How do Young Earth Creationists account for the arising of millions of species after the flood?

Bill Nye makes an assumption here that new species evolved at the same rate since the flood. However, that simply does not make sense. The 7,000 or so species on the ark would have had quite a bit of genetic diversity. Therefore, all of their offspring would have been quite different from each other and from their parents. New species would form each generation. Just as every person looks different, every animal would be drastically different. More and more species would be created each generation exponentially until they slowly lost enough genetic diversity to create such drastically different offspring. As offspring slowly became more like their parents, species would become more defined (i.e. when some humans would always have blond-haired children and others would always have black-haired children and others always have red-haired children, they become considered different species).

Thus, one could arrive at millions of species in thousands of years because the first several generations were all different species (until they lost genetic diversity). Eleven species would not have to evolve each day because thousands would evolve in one day shortly after the flood.

Note also that 16,000,000 species includes everything from mammals to insects to insects that aren't technically insects to fungus to trees. Even following Bill Nye's idea of a constant evolution of species, 6 animals would need to be created each day, and only 1 mammal per year. Given that many new species would form shortly after the flood, it is well reasonable that 9,000,000 species of animals, 5,100,000 of fungus, 400,000 of plants, and trillions of bacteria could have formed after the flood.

Bill Nye's math is based on an absolutely necessary assumption that the rate of speciation is linear; that is, for every new species that comes into existence, another species goes extinct. This assumption is absolutely necessary for the Uniformitarian model, as an exponential rate of speciation under Uniformitarian time scales would result in an absolutely untenable number of species (see edit history).

We know from observation that speciation happens, and can happen in a fairly short number of generations. In fact, one study found that speciation can happen in as few as two generations.

In the YEC model, biblical kinds (which are likely somewhere on the order of what we now call families were created with significant genetic potential, which, per the laws of thermodynamics (entropy) and information theory, are now degrading. The YEC model allows for an exponential rate of speciation which perhaps slows with time. This model would predict rapid speciation (or at least, rapid diversification) shortly after Creation. At the time of the Flood, this genetic potential may not have degraded significantly, which is the basis of estimates that the number of animals on the ark would have been perhaps in the thousands or maybe a few tens of thousands. With this genetic potential still present, further rapid speciation could be expected immediately after the flood as animals spread out to fill the recently-depopulated Earth.

Crucially, however, there is no reason to believe in the YEC model that extinctions, particularly just after the Flood, would keep pace with speciations. Growth would thus be not linear, as Nye asserts, but exponential. Assuming we started with 1,000 species (almost certainly a low estimate), it would require a mere fourteen¹ cycles of speciation to reach the "target" 1.6 million species. That's one cycle every ~285 years, or every ~60 generations (assuming a relatively conservative 5 years per generation, on average).

There is no difficulty here. Nye artificially creates a difficulty by imposing Uniformitarian presuppositions on the YEC model; his "attack" is nothing but a straw man.

As an additional note, YECs would also predict that the rate of speciation will slow and the rate of extinction will increase. This appears consistent with present observations. This does, however, raise the question of the numerous species presently extinct which exist in the fossil record. YECs would reply that, since fossilization is an abnormal occurrence (with most fossils resulting from the Flood), it is not overly difficult to surmise that these species trees petered out after the flood, either due climate change resulting from the Flood, or human activity (e.g. "dragons", which may well have been what we now call "dinosaurs", being hunted to extinction). Indeed, YECs and Uniformitarians agree that the Earth's climate was likely quite different at some point in the past (disagreeing mainly in how long ago that point was), and that many species which thrived in the previous (Mesozoic or pre-Flood) climate went extinct in the "modern" (Cenozoic or post-Flood) climate.

(¹ 1,000 species to start and 16 million currently is an increase by 16,000 times. Assuming each "cycle" results in — on average and accounting for extinctions — a single net speciation with no extinctions gives a "growth factor" of two. log₂(16,000) ≈ 14.)

YEC accounts for the diversity of species with the same ideas governing speciation (microevolution): mutations, natural selection, genetic drift, and non-random mating result in change to allelic and genotypic frequencies that results in speciation (source: Principles of Evolution class)

Bill Nye, just based on your information provided, has not given an argument against YEC unless he demonstrates the time-limiting factors such that it would prevent the diversity of species we see today, which I'm sure people have made arguments that do just that though. Otherwise, it seems reasonable to think that thousands of animals species over thousands of years and hundreds to hundreds of thousands of generations spread over millions of square mileage and various amounts of polyploidy and mutation rates could, on average, "produce" 11 species per day (though "species" is sometimes seemingly arbitrarily defined).

There are genetic limits to speciation that causes a roadblock in the extrapolation from micro-to-macroevolution (See The Natural Limits of Biological Change). So, in reality something like the creation of all the different families of animals at once is the only way to account for the diversity of species. And yes, in general, the YEC position is that all animals at approximately the family level (family then genus then species is the taxonomy) were in place at Noah's time. Source for last sentence: Answers in Genesis.

I started to comment but I think I’ll turn it into an answer

That is illogical.

You cannot take the axioms/constants of one paradigm and use them to argue against another paradigm. By design they will conflict. They have entirely different presupposition and therefore modes of interpretation.

You must prove within a paradigm that the axioms of that same paradigm are conflicting.

Thus far the Christian Young Earth paradigm is consistent both in its claims and its interpretation of the observable data because it doesn’t interpret the data from an evolutionary standpoint.

The proposal Nye is putting forth is preposterous, he is superimposing big bang evolution over Creator and creation and expecting to find what the former claims as axiomatic, to be true in the latter.

I do see his angle and for that reason he needs to correct course because his math is deceiving

Firstly he is counting from the flood, let’s say it’s 4,000 years use round numbers. He cannot include all life forms in the waters because they were not destroyed by the flood.

Also he is including microorganisms, there is no evidence they were destroyed.

Furthermore he is back tracking down to zero/one organism but the flood did not start with zero animals.

Another point even though there is much more to be said from so many other angles, each animal after its kind diversified from 1 to 2 then to 4 then to 8 then to 16, 32, 64, 128, 256, 512, 1,024, 2,048, 4,096, 8,192, 16,384, 32,768, 65,536, 131,072, 262,144, 524,288, 1,048,576...Its exponential not linear. Within 20 replication cycles you can create whole different variation from the original mother and father genome combinations. Start switching off due to environmental selection or removing certain genes from the gene pool and you’re on you way to selecting one gene over another. You don’t even need 4,000 years.

Factor into the above paragraph that most animals reproduce more than once in a life time and that they may also have many offsprings from the same copulation. That is an even greater climb than exponential growth.

average implies a linear growth when it was most likely exponential

Adding one other detail. YEC starts from the premise that the genome for each kind started whole and with different alleles but with time was selected for certain genes; genes being selected out of the gene pool. That is not very difficult to understand, the process of losing information as opposed to the evolutionary model that necessitates an increase of new information. Granted YEC starts with a Creator but within the paradigm it remains consistent. Evolutionist have not yet proven one example of novel genetic sequence that has not been introduced artificially.

So his premise is wrong. It’s an interesting idea but again intellectually dishonest because he chose not to inform himself of what YEC actually claim but rather strawmans a paradigm using axioms from a paradigm he favors and use a form of sophistry and debate rhetorics to overwhelm or command superiority when in fact it should be unemotional and well informed arguments that disprove the opposition in science not oratory !