Though the legislative maps seem to have a particularly high number of county splits. Is that because of very strict rules on population equality?
Yes, plus nesting rules, and the number of districts.
The actual range for 2010 Senate districts is -0.75% to +0.90%. Standard deviation is 0.44%, so they may have rejected a few over 1% deviation.
Senate districts nest within congressional districts (to the extent possible). House districts nest within senate districts.
There are 50 senate districts. When Iowa had 5 congressional districts, each had 10 senate districts. With 4 congressional districts, there are 12.5 senate districts in each.
One senate district is shared between IA-1 and IA-4; and one between IA-2 and IA-3. Two house districts nest within each senate district. The senate district (SD-26) that spans the IA-1/IA-4 boundary is along the IA-1 panhandle. HD-52 is in the panhandle (and in IA-1), and HD-51 is to the south.
The phenomena that permit whole-county congressional districts break down at the legislative district level.
Iowa has a large number of counties (99) and they are mostly square. You can build relatively good looking structures with a set of similar building blocks. A four-year old can probably do it.
The population is homogeneously heterogeneous. Polk is only about 2/3 the size of a congressional district, and the larger counties are relatively dispersed. This means that it is possible to draw districts with fairly large numbers of counties. The current districts have (20, 24, 16, and 39 counties). Even the district with Des Moines stretches to Nebraska.
Imagine that if you quartered the state into roughly 5x5 county areas. And let's say at each row, you could advance one county, hold the line, or retreat one county. You could do this for five rows. That is 3
5 or 243 choices. Pick the one with the smallest deviation. But you can do this in two dimensions, for all four district boundaries. 3
20. 3.5 billion is a lot of choices even when you have to equalize all four districts.
The quota for senate districts is 60,927. That is smaller than 10 counties, which must be split, and five of those are entitled to more than 2 districts. With 21 whole districts, let's assume that we can finish up four others spanning Scott-Dubuque, Linn-Johnson, Polk-Story, and Polk-Dallas lines. And then a district for the isolated counties of Black Hawk, Woodbury and Pottawatamie. That is a total of 28 districts for at least 13 counties. The other 22 districts are split between 86 counties or about four counties each. It is a lot harder to assemble four counties in groups that match a target population, and even harder in the east.
Alternatively, we are dividing 20, 24, 16, and 39 counties into 12.5 parts each (where the 1/2 part has to be exactly half the size of a full part).
Then you have to divide those senate districts into two house districts. There are four whole-county senate districts (SD-1, SD-4, SD-12, SD-38). All split a county in making the two house districts equal.
It would be better if there weren't nesting. Let's make the senate 47 members and the house 103 members, both prime, and keeping the legislature at 150 total. Then ignore nesting entirely and permit 5% deviation. I think there would be many more whole-county districts.