ported to stack-project, iterated fitness.
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@ -21,6 +21,7 @@ description: Please see the README on GitHub at <https://github.com/Drez
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dependencies:
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- base >= 4.7 && < 5
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- hmatrix
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library:
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source-dirs: src
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247
src/Environment.hs
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247
src/Environment.hs
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@ -0,0 +1,247 @@
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{-# LANGUAGE RecordWildCards #-}
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module Environment where
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import Data.Functor ((<$>))
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import Control.Applicative ((<*>))
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import Control.Monad (forM_)
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import Data.List (permutations, subsequences)
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import Numeric.LinearAlgebra
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type Probability = Double
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type Quantity = Int
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type Activation = Double
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type Amount = Double
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-- | Nutrients are the basis for any reaction and are found in the environment of the plant.
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data Nutrient = Sulfur
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| Phosphor
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| Nitrate
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| Photosynthesis
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deriving (Show, Enum, Bounded, Eq)
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-- | Fixed, non-generic Components
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data Component = PP
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| FPP
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deriving (Show, Enum, Bounded, Eq)
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-- | Compounds are either direct nutrients, already processed components or GenericEnzymes
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data Compound = Substrate Nutrient
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| Produced Component
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| GenericEnzyme Int
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deriving (Show, Eq)
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instance Enum Compound where
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toEnum x
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| x <= maxS = Substrate . toEnum $ x
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| x - (maxS+1) <= maxP = Produced . toEnum $ x - (maxS + 1)
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| otherwise = GenericEnzyme $ x - (maxS + 1) - (maxP + 1)
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where
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maxS = fromEnum (maxBound :: Nutrient)
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maxP = fromEnum (maxBound :: Component)
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fromEnum (Substrate x) = fromEnum x
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fromEnum (Produced x) = fromEnum x + maxS + 1
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where
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maxS = fromEnum (maxBound :: Nutrient)
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fromEnum (GenericEnzyme x) = x + maxS + maxP + 2
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where
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maxS = fromEnum (maxBound :: Nutrient)
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maxP = fromEnum (maxBound :: Component)
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-- | Enzymes are the main reaction-driver behind synthesis of intricate compounds.
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--
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-- They are assumed to be reversible.
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data Enzyme = Enzyme
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{ enzymeName :: String
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-- ^ Name of the Enzyme.
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, substrateRequirements :: [(Compound,Amount)]
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-- ^ needed for reaction to take place
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, synthesis :: ((Compound,Amount),(Compound,Amount))
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-- ^ given x in amount -a, this will produce y in amount b
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, dominance :: Maybe Amount
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-- ^ in case of competition for nutrients this denotes the priority
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-- Nothing = max possible
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}
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deriving (Show, Eq)
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-- | conviniently make an Enzyme using 1 of the first compund to produce 1 of the second
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makeSimpleEnzyme :: Compound -> Compound -> Enzyme
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makeSimpleEnzyme a b = Enzyme (show a ++ " -> " ++ show b) [] ((a,-1),(b,1)) Nothing
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--Example "enzymes" could be:
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pps :: Enzyme -- uses Phosphor from Substrate to produce PP
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pps = Enzyme "PPS" [(Substrate Phosphor,1)] ((Substrate Phosphor,(-1)),(Produced PP,1)) Nothing
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fpps :: Enzyme -- PP -> FPP
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fpps = makeSimpleEnzyme (Produced PP) (Produced FPP)
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-- Evironment
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-- ----------
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-- | In the environment we have predators that impact the fitness of our plants and
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-- may be resistant to some compounds the plant produces. They can also differ in
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-- their intensity.
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data Predator = Predator { resistance :: [Compound]
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-- ^ list of components this predator is resistant to
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, fitnessImpact :: Amount
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-- ^ impact on the fitness of a plant
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-- (~ agressiveness of the herbivore)
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} deriving (Show, Eq)
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-- Exemplatory:
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greenfly :: Predator -- 20% of plants die to greenfly, but the fly is
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greenfly = Predator [Produced PP] 0.2 -- killed by any Component not being PP
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-- The environment itself is just the soil and the predators. Extensions would be possible.
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data Environment =
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Environment
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{ soil :: [(Nutrient, Amount)]
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-- ^ soil is a list of nutrients available to the plant.
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, predators :: [(Predator, Probability)]
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-- ^ Predators with the probability of appearance in this generation.
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} deriving (Show, Eq)
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-- Example:
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exampleEnvironment :: Environment
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exampleEnvironment =
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Environment
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{ soil = [ (Nitrate, 2)
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, (Phosphor, 3)
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, (Photosynthesis, 10)
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]
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, predators = [ (greenfly, 0.1) ]
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}
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-- Plants
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-- ------
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-- Plants consist of a Genome responsible for creation of the PSM and also an
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-- external state how many nutrients and compounds are currently inside the plant.
