Don't share constructor code at all

function Animal(genus, species) {
    var animal = Object.create(Animal.prototype);
    animal.genus = genus;
    animal.species = species;
    return animal;
}
 
 
function Dog(species) {
    var dog = Object.create(Dog.prototype);
    dog.genus = 'Canis';
    dog.species = species;
    return dog;
}
Dog.prototype = Object.create(Animal.prototype);
Dog.prototype.constructor = Dog;

Separated init from ctor, seems convoluted

function Animal(genus, species) {
    var animal = Object.create(Animal.prototype);
    animal.init(genus, species);
    return animal;
}
 
Animal.prototype.init = function(genus, species) {
    this.genus = genus;
    this.species = species;
}
 
 
function Dog(species) {
    var dog = Object.create(Dog.prototype);
    dog.init('Canis', species);
    return dog;
}
Dog.prototype = Object.create(Animal.prototype);

Set __proto__ in child

function Animal(genus, species) {
    var animal = Object.create(Animal.prototype);
    animal.genus = genus;
    animal.species = species;
        return animal;
}


function Dog(species) {
        var dog = Animal.prototype.constructor.call(this, 'Canis', species);
        dog.__proto__ = Object.create(Dog.prototype);
        return dog;
}
Dog.prototype = Object.create(Animal.prototype);
Dog.prototype.constructor = Dog;