diff --git a/src/p2lab/genetic/operations.py b/src/p2lab/genetic/operations.py
index a117fc7..ebf814a 100644
--- a/src/p2lab/genetic/operations.py
+++ b/src/p2lab/genetic/operations.py
@@ -146,7 +146,7 @@ def locus_swap(
     team2: list[str],
     num_pokemon: int,
     allow_all: bool,
-    locus: int = None,
+    locus: int | None = None,
 ) -> tuple(list[str], list[str]):
     """
     A method of performing the crossover. Pick a 'locus' point: this
@@ -194,7 +194,7 @@ def slot_swap(
     team2: list[str],
     num_pokemon: int,
     allow_all: bool,
-    k: int = None,
+    k: int | None = None,
 ) -> tuple(list[str], list[str]):
     """
     A method of performing the crossover. This method randomly
@@ -294,7 +294,7 @@ def mutate(
     mutate_prob: float | np.ndarray,
     pokemon_population: list[str],
     allow_all: bool,
-    k: int = None,
+    k: int | None = None,
 ):
     """
     A mutation operation. At random, k members of a team are swapped with k
@@ -362,7 +362,7 @@ def fitness_mutate(
     fitness: np.array,
     pokemon_population: list[str],
     allow_all: bool,
-    k: int = None,
+    k: int | None = None,
 ):
     """
     A mutation operation. Does the same as regular mutation, except that