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type Genome = [(Enzyme, Quantity, Activation)]
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data Plant = Plant
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{ genome :: Genome
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-- ^ the genetic characteristic of the plant
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, absorbNutrients :: Environment -> [(Nutrient,Amount)]
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-- ^ the capability to absorb nutrients given an environment
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}
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instance Show Plant where
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show p = "Plant with Genome " ++ show (genome p)
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instance Eq Plant where
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a == b = genome a == genome b
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-- | The following example yields in the example-environment this population:
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--
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-- >>> printPopulation [pps, fpps] plants
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-- Population:
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-- PPS ______oöö+++______oöö+++____________oöö+++oöö+++
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-- FPPS ____________oöö+++oöö+++______oöö+++______oöö+++
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plants :: [Plant]
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plants = (\g -> Plant g defaultAbsorption) <$> genomes
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where
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enzymes = [pps, fpps]
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quantity = [1,2] :: [Quantity]
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activation = [0.7, 0.9, 1]
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genomes = do
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e <- permutations enzymes
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e' <- subsequences e
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q <- quantity
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a <- activation
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return $ (,,) <$> e' <*> [q] <*> [a]
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defaultAbsorption (Environment s _) = limit Phosphor 2
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. limit Nitrate 1
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. limit Sulfur 0
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<$> s
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-- custom absorbtion with helper-function:
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limit :: Nutrient -> Amount -> (Nutrient, Amount) -> (Nutrient, Amount)
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limit n a (n', a')
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| n == n' = (n, min a a') -- if we should limit, then we do ;)
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| otherwise = (n', a')
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-- Fitness
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-- -------
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-- The fitness-measure is central for the generation of offspring and the
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-- simulation. It evaluates the probability for passing on genes given a plant in
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-- an environment.
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type Fitness = Double
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fitness :: Environment -> Plant -> Fitness
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fitness e p = survivalRate
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where
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nutrients = absorbNutrients p e
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products = produceCompounds p nutrients
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survivalRate = deterPredators (predators e) products
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produceCompounds :: Plant -> [(Nutrient, Amount)] -> Vector Amount
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produceCompounds (Plant genes _) substrate = final
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where
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initialAmount = assoc 10 0 ((\(n,a) -> (fromEnum $ Substrate n,a)) <$> substrate)
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enzymes = (\(e,q,a) -> (synthesis e,(fromIntegral q)*a)) <$> genes -- [(((Component,Amount),(Component,Amount)),q*a)], Amount got * by quantity & activation
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positions = concat $ (\(((i,ia),(o,oa)),f) -> [((fromEnum i,fromEnum i),ia),((fromEnum o,fromEnum i),oa)]) <$> enzymes -- [((row,column),amount)]
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mat = accum (konst 0 (10::Int,10::Int)) (+) positions --accumulate all entries into one matrix.
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(l,v) = eig ((*0.01) `cmap` mat)
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final = (realPart `cmap` (v <> ((^100) `cmap` diag l) <> (tr v))) #> initialAmount
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deterPredators :: [(Predator, Probability)] -> Vector Amount -> Probability
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deterPredators ps cs' = sum $ do
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(c,a) <- cs -- for every compound
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(p,prob) <- ps -- and every predator
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return (if c `elem` (resistance p) -- if the plant cannot deter the predator
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then prob * fitnessImpact p -- impact it weighted by probability
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else 0)
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where
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cs = (zip (toEnum <$> [1..]) (toList cs')) :: [(Compound,Amount)]
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-- Mating & Creation of diversity
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-- ------------------------------
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-- Running the simulation
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-- ----------------------
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main = do
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putStrLn "Environment:"
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print exampleEnvironment
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putStrLn "Example population:"
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printPopulation [pps, fpps] plants
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-- Utility Functions
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-- -----------------
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getAmountOf :: Compound -> [(Compound, Amount)] -> Amount
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getAmountOf c = sum . fmap snd . filter ((== c) . fst)
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printPopulation :: [Enzyme] -> [Plant] -> IO ()
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printPopulation es ps = do
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let padded i str = take i $ str ++ repeat ' '
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putStrLn "Population:"
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forM_ es $ \e -> do
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putStr $ padded 8 (show e)
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forM_ ps $ \(Plant g _) -> do
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let curE = sum $ map (\(_,q,a) -> (fromIntegral q)*a)
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. filter (\(e',_,_) -> e == e')
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$ g
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plot x
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| x > 2 = "O"
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| x > 1 = "+"
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| x > 0.7 = "ö"
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| x > 0.5 = "o"
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| x > 0 = "."
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| otherwise = "_"
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putStr (plot curE)
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putStrLn ""
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