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Immigration can occur at any time once per season. Smaller migrant waves of 2 to 10 seem typical in early seasons, followed by a large wave in the low double digits in the second Spring, one year after embark. It may be the case that the first 2 migrant waves are special and possibly generated out of thin air, like all waves used to be. Even if your parent civilization is extinct, two waves will still show up. Each group of migrants will often include domestic animals, either as a pet or unclaimed livestock. Be prepared with adequate food, drink, and beds, among other things. Max wave size reported to date is 77.Source
Migrants will have skills that match your fortress' needs: Migrants with skills your fortress uses a lot or skills that your fortress doesn't have at all are more likely to show up at your gates. Important skills (mining, food production, and basic crafting, according to Toady) are weighed more heavily than other skills.Source
Migration waves are generally a good thing-- if you're prepared for them.
 Labor preference bug
Each migrant can arrive with a wide collection of often unrelated skills, far greater than possible with one of the starting 7 dwarves, and experience levels as high as Legendary. Any and all skills might be represented, including obscure military skills (like blowgunner), high levels of one or more social skills, crutch walker, concentration and others. It's even possible to have dwarves with skills that may not be obtainable by other means, like military tactics or tracking.
Immigrants may have high skills in certain labors without actually having them enabled in their labor preferences. This leads to dwarves either doing jobs from an area they are not labeled for or no work at all. For example, an adequate cheese maker (with the cheese making labor turned on) may also have the skill bone carving on "high master", albeit turned off in his preferences. The dwarf in question is listed as a bone carver on screen and in the status tab, but will only perform the cheese making labor. Individually checking each immigrant for skills and labor preferences is the only workaround so far. But the use of programs such as Dwarf Therapist can greatly decrease the time taken to check each dwarf's skills.
As of v34.04, migrants may arrive with all labors except hauling, cleaning, recovering wounded, and caring for wounded disabled, depending on the settings one has entered into data/init.txt.
 Historical migrants
Some immigrants are historical figures. These immigrants come to your fortress with skills representing their history, and may come to your fortress with wounds they have suffered during world generation. Immigrants may even be vampires.
 Limiting/preventing immigration
If the fortress population exceeds the population cap when the dwarven liaison is visiting he will note that you don't want any more dwarves. On his safe return to the dwarven homeland he then will see that no migrants are sent that year. So you can stop immigration by setting the POPULATION_CAP option in d_init.txt to a number lower than your current population, the change will only take effect after the dwarven caravan visits so you may get up to three waves of migrants before the change takes effect.Verify
The first two immigrant waves are hardcoded so you will always receive them, and if you have less than 4 dwarves POPULATION_CAP is ignoredVerify. The number of migrants depends on the created wealth of your fortress and so is affected by your dwarves activities. Note that if your fortress should ever become a mountainhome, you will receive an additional migration wave with the promotion, regardless of your population cap. The number of migrants is not affected by how far below the population cap your fortress was. One dwarf short, or twenty - it's all the same.
It is worth noting that you need a certain minimum population size before any of your dwarves will experience strange moods. Additionally, POPULATION_CAP still allows babies to be born. You will need to alter BABY_CAP in order to change it.
To reiterate, the population cap is not a hard limit on the number of dwarves in your fortress; It is a soft cap on immigration that only is checked when a liaison successfully reports back to your home civ. If a player is as little as 1 dwarf under their population cap when the liaison leaves, they will be eligible for a full year of normal immigration. As such, it is recommended that players set their population cap at 20-30 dwarves below the number of dwarves they actually want in their fort.
 Immigration mechanics
The date on which immigrants appear in a season seems to be fixed at the start of that season, but the number of immigrants and their skills are determined when the migrant wave arrives.
There is never a migration in the first winter. There won't even be a The fortress attracted no migrants this season message.
Migrant skill levels seem to depend on the size of the home civilization; a difference will be noticed if you picked a dwarven civilization that was not well established (few towns or none) compared to a well established one.
 Migrant wave sizes
The first two migrant waves have a minimum size of 2 and a maximum size of 10. The size of these waves are unaffected by fortress wealth.
The third migrant wave and on are influenced by the created wealth of the fortress, with more wealth attracting more immigrants (more research is needed to determine specifics). Specifically, they're influenced by the fortress wealth as reported by the last outgoing dwarven caravan. Wealth created after the caravan leaves has no influence until the next year's caravan leaves. If the caravan fails to make it out then the fortress' wealth is not reported. The dwarven liaison does not report on fortress wealth, in those circumstances where the liaison makes it out but the caravan doesn't.
Imported wealth, caravan sales figures, absolute caravan profit and caravan profit margin either have no effect on migration numbers, or only have an effect by applying a percent modification to the numbers driven by created wealth. If a fortress manages to trade (not offer) away 100% of its created wealth then no immigrants will come the next season. More research is needed to determine if the aforementioned statistics have any influence on migration numbers.
One factor which is known to affect migrant wave size is the total size of your fortress'snits list (all 4 categories), which consists of dwarves, invaders, merchants, and animals which either died or currently live at your fortress. As this number increases, the maximum size of migrant waves will be reduced: starting at a local population of 1000, migrant wave sizes are limited to 10, and at subsequent levels of 1300, 1600, 1800, 2000, 2200, 2400, 2600, 2800, and 2900, the limit is decreased by 1, and once you reach a local population of 3000 you will cease to get migrants at all.
 Adventure mode
In certain locations in adventure mode, you may come across a Migrating Group. One such location is near a recently abandoned fortress; choosing to travel to the group will allow you to talk to the members of your former fortress as they travel back to dwarven civilization.
 Fortress Failure Migration
If any migrants to your fort were formerly traders or soldiers with a trade caravan, then they will be marked as a "friendly" Trader, stand around at the map edge for a while (blocking the rest of the migrants, and caravans or even a Monarch), and then wander around randomly, unable to be assigned labors. Bug:5098 DFHack includes a command "tweak fixmigrant" as a workaround for this bug. This bug occurs most often if your starting dwarven civilization at embark is a very small one with few or even no towns at all.
Also, some migrants will be incorrectly listed as babies or children, when they are not in the expected age range for those categories. This will automatically fix itself when they have their next birthday. Some baby migrants may have future birth dates. Bug:3945