History and Philosophy of Biology - Science topic

Habitat is a place where an organism lives in nature.

Environment is the sum total of all physical, chemical, biotic and cultural factors that affects life of organism in any way.

Ecological niche is physical space occupied by an organism, its functional role in community and its position in environmental gradients including other conditions of existence. These three aspects of ecological niche are designated as follows:

(i) the spatial niche (physical space occupied)

(ii) the trophic niche (functional role i.e. trophic position); and

(iii) the multidimensional or hypervolume niche (position in the environmental gradients)

One of the central tenants of Darwinian selection is that natural selection acts on preexisting genetic variation. So the neo-Darwinian theory of evolution is indeed falsifiable to some extent. All you need to do is find an instance where genetic changes occurred as a result of selection rather than prior to it. Specifically, these changes must occur highly disproportionately at the sites of selection, rather than just having an overall increased mutation rate. An example of this type of challenge was in 1988 when John Cairns proposed a possible example of directed mutation in the lactose operon in E. coli. This stimulated a fair amount of research into the phenomenon, with the final consensus being that the phenomenon was consistent with neo-Darwinian theory, and the Lamarckian appearance of the phenomenon was an artifact. The literature on the subject is quite rich, and worth looking into for anyone who wants to see what a real scientific challenge to neo-Darwinian theory looks like, and how it is investigated by empirical scientists.

First, look particularly to A. H. Louie. Rosen's arguments, right or wrong, are profound, relate to complex and nuanced issues, and most importantly are never expressed in some singular, explicit form the way a proof that "(M,R)-systems are necessarily non-computable" require. This is not to demean or in any way detract from Rosen, simply to recognize (as his foremost proponents do) that the development of his ideas over time were never expressed in a formal proof. This is not true of those who have built on his work, hence Louie.

Second, Rosen doesn't argue that physical reality is "non-mathematisability". He argues that living systems are closed to efficient causation, and therefore must have non-computable models. This differs from your description in two extremely important ways. One is the restriction to living systems (Rosen's argument rests on "(M,R)-systems", or anticipatory systems defined in this case specifically in terms of metabolism-repair). This in no ways entails, implies, or otherwise suggests that physical reality itself is non-computable sui generis. It entails that a tiny subset of physical systems are. Another issue is that "non-mathematisability" is not equivalent to "non-computable" or incomputable. We define computability mathematically, which means we can determine what is incomputable mathematically, and this alone entails that what is incomputable/non-computable can be represented mathematically.