# LineageOT with static lineage tracing¶

While designed for dynamic lineage tracing with continuously edited barcodes, LineageOT can be applied to any time course where a lineage tree can be created, including static barcoding data.

With some forms of static barcoding, more information is available than LineageOT uses. LineageOT does not account for the possibility that the same barcode could be observed at multiple time points. If that happens in your data, you can still use LineageOT, but should also consider other methods.

```import anndata
import lineageot
import numpy as np

rng = np.random.default_rng()
```

## Creating data¶

First we make a minimal fake AnnData object to run LineageOT on. Here, the lineage information is encoded in a Boolean matrix with cells as rows and clones as column, where entry `[i, j]` is 1 if and only if cell `i` belongs to clone `j`. This example has two initial clones labeled at time 0 and four subclones labeled at time 7.

In addition to the clone identities, LineageOT also needs a time for each clone. This is encoded in the vector `clone_times`, whose entries give the time of labeling of the clones.

```t1 = 5;
t2 = 10;

n_cells_1 = 4;
n_cells_2 = 8;
n_cells = n_cells_1 + n_cells_2;

n_genes = 5;

# clones labeled at time 0
time_0_clones = np.concatenate([np.kron(np.identity(2), np.ones((2,1))),
np.kron(np.identity(2), np.ones((4,1)))])
# clones labeled at time 7
time_7_clones = np.concatenate([np.zeros((4,4)),
np.kron(np.identity(4), np.ones((2,1)))])
clones = np.concatenate([time_0_clones, time_7_clones], 1)

clone_times = np.array([0, 0, 7, 7, 7, 7])

adata = anndata.AnnData(X = np.random.rand(n_cells, n_genes),
obs = {"time" : np.concatenate([t1*np.ones(n_cells_1), t2*np.ones(n_cells_2)])},
obsm = {"X_clone" : clones}
)

print(clones)
```

Out:

```[[1. 0. 0. 0. 0. 0.]
[1. 0. 0. 0. 0. 0.]
[0. 1. 0. 0. 0. 0.]
[0. 1. 0. 0. 0. 0.]
[1. 0. 1. 0. 0. 0.]
[1. 0. 1. 0. 0. 0.]
[1. 0. 0. 1. 0. 0.]
[1. 0. 0. 1. 0. 0.]
[0. 1. 0. 0. 1. 0.]
[0. 1. 0. 0. 1. 0.]
[0. 1. 0. 0. 0. 1.]
[0. 1. 0. 0. 0. 1.]]
```

## Fitting a lineage tree¶

Before running LineageOT, we need to build a lineage tree from the observed barcodes. For static lineage tracing data, we provide an algorithm to construct a tree of possibly-nested clones, assuming there are no barcode collisions across clones so the phylogeny is straightforward to reconstruct. This step is not optimized. Feel free to use your own preferred tree construction algorithm. You can import a tree saved in Newick format with `lineageot.read_newick`.

The tree should be formatted as a NetworkX `DiGraph` in the same way as the output of `lineageot.fit_tree()` Each node is annotated with `'time'` (which indicates either the time of sampling (for observed cells) or the time of division (for unobserved ancestors). Edges are directed from parent to child and are annotated with `'time'` equal to the child node’s `'time_to_parent'`. Observed node indices correspond to their row in `adata[adata.obs['time'] == t2]`.

```lineage_tree_t2 = lineageot.fit_tree(adata[adata.obs['time'] == t2], t2, clone_times = clone_times, method = 'clones')
```

## Running LineageOT¶

Once we have a lineage tree annotated with time, we can compute a LineageOT coupling.

```coupling = lineageot.fit_lineage_coupling(adata, t1, t2, lineage_tree_t2)
```

Out:

```/home/docs/checkouts/readthedocs.org/user_builds/lineageot/envs/latest/lib/python3.7/site-packages/ot/bregman.py:517: UserWarning: Sinkhorn did not converge. You might want to increase the number of iterations `numItermax` or the regularization parameter `reg`.
warnings.warn("Sinkhorn did not converge. You might want to "
```

## Saving¶

The LineageOT package does not include functionality for downstream analysis and plotting. We recommend transitioning to other packages, like Waddington-OT, after computing a coupling. This saves the fitted coupling in a format Waddington-OT can import.

```lineageot.save_coupling_as_tmap(coupling, t1, t2, './tmaps/example')
```

Total running time of the script: ( 0 minutes 0.221 seconds)

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