Lightning and Death Itself Population Estimate

Just for fun, let's consider what will happen to the Night Fury population over the next few years, using Ending #1 as a starting point.

We'll make the following assumptions:

=Hiccup and Astrid are the first mating pair.
=Toothless and Guana immediately form the second mating pair.
=Guana will transform a human into a Night Fury very soon. That new Night Fury will also transform a human of the opposite sex, to make a third mating pair.
=Night Furies reach physical maturity at age 3.
=Once they pair off, they stay paired off for life.
=When a Night Fury reaches the age of 2, he/she will search for a suitable human of the opposite sex who will make a good Night Fury, and transform him/her near the end of that second year. Thus, as soon as a Night Fury reaches maturity, his/her partner will be there and ready to mate.
=Nobody dies of accidents, sickness, or violence.
=Just to keep it simple, we'll say Astrid will not lay any more twins, and none of her children will inherit that tendency from her. We'll assume one egg per couple per year.
=We won't consider Night Furies who might be living elsewhere; we'll look only at the ones who live in or near Berk.

Given these assumptions, how fast will our friendly dragons repopulate their race?

When the story starts, there is only Toothless. The Night Fury population is 1. But Toothless pulls the transformation of the century, and gets the ball rolling.

At the end of year 1, we have Hiccup and Astrid and their hatchling twins, Toothless and Guana, and the dragon Guana transforms, along with that dragon's newly-transformed mate. That gives us six adults and two hatchlings, for a Night Fury population of 8.

At the end of year 2, the hatchling twins are now yearlings. Three new hatchlings from the three adult pairs take their places. The number of adults is unchanged. Our Night Fury population is up to 11.

In year 3, we've got three new hatchlings, three yearlings (last year's hatchlings), the twins are now two years old, they've both transformed their future mates, and we still have our original six adults. Now we've got 16 Night Furies. Looking good so far!

In year 4, the three hatchlings from Year 2 are now two and transform their future mates, and the twins and their mates begin laying eggs themselves. Our population jumps to 23.

I won't bore you with all the math from here on, but let's skip ahead to year 10. At that point, if I've figured it right, we'll have 36 newly-hatched babies, 25 yearlings, 18 two-year-olds and 18 newly-transformed mates-to-be, and 104 adults, for a total of 183 Night Furies. It looks like the race is being repopulated pretty well, wouldn't you agree?

As more time passes, the numbers will mount up even faster. If Astrid or any of her children lay twins at any point, they'll climb faster yet. For instance, one set of twins in Year 4 jumps the year-10 population from 183 to 189.

Every single one of them can trace his/her existence back to Toothless. Look what you've started, you useless reptile!