、。
It's because there were no large carnivores on the island of New Guinea.
Literal
New Guinea-island [on-には], large-type carnivorous-beasts [subject-が] did-not-exist [because-of-ためです].
A cause-giving explanation. ~ためです ('it's because X,' 'the reason is X') is an explanatory predicate frame — combines the noun ため ('reason, sake, cause') with です. Used at the end of a sentence to provide a direct answer to a 'why?' question. Here it answers something earlier in context (probably 'why did X become/evolve/survive on New Guinea?'). 大型 ('large-type,' 'large-sized') and 小型 ('small-type,' 'small-sized') are productive classifier prefixes — 大型犬 (large dog), 小型車 (compact car). 肉食獣 ('carnivorous beast') is 肉 (meat) + 食 (eat) + 獣 (beast/wild animal), a standard zoology compound.