From my limited knowledge at uni - I would say this has a lot more to do with biogeography than climate. The northern hemisphere is characterised by much more land area than southern, especially at high latitudes. This provides vast expanses of habitat that is only productive during summer months (I.e breeding season). In the southern hemisphere, around 80% of land excluding Antarctica is tropical/semi tropical, reducing the need for migration, meaning little evolutionary pressure to evolve migration with lack of seasonality. If you look at a biome map the temperate zone (migration zone) is pretty small in the southern hemisphere. This means its pretty difficult for a species to evolve similar, inverted life histories in the two different hemispheres.
The only examples I can think of are larger evolutionary clades like Albatrosses which have largely ceased inter-hemisphere migrations, and have become isolated towards each of the poles.
Im definitely not an expert on the subject but its really interesting! There might be some examples out there!
This has been prompted from reading about the Bar-tailed Godwit that did a non-stop flight from Alaska to Tasmania.
Bar-tailed Godwits breed in the northern hemisphere in summer, and then fly to the south for the summer there to "winter" because presumably it's a better strategy than staying in the northern cold. So are there any of the same species that breed in the southern hemisphere in its summer and then come north to our summer to "winter". And if not, why not? Surely it has the same advantages.
Are there any birds where the population is split in two with some having a migratory lifestyle that is 180 degrees and 6 months out of phase from the rest of the population? Or would this very quickly lead to sub-species and separate species? But even then, it should be possible to say that species X is the southern hemisphere "inversion" of species Y - are there any examples of this?
