diff --git a/src/pycea/tl/ancestral_linkage.py b/src/pycea/tl/ancestral_linkage.py
index b285a4a..8a173e3 100644
--- a/src/pycea/tl/ancestral_linkage.py
+++ b/src/pycea/tl/ancestral_linkage.py
@@ -477,6 +477,7 @@ def ancestral_linkage(
     metric: _TreeMetric = "path",
     symmetrize: Literal["mean", "max", "min", None] = None,
     test: Literal["permutation", None] = None,
+    normalize: bool = False,
     alternative: Literal["two-sided", None] = None,
     permutation_mode: Literal["all", "non_target"] = "all",
     n_permutations: int = 100,
@@ -499,6 +500,7 @@ def ancestral_linkage(
     metric: _TreeMetric = "path",
     symmetrize: Literal["mean", "max", "min", None] = None,
     test: Literal["permutation", None] = None,
+    normalize: bool = False,
     alternative: Literal["two-sided", None] = None,
     permutation_mode: Literal["all", "non_target"] = "all",
     n_permutations: int = 100,
@@ -519,6 +521,7 @@ def ancestral_linkage(
     metric: _TreeMetric = "path",
     symmetrize: Literal["mean", "max", "min", None] = None,
     test: Literal["permutation", None] = None,
+    normalize: bool = False,
     alternative: Literal["two-sided", None] = None,
     permutation_mode: Literal["all", "non_target"] = "all",
     n_permutations: int = 100,
@@ -577,8 +580,12 @@ def ancestral_linkage(
 
         - ``'permutation'``: randomly shuffle cell-category labels ``n_permutations``
           times and recompute linkage each time to build a null distribution.
-          Z-scores and p-values are added to the stats table.  The stored linkage
-          matrix is replaced by z-scores when this test is run.
+          Z-scores and p-values are added to the stats table.
+    normalize
+        If ``True`` and ``test='permutation'``, subtract the permuted mean from the
+        observed values: pairwise linkage matrix becomes ``observed - permuted_mean``;
+        single-target ``tdata.obs['{target}_linkage']`` becomes
+        ``cell_score - category_permuted_mean``.  Ignored when ``test=None``.
     alternative
         The alternative hypothesis for the permutation test (ignored when
         ``test=None``):
@@ -636,10 +643,13 @@ def ancestral_linkage(
     Sets the following fields:
 
     * ``tdata.obs['{target}_linkage']`` : :class:`Series <pandas.Series>` (dtype ``float``) – single-target mode only.
-        Per-cell distance to the nearest cell of the target category.
+        Per-cell distance to the nearest cell of the target category.  When
+        ``normalize=True`` and ``test='permutation'``, replaced by
+        ``cell_score - category_permuted_mean``.
     * ``tdata.uns['{key_added}_linkage']`` : :class:`DataFrame <pandas.DataFrame>` – pairwise mode only.
         Category × category linkage matrix (source rows, target columns).
-        Contains z-scores instead of raw distances when ``test='permutation'``.
+        When ``normalize=True`` and ``test='permutation'``, contains
+        ``observed - permuted_mean`` instead of raw distances.
     * ``tdata.uns['{key_added}_linkage_params']`` : ``dict`` – pairwise mode only.
         Parameters used to compute the linkage matrix.
     * ``tdata.uns['{key_added}_linkage_stats']`` : :class:`DataFrame <pandas.DataFrame>` – pairwise mode only.
@@ -710,32 +720,28 @@ def ancestral_linkage(
 
         # Always use "closest": min path or max lca
         single_agg: str = "max" if metric == "lca" else "min"
-        all_scores = _compute_scores(tdata, trees, leaf_to_cat, [target], single_agg, metric, depth_key)
+        sign = 1.0 if metric == "lca" else -1.0
 
-        # Per-leaf scores
-        score_map = {leaf: scores.get(target, np.nan) for leaf, scores in all_scores.items()}
-        tdata.obs[f"{target}_linkage"] = tdata.obs.index.map(pd.Series(score_map, dtype=float))
-
-        if test == "permutation":
-            # Observed: mean per source category
-            obs_cat_scores: dict = {}
+        def _run_single_perm(single_tree, tree_lc, tree_sm, tree_cl, extra_row_fields=None):
+            """Run the permutation test for one tree (or globally) and return (rows, cat_null_mean)."""
+            tree_obs_cat: dict = {}
             for cat in all_cats:
-                vals = [score_map[l] for l in cat_to_leaves[cat] if l in score_map and not np.isnan(score_map[l])]
-                obs_cat_scores[cat] = float(np.mean(vals)) if vals else np.nan
+                vals = [tree_sm[l] for l in tree_cl[cat] if l in tree_sm and not np.isnan(tree_sm[l])]
+                tree_obs_cat[cat] = float(np.mean(vals)) if vals else np.nan
 
