Not fully understanding closures and recursive functions in this problem

finding_father.js

var ANCESTRY_FILE = "[\n  " + [
        '{"name": "Carolus Haverbeke", "sex": "m", "born": 1832, "died": 1905, "father": "Carel Haverbeke", "mother": "Maria van Brussel"}',
        '{"name": "Emma de Milliano", "sex": "f", "born": 1876, "died": 1956, "father": "Petrus de Milliano", "mother": "Sophia van Damme"}',
        '{"name": "Maria de Rycke", "sex": "f", "born": 1683, "died": 1724, "father": "Frederik de Rycke", "mother": "Laurentia van Vlaenderen"}',
        '{"name": "Jan van Brussel", "sex": "m", "born": 1714, "died": 1748, "father": "Jacobus van Brussel", "mother": "Joanna van Rooten"}',
        '{"name": "Philibert Haverbeke", "sex": "m", "born": 1907, "died": 1997, "father": "Emile Haverbeke", "mother": "Emma de Milliano"}',
        '{"name": "Jan Frans van Brussel", "sex": "m", "born": 1761, "died": 1833, "father": "Jacobus Bernardus van Brussel", "mother":null}',
        '{"name": "Pauwels van Haverbeke", "sex": "m", "born": 1535, "died": 1582, "father": "N. van Haverbeke", "mother":null}',
        '{"name": "Clara Aernoudts", "sex": "f", "born": 1918, "died": 2012, "father": "Henry Aernoudts", "mother": "Sidonie Coene"}',
        '{"name": "Emile Haverbeke", "sex": "m", "born": 1877, "died": 1968, "father": "Carolus Haverbeke", "mother": "Maria Sturm"}',
        '{"name": "Lieven de Causmaecker", "sex": "m", "born": 1696, "died": 1724, "father": "Carel de Causmaecker", "mother": "Joanna Claes"}',
        '{"name": "Pieter Haverbeke", "sex": "m", "born": 1602, "died": 1642, "father": "Lieven van Haverbeke", "mother":null}',
        '{"name": "Livina Haverbeke", "sex": "f", "born": 1692, "died": 1743, "father": "Daniel Haverbeke", "mother": "Joanna de Pape"}',
        '{"name": "Pieter Bernard Haverbeke", "sex": "m", "born": 1695, "died": 1762, "father": "Willem Haverbeke", "mother": "Petronella Wauters"}',
        '{"name": "Lieven van Haverbeke", "sex": "m", "born": 1570, "died": 1636, "father": "Pauwels van Haverbeke", "mother": "Lievijne Jans"}',
        '{"name": "Joanna de Causmaecker", "sex": "f", "born": 1762, "died": 1807, "father": "Bernardus de Causmaecker", "mother":null}',
        '{"name": "Willem Haverbeke", "sex": "m", "born": 1668, "died": 1731, "father": "Lieven Haverbeke", "mother": "Elisabeth Hercke"}',
        '{"name": "Pieter Antone Haverbeke", "sex": "m", "born": 1753, "died": 1798, "father": "Jan Francies Haverbeke", "mother": "Petronella de Decker"}',
        '{"name": "Maria van Brussel", "sex": "f", "born": 1801, "died": 1834, "father": "Jan Frans van Brussel", "mother": "Joanna de Causmaecker"}',
        '{"name": "Angela Haverbeke", "sex": "f", "born": 1728, "died": 1734, "father": "Pieter Bernard Haverbeke", "mother": "Livina de Vrieze"}',
        '{"name": "Elisabeth Haverbeke", "sex": "f", "born": 1711, "died": 1754, "father": "Jan Haverbeke", "mother": "Maria de Rycke"}',
        '{"name": "Lievijne Jans", "sex": "f", "born": 1542, "died": 1582, "father":null, "mother":null}',
        '{"name": "Bernardus de Causmaecker", "sex": "m", "born": 1721, "died": 1789, "father": "Lieven de Causmaecker", "mother": "Livina Haverbeke"}',
