BindablePicker with on the fly updating

I have a great BindablePicker found on these forums below. However, it only works if the bound collection already contains its items at the time of binding. How can I modify this code so that adding items to the underlying ItemsSource -after- the binding has been set updates the items in the picker?

Thanks guys!!

public class BindablePicker : Picker
{
    public static readonly BindableProperty HasBorderProperty =
        BindableProperty.Create<BindablePicker, bool>(p => p.HasBorder, false);

    public bool HasBorder
    {
        get { return (bool)GetValue(HasBorderProperty); }
        set { SetValue(HasBorderProperty, value); }
    }

    public BindablePicker()
    {
        this.SelectedIndexChanged += OnSelectedIndexChanged;
    }

    public static BindableProperty ItemsSourceProperty =
        BindableProperty.Create<BindablePicker, IEnumerable>(o => o.ItemsSource, default(IEnumerable),
            propertyChanged: OnItemsSourceChanged);

    public static BindableProperty SelectedItemProperty =
        BindableProperty.Create<BindablePicker, object>(o => o.SelectedItem, default(object),
            propertyChanged: OnSelectedItemChanged);


    public IList ItemsSource
    {
        get { return (IList)GetValue(ItemsSourceProperty); }
        set { SetValue(ItemsSourceProperty, value); }
    }

    public object SelectedItem
    {
        get { return (object)GetValue(SelectedItemProperty); }
        set { SetValue(SelectedItemProperty, value); }
    }

    private static void OnItemsSourceChanged(BindableObject bindable, IEnumerable oldvalue, IEnumerable newvalue)
    {
        var picker = bindable as BindablePicker;
        picker.Items.Clear();

        if (newvalue != null)
        {
            foreach (var item in newvalue)
            {
                picker.Items.Add(item.ToString());
            }
        }
    }

    private void OnSelectedIndexChanged(object sender, EventArgs eventArgs)
    {
        if (SelectedIndex < 0 || SelectedIndex > Items.Count - 1)
        {
            SelectedItem = null;
        }
        else
        {
            SelectedItem = Items[SelectedIndex];
        }
    }

    private static void OnSelectedItemChanged(BindableObject bindable, object oldvalue, object newvalue)
    {
        var picker = bindable as BindablePicker;
        if (newvalue != null)
        {
            picker.SelectedIndex = picker.Items.IndexOf(newvalue.ToString());
        }
    }
}