-            all_leaf_list = list(leaf_to_cat.keys())
+            tree_leaf_list = list(tree_lc.keys())
             perm_seeds = np.random.randint(0, 2**31, size=n_permutations)
 
             if permutation_mode == "non_target":
-                t_leaves = cat_to_leaves[target]
-                t_set = set(t_leaves)
-                nt_leaves = [l for l in all_leaf_list if l not in t_set]
+                t_lv = tree_cl[target]
+                t_set = set(t_lv)
+                nt_lv = [l for l in tree_leaf_list if l not in t_set]
                 _PERM_SINGLE_NON_TARGET_DATA.clear()
                 _PERM_SINGLE_NON_TARGET_DATA.update({
-                    "fixed_scores": score_map,  # precomputed above, target leaves fixed
-                    "target_leaves": list(t_leaves),
-                    "nt_leaves": nt_leaves,
-                    "nt_cats": [leaf_to_cat[l] for l in nt_leaves],
+                    "fixed_scores": tree_sm,
+                    "target_leaves": list(t_lv),
+                    "nt_leaves": nt_lv,
+                    "nt_cats": [tree_lc[l] for l in nt_lv],
                     "target": target,
                     "all_cats": all_cats,
                 })
@@ -744,9 +750,9 @@ def ancestral_linkage(
                 _PERM_SINGLE_DATA.clear()
                 _PERM_SINGLE_DATA.update({
                     "tdata": tdata,
-                    "trees": trees,
-                    "all_leaves": all_leaf_list,
-                    "all_cat_vals": [leaf_to_cat[l] for l in all_leaf_list],
+                    "trees": single_tree,
+                    "all_leaves": tree_leaf_list,
+                    "all_cat_vals": [tree_lc[l] for l in tree_leaf_list],
                     "target": target,
                     "single_agg": single_agg,
                     "metric": metric,
@@ -755,19 +761,20 @@ def ancestral_linkage(
                 })
                 null_results = _run_parallel(_perm_single_target_worker, perm_seeds, n_threads)
 
-            null_cat_scores: dict = defaultdict(list)
+            null_cat: dict = defaultdict(list)
             for perm_result in null_results:
                 for cat in all_cats:
-                    null_cat_scores[cat].append(perm_result[cat])
+                    null_cat[cat].append(perm_result[cat])
 
-            rows = []
+            rows: list = []
+            cat_null_mean: dict = {}
             for cat in all_cats:
-                obs_val = obs_cat_scores[cat]
-                null_vals = np.array([v for v in null_cat_scores[cat] if not np.isnan(v)], dtype=float)
+                obs_val = tree_obs_cat[cat]
+                null_vals = np.array([v for v in null_cat[cat] if not np.isnan(v)], dtype=float)
                 if len(null_vals) > 0:
                     perm_val = float(np.mean(null_vals))
-                    sign = 1.0 if metric == "lca" else -1.0
-                    z = sign * (obs_val - perm_val) / (float(np.std(null_vals)) + 1e-10)
+                    null_std = float(np.std(null_vals))
+                    z = sign * (obs_val - perm_val) / (null_std + 1e-10)
                     if alternative == "two-sided":
                         p = float(np.mean(np.abs(null_vals - perm_val) >= abs(obs_val - perm_val)))
                     elif metric == "lca":
@@ -775,32 +782,79 @@ def ancestral_linkage(
                     else:
                         p = float(np.mean(null_vals <= obs_val))
                 else:
-                    perm_val, z, p = np.nan, np.nan, np.nan
-                rows.append(
-                    {
-                        "source": cat,
-                        "target": target,
-                        "value": obs_val,
-                        "permuted_value": perm_val,
-                        "z_score": z,
-                        "p_value": p,
-                    }
-                )
+                    perm_val, null_std, z, p = np.nan, 0.0, np.nan, np.nan
+                cat_null_mean[cat] = perm_val
+                row: dict = {"source": cat, "target": target, "value": obs_val,
+                             "permuted_value": perm_val, "z_score": z, "p_value": p}
+                if extra_row_fields:
+                    row.update(extra_row_fields)
+                rows.append(row)
+
+            return rows, cat_null_mean
+
+        if by_tree and test == "permutation":
+            # Per-tree: compute scores, run permutation, normalize per cell independently
+            merged_score_map: dict = {}
+            merged_norm_map: dict = {}
+            all_rows: list = []
+
+            for tree_key, t in trees.items():
+                t_nodes = set(t.nodes())
+                single_tree = {tree_key: t}
+                tree_lc: dict = {l: c for l, c in leaf_to_cat.items() if l in t_nodes}
+                tree_cl: dict = defaultdict(list)
+                for l, c in tree_lc.items():
+                    tree_cl[c].append(l)
 
