According to the seminal Scott Hanselman article on the complexities of the ASP.NET Wire Format for Model Binding to Arrays, Lists, Collections, Dictionaries:
We read in the properties by looking for
parameterName[index].PropertyName
The index must be zero-based and unbroke
So this HTML:
<input type="text" name="People[0].FirstName" value="George" />
<input type="text" name="People[1].FirstName" value="Abraham" />
<input type="text" name="People[2].FirstName" value="Thomas" />
Which will post like this:

However, if I load a new person into my model over AJAX, I lose the context for building that person into the model and get the following output:
<input type="text" name="FirstName" value="New" />

Which won't get picked up by the model binder.
Q: How can I preserve the expression tree when dynamically adding new elements over AJAX?
Here's an MVCE
Model: /Model/Person.cs
public class PersonViewModel
{
    public List<Person> People { get; set; }
}
public class Person
{
    public String FirstName { get; set; }
    public String LastName { get; set; }
}
Controller: Controllers/PersonController.cs
[HttpGet]
public ActionResult Index()
{
    List<Person> people = new List<Person> {
        new Person { FirstName = "George" , LastName = "Washington"},
        new Person { FirstName = "Abraham" , LastName = "Lincoln"},
        new Person { FirstName = "Thomas" , LastName = "Jefferson"},
    };
    PersonViewModel model = new PersonViewModel() {People = people};
    return View(model);
}
[HttpPost]
public ActionResult Index(PersonViewModel model)
{
    return View(model);
}
public ActionResult AddPerson(String first, String last)
{
    Person newPerson = new Person { FirstName = first, LastName = last };
    return PartialView("~/Views/Person/EditorTemplates/Person.cshtml", newPerson);
}
View: Views/Person/Index.cshtml
@model PersonViewModel
@using (Html.BeginForm()) {
    <table id="table">
        <thead>
            <tr>
                <th>@Html.DisplayNameFor(model => model.People.First().FirstName)</th>
                <th>@Html.DisplayNameFor(model => model.People.First().LastName)</th>
            </tr>
        </thead>
        <tbody>
            @for (int i = 0; i < Model.People.Count; i++)
            {
                @Html.EditorFor(model => model.People[i])
            }
        </tbody>
    </table>
    <input type="button" value="Add Person" id="add"/>
    <input type="submit" value="Save" />
}
<script type="text/javascript">
    $("#add").click(function() {
        var url = "@Url.Action("AddPerson")?" + $.param({ first: "", last: "" });
        $.ajax({
            type: "GET",
            url: url,
            success: function(data) {
                $("#table tbody").append(data);
            }
        });
    });
</script>
View: Views/Person/EditorTemplates/Person.cshtml
@model Person
<tr>
    <td>@Html.EditorFor(model => model.FirstName)</td>
    <td>@Html.EditorFor(model => model.LastName)</td>
</tr>
NOTE: There are other complexities when deleting an item that I'm not looking to address here per se. I'd just like to add an element and know that it belongs in a nested context alongside other properties.
