Homo heidelbergensis was likely also the same species. Neanderthal genes have been found in most modern humans, indicating that some level of interbreeding occurred: this suggests that Neanderthal and sapiens are closely-related enough to be considered the same species.
is this in the same way that most canines can reproduce, even though they are not the same species?
It all depends on where you want to draw your arbitrary lines.
of course, I absolutely agree, and I am not trying to argue really or disagree with you on purpose, I just have different thoughts (my arbitrary line is elsewhere). I tend to side with more diversity in species.
I think the only "European" Homo erectus known is from the Caucasus, and it was from well before the first Neanderthals or heidelbergines began to appear there.
once again it depends on where you want to split the hairs. Boxgrove Man for instance is either Homo Erectus or very early Heidelbergensis, depends. They both had the same acheulean tool kit.
what about Pakefield?
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And, it isn't about whether the three species ever encountered each other. Homo erectus evolved in Africa and expanded into Asia. Meanwhile, heidelbergensis evolved in Africa, then expanded into Europe, and gradually diverged into a European form (neanderthalensis) and an African form (sapiens). At some later point in time, sapiens expanded and came into contact with the other species, but only after they had been partially isolated for some time, and had already evolved into distinct "species" during their isolation.
I am not saying you are wrong, but I think erectus came to europe and then evolved into heidelbergensis. More due to the pakefield dates and the consensus on the earliest heidelbergensis dates. I agree its arbitrary and spitting hairs, but then why else are we here talking about this stuff?
By comparison, habilis, rudolfensis and ergaster not only lived in the same location at the same time, but also apparently evolved into distinct "species" in the same location and at around the same time. This is called "sympatric speciation": something other than geography was a barrier to interbreeding between these "species."
ok now we are getting somewhere, yes this is very interesting.