-            test_df = pd.DataFrame(rows)
+                tree_all_scores = _compute_scores(
+                    tdata, single_tree, tree_lc, [target], single_agg, metric, depth_key
+                )
+                tree_sm: dict = {l: s.get(target, np.nan) for l, s in tree_all_scores.items()}
+                merged_score_map.update(tree_sm)
+
+                rows, cat_null_mean = _run_single_perm(single_tree, tree_lc, tree_sm, tree_cl,
+                                                       extra_row_fields={"tree": tree_key})
+                all_rows.extend(rows)
+                if normalize:
+                    for leaf, score in tree_sm.items():
+                        cat = tree_lc.get(leaf)
+                        perm_val = cat_null_mean.get(cat, np.nan) if cat is not None else np.nan
+                        merged_norm_map[leaf] = (score - perm_val) if not np.isnan(score) else np.nan
+
+            tdata.obs[f"{target}_linkage"] = tdata.obs.index.map(pd.Series(merged_score_map, dtype=float))
+            if normalize:
+                tdata.obs[f"{target}_linkage"] = tdata.obs.index.map(pd.Series(merged_norm_map, dtype=float))
+            test_df = pd.DataFrame(all_rows)
             tdata.uns[f"{key_added}_test"] = test_df
             if copy:
                 return test_df
 
-        if copy:
-            result_series = pd.Series(
-                {
-                    cat: float(np.nanmean([score_map.get(l, np.nan) for l in cat_to_leaves[cat]]))
-                    for cat in all_cats
-                },
-                name=f"{target}_linkage",
-            )
-            return result_series.to_frame()
+        else:
+            # Global (non-by_tree) path
+            all_scores = _compute_scores(tdata, trees, leaf_to_cat, [target], single_agg, metric, depth_key)
+            score_map = {leaf: scores.get(target, np.nan) for leaf, scores in all_scores.items()}
+            tdata.obs[f"{target}_linkage"] = tdata.obs.index.map(pd.Series(score_map, dtype=float))
+
+            if test == "permutation":
+                rows, cat_null_mean = _run_single_perm(trees, leaf_to_cat, score_map, cat_to_leaves)
+                if normalize:
+                    norm_map = {
+                        leaf: (score - cat_null_mean.get(leaf_to_cat.get(leaf), np.nan))
+                        if not np.isnan(score) else np.nan
+                        for leaf, score in score_map.items()
+                    }
+                    tdata.obs[f"{target}_linkage"] = tdata.obs.index.map(pd.Series(norm_map, dtype=float))
+                test_df = pd.DataFrame(rows)
+                tdata.uns[f"{key_added}_test"] = test_df
+                if copy:
+                    return test_df
+
+            if copy:
+                result_series = pd.Series(
+                    {cat: float(np.nanmean([score_map.get(l, np.nan) for l in cat_to_leaves[cat]])) for cat in all_cats},
+                    name=f"{target}_linkage",
+                )
+                return result_series.to_frame()
 
     # ── pairwise mode ─────────────────────────────────────────────────────────
     else:
@@ -886,8 +940,8 @@ def ancestral_linkage(
                         row["p_value"] = global_p_df.loc[src_cat, tgt_cat]
                     stats_rows.append(row)
 
-        # uns[linkage] = observed - permuted_mean (symmetrized) if test ran, else raw linkage (symmetrized)
-        output_df: pd.DataFrame = (linkage_df - global_null_mean_df) if test == "permutation" else linkage_df
+        # uns[linkage] = observed - permuted_mean if normalize, else raw linkage (both symmetrized if requested)
+        output_df: pd.DataFrame = (linkage_df - global_null_mean_df) if (test == "permutation" and normalize) else linkage_df
         if symmetrize is not None:
             output_df = _symmetrize_matrix(output_df, symmetrize)
 
@@ -897,6 +951,7 @@ def ancestral_linkage(
             "metric": metric,
             "symmetrize": symmetrize,
             "test": test,
+            "normalize": normalize,
             "by_tree": by_tree,
             "depth_key": depth_key,
         }
diff --git a/tests/test_ancestral_linkage.py b/tests/test_ancestral_linkage.py
index 172082f..382d359 100644
--- a/tests/test_ancestral_linkage.py
+++ b/tests/test_ancestral_linkage.py
@@ -669,3 +669,106 @@ def test_symmetrize_invalid_raises():
 
