<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:

def lineages_through_time(self, present_day=None, show_plot=True, color='#000000', xmin=None, xmax=None, ymin=None, ymax=None, title=None, xlabel=None, ylabel=None):
        '''Compute the number of lineages through time. If seaborn is installed, a plot is shown as well

        Args:
            ``present_day`` (``float``): The time of the furthest node from the root. If ``None``, the top of the tree will be placed at time 0

            ``show_plot`` (``bool``): ``True`` to show the plot, otherwise ``False`` to only return the dictionary. To plot multiple LTTs on the same figure, set ``show_plot`` to False for all but the last plot

            ``color`` (``str``): The color of the resulting plot

            ``title`` (``str``): The title of the resulting plot

            ``xmin`` (``float``): The minimum value of the horizontal axis in the resulting plot

            ``xmax`` (``float``): The maximum value of the horizontal axis in the resulting plot

            ``xlabel`` (``str``): The label of the horizontal axis in the resulting plot

            ``ymin`` (``float``): The minimum value of the vertical axis in the resulting plot

            ``ymax`` (``float``): The maximum value of the vertical axis in the resulting plot

            ``ylabel`` (``str``): The label of the vertical axis in the resulting plot

        Returns:
            ``dict``: A dictionary in which each ``(t,n)`` pair denotes the number of lineages ``n`` that existed at time ``t``
        '''
        if present_day is not None and not isinstance(present_day,int) and not isinstance(present_day,float):
            raise TypeError("present_day must be a float")
        time = dict()
        if self.root.edge_length is None:
            tmproot = self.root
        else:
            tmproot = Node(); tmproot.add_child(self.root)
        for node in tmproot.traverse_preorder():
            if node.is_root():
                time[node] = 0.
            else:
                time[node] = time[node.parent]
                if node.edge_length is not None:
                    time[node] += node.edge_length
        nodes = sorted((time[node],node) for node in time)
        lineages = {nodes[0][0]:0}
        for i in range(len(nodes)):
            if nodes[i][0] not in lineages:
                lineages[nodes[i][0]] = lineages[nodes[i-1][0]]
            if nodes[i][1].edge_length is not None:
                if nodes[i][1].edge_length >= 0:
                    lineages[nodes[i][0]] -= 1
                else:
                    lineages[nodes[i][0]] += 1
            for c in nodes[i][1].children:
                if c.edge_length >= 0:
                    lineages[nodes[i][0]] += 1
                else:
                    lineages[nodes[i][0]] -= 1
        if present_day is not None:
            shift = present_day - max(lineages.keys())
        else:
            shift = max(0,-min(lineages.keys()))
        if shift != 0:
            tmp = dict()
            for t in lineages:
                tmp[t+shift] = lineages[t]
            lineages = tmp
        if tmproot != self.root:
            self.root.parent = None
        try:
            plot_ltt(lineages, show_plot=show_plot, color=color, xmin=xmin, xmax=xmax, ymin=ymin, ymax=ymax, title=title, xlabel=xlabel, ylabel=ylabel)
        except Exception as e:
            warn("Unable to produce visualization (but dictionary will still be returned)"); print(e)
        return lineages