diff --git a/docs/notebooks b/docs/notebooks
index bd10c2c1a..6777840bc 160000
--- a/docs/notebooks
+++ b/docs/notebooks
@@ -1 +1 @@
-Subproject commit bd10c2c1a7f7ddf5674403997bc2704533b85367
+Subproject commit 6777840bcc146924d208c0b9b02677da63620805
diff --git a/pyproject.toml b/pyproject.toml
index 540f751da..4d094a94b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -45,7 +45,7 @@ maintainers = [
 
 
 dependencies = [
-    "anndata>=0.8",
+    "anndata>=0.9",
     "docrep>=0.3.0",
     "joblib>=0.13.1",
     "matplotlib>=3.5.0,<3.7.2",
@@ -74,6 +74,7 @@ test = [
     "pytest-mock>=3.5.0",
     "pytest-cov>=4",
     "coverage[toml]>=7",
+    "zarr",
     "igraph",
     "leidenalg",
     "Pillow",
diff --git a/src/cellrank/_utils/_lineage.py b/src/cellrank/_utils/_lineage.py
index 104467339..1531a9b4c 100644
--- a/src/cellrank/_utils/_lineage.py
+++ b/src/cellrank/_utils/_lineage.py
@@ -1195,17 +1195,15 @@ def _mutual_info(reference, query):
     return weights
 
 
-_SPEC = IOSpec("array", "0.2.0")
-
-
-@_REGISTRY.register_write(H5Group, Lineage, _SPEC)
-@_REGISTRY.register_write(H5Group, LineageView, _SPEC)
-@_REGISTRY.register_write(ZarrGroup, Lineage, _SPEC)
-@_REGISTRY.register_write(ZarrGroup, LineageView, _SPEC)
+@_REGISTRY.register_write(H5Group, Lineage, IOSpec("array", "0.2.0"))
+@_REGISTRY.register_write(H5Group, LineageView, IOSpec("array", "0.2.0"))
+@_REGISTRY.register_write(ZarrGroup, Lineage, IOSpec("array", "0.2.0"))
+@_REGISTRY.register_write(ZarrGroup, LineageView, IOSpec("array", "0.2.0"))
 def _write_lineage(
     f: Any,
     k: str,
     elem: Union[Lineage, LineageView],
+    _writer: Any,
     dataset_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
 ) -> None:
-    write_basic(f, k, elem=elem.X, dataset_kwargs=dataset_kwargs)
+    write_basic(f, k, elem=elem.X, _writer=_writer, dataset_kwargs=dataset_kwargs)
diff --git a/tests/test_lineage.py b/tests/test_lineage.py
index 6fca7343e..039bcf513 100644
--- a/tests/test_lineage.py
+++ b/tests/test_lineage.py
@@ -11,6 +11,8 @@
 
 from matplotlib import colors
 
+from anndata import AnnData, read_h5ad, read_zarr
+
 from cellrank._utils import Lineage
 from cellrank._utils._colors import _compute_mean_color, _create_categorical_colors
 from cellrank._utils._lineage import _HT_CELLS, LineageView, PrimingDegree
@@ -973,7 +975,7 @@ def test_double_view_owner(self, lineage: Lineage):
         assert x.owner is lineage
 
 
-class TestPickling:
+class TestIO:
     def test_pickle_normal(self, lineage: Lineage):
         handle = io.BytesIO()
 
@@ -1015,6 +1017,24 @@ def test_pickle_transposed(self, lineage: Lineage):
         assert res._n_lineages == lineage._n_lineages
         assert res._is_transposed == lineage._is_transposed
 
+    def test_anndata_write(self, lineage: Lineage, tmp_path):
+        rng = np.random.default_rng(0)
+        adata = AnnData(rng.normal(size=(lineage.shape[0], 13)))
+        adata.obsm["lin"] = lineage
+
+        assert isinstance(adata.obsm["lin"], Lineage)
+
+        adata.write_h5ad(tmp_path / "tmp.h5ad")
+        adata.write_zarr(tmp_path / "tmp.zarr")
+
+        adata_h5ad = read_h5ad(tmp_path / "tmp.h5ad")
+        adata_zarr = read_zarr(tmp_path / "tmp.zarr")
+
+        assert isinstance(adata_h5ad.obsm["lin"], np.ndarray)
+        assert isinstance(adata_zarr.obsm["lin"], np.ndarray)
+        np.testing.assert_array_equal(adata_h5ad.obsm["lin"], adata.obsm["lin"].X)
+        np.testing.assert_array_equal(adata_zarr.obsm["lin"], adata.obsm["lin"].X)
+
 
 class TestPriming:
     def test_invalid_method(self, lineage: Lineage):