Natural Solution
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
SLIDE 4 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, : ℵ2 → 0,1 is the positive effect of y over x, : ℵ2 → 0,1 is the negative effect of y over x, and 0 ≤ , + , ≤
- 1. Level of uncertainty : ℵ2 → 0,1 can be defined as
, = 1 − , − , .
SLIDE 5 Neutralism describes the relationship between two objects which interact but do not affect each other.
Neutralism
Effect Effect Intuitionistic Fuzzy Extreme crisp case
, = 0, , = 0
Definition
, = 0, , = 0
, = , , = ,
, = 0.5 , = 0.5 , = 0.5
SLIDE 6 Amensalism between two objects x, y involves y impeding the success of x while the x has no effect on y
Amensalism
Effect Effect Intuitionistic Fuzzy Extreme crisp case
, = 0, , = 0
Effect
Effect
Intuitionistic Fuzzy Definition Extreme crisp case
, = 0, , = 0
μy, x = ϑy, x
ϑx, y = 1 μy, x = 0.5 ϑy, x = 0.5
SLIDE 7 Commensalism between two objects x, y occurs when x benefits from y, while x has no effect on y
Commensalism
Effect Effect Intuitionistic Fuzzy Extreme crisp case
, = 0, , = 0
Effect
Effect
Intuitionistic Fuzzy Definition Extreme crisp case
, = 0, , = 0
+ μx, y > x, y μy, x = ϑy, x
ϑx, y = 0 μy, x = 0.5 ϑy, x = 0.5
SLIDE 8 Competition is an interaction between two objects that is mutually detrimental.
Competition
Effect Effect Intuitionistic Fuzzy Extreme crisp case
, = 0, , = 0
Effect
Effect
Intuitionistic Fuzzy Definition Extreme crisp case
, = 0, , = 0
μy, x < y, x
ϑx, y = 1 μy, x = 0 ϑy, x = 1
SLIDE 9 Mutualism is an interaction between two objects, which is mutually beneficial.
Mutualism
Effect Effect Intuitionistic Fuzzy Extreme crisp case
, = 0, , = 0
Effect
Effect
Intuitionistic Fuzzy Definition Extreme crisp case
, = 0, , = 0
+ + μx, y > x, y μy, x > y, x
ϑx, y = 0 μy, x = 1 ϑy, x = 0
SLIDE 10 Predation or Parasitism between two x,y organisms is when x benefits at the expense of the y
Predation / Parasitism
Effect
Effect
Intuitionistic Fuzzy Definition Extreme crisp case
, = 0, , = 0
Definition
, = 0, , = 0
+
μy, x < y, x
ϑx, y = 0 μy, x = 0 ϑy, x = 1
SLIDE 11 We can construct the following Indexed matrix
Interaction 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
- bject ', and '
- , where ,, - = 1,2, … )
SLIDE 12
Initially all interactions are unknown and
Initialization
,,- = -,, = 1 '1 '2 ⋯ ') '1 '2 ⋯ ') '1 0,0 0,0 ⋯ 0,0 '2 0,0 0,0 ⋯ 0,0 ⋮ ⋮ ⋮ ⋱ ⋮ ') 0,0 0,0 ⋯ 0,0
SLIDE 13 Update Rule
Let /,,- be the k-th observation of the effect of object j on object i /,,- = /0,, -, /0,, -, where ,, - ∈ ℵ & 0 ≤ /0, + /0, ≤ 1 ,, - ∈ ℵ & 0 ≤ /0, + /0, ≤ 1 then the k-th intuitionistic fuzzy interaction estimation for the
- bjects I, j can be obtained as a weighted combination of the
2,,-
0−1 and the observation /,,-
SLIDE 14
Update rule
2,,- = 0,, -, 0,, - 0,, - = 0 − 10−1,, -+/0,, - 0,, - = 0 − 10−1,, -+/0,, -
SLIDE 15 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
Challenges
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
SLIDE 16 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
Next steps
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
SLIDE 17
Thank you!
and Escher…