        '{"name": "Jacoba Lammens", "sex": "f", "born": 1699, "died": 1740, "father": "Lieven Lammens", "mother": "Livina de Vrieze"}',
        '{"name": "Pieter de Decker", "sex": "m", "born": 1705, "died": 1780, "father": "Joos de Decker", "mother": "Petronella van de Steene"}',
        '{"name": "Joanna de Pape", "sex": "f", "born": 1654, "died": 1723, "father": "Vincent de Pape", "mother": "Petronella Wauters"}',
        '{"name": "Daniel Haverbeke", "sex": "m", "born": 1652, "died": 1723, "father": "Lieven Haverbeke", "mother": "Elisabeth Hercke"}',
        '{"name": "Lieven Haverbeke", "sex": "m", "born": 1631, "died": 1676, "father": "Pieter Haverbeke", "mother": "Anna van Hecke"}',
        '{"name": "Martina de Pape", "sex": "f", "born": 1666, "died": 1727, "father": "Vincent de Pape", "mother": "Petronella Wauters"}',
        '{"name": "Jan Francies Haverbeke", "sex": "m", "born": 1725, "died": 1779, "father": "Pieter Bernard Haverbeke", "mother": "Livina de Vrieze"}',
        '{"name": "Maria Haverbeke", "sex": "m", "born": 1905, "died": 1997, "father": "Emile Haverbeke", "mother": "Emma de Milliano"}',
        '{"name": "Petronella de Decker", "sex": "f", "born": 1731, "died": 1781, "father": "Pieter de Decker", "mother": "Livina Haverbeke"}',
        '{"name": "Livina Sierens", "sex": "f", "born": 1761, "died": 1826, "father": "Jan Sierens", "mother": "Maria van Waes"}',
        '{"name": "Laurentia Haverbeke", "sex": "f", "born": 1710, "died": 1786, "father": "Jan Haverbeke", "mother": "Maria de Rycke"}',
        '{"name": "Carel Haverbeke", "sex": "m", "born": 1796, "died": 1837, "father": "Pieter Antone Haverbeke", "mother": "Livina Sierens"}',
        '{"name": "Elisabeth Hercke", "sex": "f", "born": 1632, "died": 1674, "father": "Willem Hercke", "mother": "Margriet de Brabander"}',
        '{"name": "Jan Haverbeke", "sex": "m", "born": 1671, "died": 1731, "father": "Lieven Haverbeke", "mother": "Elisabeth Hercke"}',
        '{"name": "Anna van Hecke", "sex": "f", "born": 1607, "died": 1670, "father": "Paschasius van Hecke", "mother": "Martijntken Beelaert"}',
        '{"name": "Maria Sturm", "sex": "f", "born": 1835, "died": 1917, "father": "Charles Sturm", "mother": "Seraphina Spelier"}',
        '{"name": "Jacobus Bernardus van Brussel", "sex": "m", "born": 1736, "died": 1809, "father": "Jan van Brussel", "mother": "Elisabeth Haverbeke"}'
    ].join(",\n  ") + "\n]";

var ancestry = JSON.parse(ANCESTRY_FILE);
var byName = {};

ancestry.forEach(function(person){
    byName[person.name] = person;
});

function reduceAncestors(person, func, defaultValue) {
    function valueFor(person) {
        if (person == null) {
            return defaultValue;
        }
        else {
            return func(person, valueFor(byName[person.mother]), valueFor(byName[person.father]));
        }
    }
    return valueFor(person);
}

function sharedDNA(person, fromMother, fromFather) {
    if (person.name == "Pauwels van Haverbeke") {
        return 1;
    }
    else {
        return (fromMother + fromFather) / 2;
    }
}

var ph = byName["Philibert Haverbeke"];
console.log(reduceAncestors(ph, sharedDNA, 0) / 4);