удаление элемента LinkedList

у меня есть класс

public class AnimalList<Animal> {
    private class Node<N> {
        Node<N> prev;
        Animal data;
        Node<N> next;
        Node() {
            prev = null;
            data = null;
            next = null;
        }
        Node(Animal input) {
            prev = null;
            data = input;
            next = null;
        }
        Node(Animal input, Node current) {
            prev = current;
            data = input;
            if (current != null)
                next = current.next;
            current.next = this;
            if (next != null)
                next.prev = this;
        }
    }
    private Node<Animal> first;
    private Node<Animal> last;
    private int counter;
    AnimalList() {
        first = null;
        last = null;
        counter = 0;
    }
    private boolean isEmpty() {
        return counter == 0;
    }
    public Node<Animal> getNode(int position) {
        if (position < 0)
            throw new IllegalArgumentException();
        if (isEmpty())
            return null;
        if (position >= counter - 1)
            return last;
        if (position == 0)
            return first;
        Node<Animal> animal = first;
        for (int i = 0; i < position; i++)
            animal = animal.next;
        return animal;
    }
    public Animal getDataAt(int position) {
        if (isEmpty())
            throw new NullPointerException();
        return getNode(position).data;
    }
    public void add(Animal input) {
        if (input == null)
            throw new IllegalArgumentException();
        if (isEmpty()) {
            first = new Node<Animal>(input);
            last = first;
            counter++;
            return;
        }
        last = new Node<Animal>(input, last);
        counter++;
    }
    public void addAtPosition(Animal input, int position) {
        if (input == null || position < 0) throw new IllegalArgumentException();
        if (position >= counter - 1) {
            add(input);
            return;
        }
        if(position == 0){
            Node<Animal> anml = new Node<Animal>(input);
            first.prev = anml;
            anml.next = first;
            first = anml;
            counter++;
            return;
        }
        Node<Animal> animal = getNode(position-1);
        animal = new Node<Animal>(input, animal);
        counter++;
    }
    public void deleteAtPosition(int position){
        if(position < 0) throw new IllegalArgumentException();
        if(position >= counter - 1){
            Node<Animal> anima_l = getNode(counter-1);
            anima_l = null;
        }
        else {
         Node<Animal> animal = getNode(position);
         animal = animal.next;
        }
    }
    public void delete(Animal input){
        if(input == null) throw new IllegalArgumentException();
        if(isEmpty()) throw new NullPointerException();
        if(!isEmpty()){
        }
    }
    public String toString() {
        String res = "";
        Node<Animal> one = first;
        while (one != null) {
            res += one.data.toString() + " ";
            one = one.next;
        }
        return res;
    }
}

как мне дописать удаление элемента по String и по номеру элемента?