diff --git a/monad-bayes.cabal b/monad-bayes.cabal
index f4c26287..ab68cf98 100644
--- a/monad-bayes.cabal
+++ b/monad-bayes.cabal
@@ -101,6 +101,7 @@ library
     Control.Monad.Bayes.Inference.TUI
     Control.Monad.Bayes.Integrator
     Control.Monad.Bayes.Population
+    Control.Monad.Bayes.Population.Applicative
     Control.Monad.Bayes.Sampler.Lazy
     Control.Monad.Bayes.Sampler.Strict
     Control.Monad.Bayes.Sequential.Coroutine
diff --git a/src/Control/Applicative/List.hs b/src/Control/Applicative/List.hs
index 557c218a..a6a0a99a 100644
--- a/src/Control/Applicative/List.hs
+++ b/src/Control/Applicative/List.hs
@@ -4,11 +4,7 @@ module Control.Applicative.List where
 
 -- base
 import Control.Applicative
--- transformers
-import Control.Monad.Trans.Writer.Strict
 import Data.Functor.Compose
--- log-domain
-import Numeric.Log (Log)
 
 -- * Applicative ListT
 
@@ -17,22 +13,11 @@ import Numeric.Log (Log)
 newtype ListT m a = ListT {getListT :: Compose m [] a}
   deriving newtype (Functor, Applicative, Alternative)
 
+listT :: m [a] -> ListT m a
+listT = ListT . Compose
+
 lift :: (Functor m) => m a -> ListT m a
 lift = ListT . Compose . fmap pure
 
 runListT :: ListT m a -> m [a]
 runListT = getCompose . getListT
-
--- * Applicative Population transformer
-
--- WriterT has to be used instead of WeightedT,
--- since WeightedT uses StateT under the hood,
--- which requires a Monad (ListT m) constraint.
-newtype PopulationT m a = PopulationT {getPopulationT :: WriterT (Log Double) (ListT m) a}
-  deriving newtype (Functor, Applicative, Alternative)
-
-runPopulationT :: PopulationT m a -> m [(a, Log Double)]
-runPopulationT = runListT . runWriterT . getPopulationT
-
-fromWeightedList :: m [(a, Log Double)] -> PopulationT m a
-fromWeightedList = PopulationT . WriterT . ListT . Compose
diff --git a/src/Control/Monad/Bayes/Population.hs b/src/Control/Monad/Bayes/Population.hs
index 9b97dc31..aa177de1 100644
--- a/src/Control/Monad/Bayes/Population.hs
+++ b/src/Control/Monad/Bayes/Population.hs
@@ -40,7 +40,6 @@ module Control.Monad.Bayes.Population
 where
 
 import Control.Applicative (Alternative)
-import Control.Applicative.List qualified as ApplicativeListT
 import Control.Arrow (second)
 import Control.Monad (MonadPlus, replicateM)
 import Control.Monad.Bayes.Class
@@ -49,6 +48,7 @@ import Control.Monad.Bayes.Class
     MonadMeasure,
     factor,
   )
+import Control.Monad.Bayes.Population.Applicative qualified as Applicative
 import Control.Monad.Bayes.Weighted
   ( WeightedT,
     applyWeight,
@@ -70,6 +70,11 @@ import Numeric.Log qualified as Log
 import Prelude hiding (all, sum)
 
 -- | A collection of weighted samples, or particles.
+--
+-- This monad transformer is internally represented as a free monad,
+-- which means that each layer of its computation contains a collection of weighted samples.
+-- These can be flattened with 'flatten',
+-- but the result is not a monad anymore.
 newtype PopulationT m a = PopulationT {getPopulationT :: WeightedT (FreeT [] m) a}
   deriving newtype (Functor, Applicative, Alternative, Monad, MonadIO, MonadPlus, MonadDistribution, MonadFactor, MonadMeasure)
 
@@ -278,12 +283,12 @@ hoist ::
   PopulationT n a
 hoist f = PopulationT . Weighted.hoist (hoistFreeT f) . getPopulationT
 
--- | Flatten all layers of the free structure
-flatten :: (Monad m) => PopulationT m a -> ApplicativeListT.PopulationT m a
-flatten = ApplicativeListT.fromWeightedList . runPopulationT
+-- | Flatten all layers of the free structure.
+flatten :: (Monad m) => PopulationT m a -> Applicative.PopulationT m a
+flatten = Applicative.fromWeightedList . runPopulationT
 
 -- | Create a population from a single layer of branching computations.
 --
 -- Similar to 'fromWeightedListT'.
-single :: (Monad m) => ApplicativeListT.PopulationT m a -> PopulationT m a
-single = fromWeightedList . ApplicativeListT.runPopulationT
+single :: (Monad m) => Applicative.PopulationT m a -> PopulationT m a
+single = fromWeightedList . Applicative.runPopulationT
diff --git a/src/Control/Monad/Bayes/Population/Applicative.hs b/src/Control/Monad/Bayes/Population/Applicative.hs
new file mode 100644
index 00000000..7f13d484
--- /dev/null
+++ b/src/Control/Monad/Bayes/Population/Applicative.hs
@@ -0,0 +1,29 @@
+-- | 'PopulationT' turns a single sample into a collection of weighted samples.
+--
+-- This module contains an _'Applicative'_ transformer corresponding to the Population monad transformer from the article.
+-- It is based on the old-fashioned 'ListT', which is not a valid monad transformer, but a valid applicative transformer.
+-- The corresponding monad transformer is contained in 'Control.Monad.Bayes.Population'.
+-- One can convert from the monad transformer to the applicative transformer by 'flatten'ing.
+module Control.Monad.Bayes.Population.Applicative where
+
+import Control.Applicative
+import Control.Applicative.List
+import Control.Monad.Trans.Writer.Strict
+import Data.Functor.Compose
+import Numeric.Log (Log)
+
+-- * Applicative Population transformer
+
+-- WriterT has to be used instead of WeightedT,
+-- since WeightedT uses StateT under the hood,
+-- which requires a Monad (ListT m) constraint.
+
+-- | A collection of weighted samples, or particles.
+newtype PopulationT m a = PopulationT {getPopulationT :: WriterT (Log Double) (ListT m) a}
+  deriving newtype (Functor, Applicative, Alternative)
+
+runPopulationT :: PopulationT m a -> m [(a, Log Double)]
+runPopulationT = runListT . runWriterT . getPopulationT
+
+fromWeightedList :: m [(a, Log Double)] -> PopulationT m a
+fromWeightedList = PopulationT . WriterT . listT