As per my understanding, Pratityasamutpada is not about simple cause-and-effect chaining.
Starting from a name: pratitya means "based on", "in dependence on", sam- means "co-" or "together" and utpada means "arising" or "coming forth". Together Pratityasamutpada means "arising in dependence on each other" or "dependent co-arising" or "interdependent origination".
Dependent co-arising is closely related with Idaṃpratyayatā (Pali Idappaccayatā) or "this/that conditionality":
And what is the noble method that is rightly seen and rightly ferreted
out by discernment? There is the case where a disciple of the noble
When this is, that is.
From the arising of this comes the arising of that.
When this isn't, that isn't.
From the cessation of this comes the cessation of that.
As I explained in "What exactly is the logical relation between the links in the twelvefold chain of Pratītyasamutpāda?", the relationship is that of mutual implication.
Mutual implication means one of the categories serves as context for the other and the other way around. When affirmation takes place, the implicitly negated complement simultaneously arises. Top is defined against bottom and vice verse. This (upclose) is defined against That (far). Subjective is defined against Objective. Nirvana is defined against Samsara.
As (Buddha's Chinese near-contemporary) Lao-Tzu beautifully puts it:
Tao Te Ching #2
When beauty is recognized as beauty, therein is ugliness.
When goodness is affirmed as goodness, therein is evil.
Therefore, being and non-being are mutually posited in their emergence.
Difficult and easy are mutually posited in their complementariness.
High and low create each other in their positions.
Long and short formulate each other in their contradiction.
As Nanavira Thera rightly assumes in his "Notes on Dhamma" and Buddhadasa correctly postulates in his lectures, the twelve nidanas are meant to explain how the problem of Life-and-Death and indeed the very Enlightenment hinges on the notion of Substantial Independent "I", and how this "I" itself comes forth as a result of an atemporal chain of logical implication.
Indeed, if we think about Death not in terms of its natural causes, but in context of its emergence from non-duality, it will become clear that Death and Birth indeed depend on each other in their juxtaposition. In this sense the notion of Birth could be seen as the cause of the notion of Death. Following the same principle, Birth is not just something that happens for natural reasons, it is a phenomena that depends on delineation of a separate living being, etc.
This way, Pratityasamutpada goes on defining Separate Being by implication from clinging/sustaining (basically, acting out of craving), defining the clinging/sustaining by implication from craving etc. all the way until Ignorance (of Pratityasamutpada) as the root.