     with pytest.raises(ValueError, match="symmetrize"):
         tl.ancestral_linkage(tdata, groupby="ct", symmetrize="meen")
+
+
+# ── normalize parameter tests ──────────────────────────────────────────────────
+
+
+def test_pairwise_normalize_stores_value_minus_permuted(balanced_tdata):
+    """normalize=True stores observed - permuted_mean in the pairwise linkage matrix."""
+    tdata = balanced_tdata
+    tl.ancestral_linkage(
+        tdata, groupby="celltype", test="permutation", normalize=True,
+        n_permutations=20, random_state=0,
+    )
+    linkage = tdata.uns["celltype_linkage"]
+    stats = tdata.uns["celltype_linkage_stats"]
+    for _, row in stats.iterrows():
+        expected = row["value"] - row["permuted_value"]
+        assert linkage.loc[row["source"], row["target"]] == pytest.approx(expected, abs=1e-9)
+
+
+def test_pairwise_no_normalize_stores_raw_linkage(balanced_tdata):
+    """normalize=False (default) stores raw linkage even when test='permutation'."""
+    tdata = balanced_tdata
+    tl.ancestral_linkage(
+        tdata, groupby="celltype", test="permutation", normalize=False,
+        n_permutations=20, random_state=0,
+    )
+    linkage = tdata.uns["celltype_linkage"]
+    stats = tdata.uns["celltype_linkage_stats"]
+    for _, row in stats.iterrows():
+        assert linkage.loc[row["source"], row["target"]] == pytest.approx(row["value"], abs=1e-9)
+
+
+def test_single_target_normalize_overwrites_linkage(balanced_tdata):
+    """normalize=True replaces _linkage in obs with score - category_permuted_mean."""
+    tdata = balanced_tdata
+    # Raw linkage without normalize
+    tl.ancestral_linkage(tdata, groupby="celltype", target="B", test="permutation",
+                         normalize=False, n_permutations=30, random_state=1)
+    raw = tdata.obs["B_linkage"].copy()
+
+    # Normalized linkage
+    tl.ancestral_linkage(tdata, groupby="celltype", target="B", test="permutation",
+                         normalize=True, n_permutations=30, random_state=1)
+    norm = tdata.obs["B_linkage"].copy()
+    test_df = tdata.uns["celltype_test"]
+
+    # Normalized values should differ from raw (permuted_mean is non-trivial)
+    # And for each cell: norm = raw - cat_permuted_mean
+    for cell in ["a1", "a2", "b1", "b2"]:
+        cat = tdata.obs.loc[cell, "celltype"]
+        perm_val = test_df.loc[test_df["source"] == cat, "permuted_value"].iloc[0]
+        assert norm[cell] == pytest.approx(raw[cell] - perm_val, abs=1e-9)
+
+    assert "B_norm_linkage" not in tdata.obs.columns
+
+
+def test_single_target_no_normalize_keeps_raw(balanced_tdata):
+    """normalize=False (default) does not overwrite _linkage in obs."""
+    tdata = balanced_tdata
+    tl.ancestral_linkage(tdata, groupby="celltype", target="B", test="permutation",
+                         normalize=False, n_permutations=20, random_state=2)
+    # With normalize=False, a1 (category A, not in B) has raw min-path score 2.0
+    assert tdata.obs.loc["a1", "B_linkage"] == pytest.approx(2.0)
+
+
+def test_single_target_by_tree_permutation(three_cat_tdata):
+    """by_tree=True with single target + permutation runs per-tree (stats has tree column)."""
+    tdata = three_cat_tdata
+    tl.ancestral_linkage(
+        tdata, groupby="celltype", target="A", test="permutation", by_tree=True,
+        n_permutations=20, random_state=7,
+    )
+    assert "A_linkage" in tdata.obs.columns
+    assert "A_norm_linkage" not in tdata.obs.columns
+    test_df = tdata.uns["celltype_test"]
+    assert "tree" in test_df.columns
+    for tree_key in tdata.obst:
+        assert tree_key in test_df["tree"].values
+
+
+def test_single_target_by_tree_normalize(three_cat_tdata):
+    """by_tree=True + normalize=True normalizes each cell using its own tree's null distribution."""
+    tdata = three_cat_tdata
+    tl.ancestral_linkage(
+        tdata, groupby="celltype", target="A", test="permutation",
+        by_tree=True, normalize=True, n_permutations=20, random_state=7,
+    )
+    assert "A_linkage" in tdata.obs.columns
+    assert "A_norm_linkage" not in tdata.obs.columns
+    # _linkage values should be finite for leaves with valid scores
+    assert tdata.obs["A_linkage"].notna().any()
+
+
+def test_single_target_by_tree_perm_non_target(balanced_tdata):
+    """by_tree + permutation_mode='non_target' in single-target mode produces tree column in stats."""
+    tdata = balanced_tdata
+    tl.ancestral_linkage(
+        tdata, groupby="celltype", target="B", test="permutation",
+        by_tree=True, permutation_mode="non_target", n_permutations=20, random_state=3,
+    )
+    assert "B_norm_linkage" not in tdata.obs.columns
+    test_df = tdata.uns["celltype_test"]
+    assert "tree" in test_df.columns