CREATE TABLE inventory
    (`animal` varchar(6), `date` date, `quantity` int);
INSERT INTO inventory
    (`animal`, `date`, `quantity`)
VALUES
    ('dog', '2015-01-01', 400),
    ('cat', '2015-01-01', 300),
    ('dog', '2015-01-02', 402),
    ('rabbit', '2015-01-01', 500),
    ('cat', '2015-01-02', 304),
    ('rabbit', '2015-01-02', 508),
       ('rabbit', '2015-01-03', 524),
       ('rabbit', '2015-01-04', 556),
       ('rabbit', '2015-01-05', 620),
    ('rabbit', '2015-01-06', 748);

+--------+------------+----------+---------------+
| animal | date       | quantity | quantity_diff |
+--------+------------+----------+---------------+
| rabbit | 2015-01-01 |      500 |             8 |
| rabbit | 2015-01-02 |      508 |            16 |
| rabbit | 2015-01-03 |      524 |            32 |
| rabbit | 2015-01-04 |      656 |            64 |
| rabbit | 2015-01-05 |      620 |           128 |
| rabbit | 2015-01-06 |      748 |          null |
+--------+------------+----------+---------------+

set @qt:=null;
select animal,
       `date`,
       quantity,
       lead-quantity quantity_diff
from ( select i.animal,
              i.`date`,
              @qt as lead,
              @qt := i.quantity as quantity
        from inventory i
       where i.animal = 'rabbit'
       order by `date` desc
     ) tab
order by `date`;