For some birds the sense of smell appears to play a role in navigation, since pigeons with surgically removed olfactory nerves were found to have increased difficulties in homing.
Hi Abhishek,
Great question!!
Your doubt brings to surface a very interesting aspect of usage of "have". The word "has/have" can be used in two different roles:
1: As a complete verb meaning "possess". - Children have many toys. Here "have" = "possess"
2: As a helping verb to form perfect tense with the main verb. - Children have played with their toys. Here "have" is used to form perfect tense with the main verb - played.
I will re-write the above two sentences in the same form as used in the sentence in question:
Children are known to have many toys (have = possess)
Children are known to have played with many toys (have = to form perfect tense)
From the above two sentences, the role played by have is very clear. There is no doubt in mind. Thus, we can determine the role of "has/have" from the meaning of the sentence.
So now lets understand the meaning of the original sentence to determine the role that "have" plays.
For some birds the sense of smell appears to play a role in navigation, since pigeons with surgically removed olfactory nerves were found to have increased difficulties in homing.
In this sentence, the author states a fact that for some birds sense of smell is used to play a role in navigation. He supports this fact by stating an observation of pigeons who did not have a sense of smell. These pigeons faced increased difficulties in homing.
Thus, in the context of this sentence - "have" = possess.
And as you yourself notes, in the context of this sentence, it does not make sense to say that pigeons themselves increased the difficulties in homing.
Thus, as you can see, "have" plays one of the two roles in this construction. If however, we use the expression "increasing difficulty", then it will change the intended meaning since as noted in the previous post, it will imply that difficulty is still increasing.
I hope this helps address your concern.
Regards,
Payal