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Basic Perks
Agility
This perk is extremely useful if combat speed is a bottleneck. This perk will not affect the time it takes to move a cell after killing an enemy, nor will it affect the time between one group of trimp dying and another starting the fight (if there is one; needs verification).
The perk is considerably resources is a bottleneck, or if the time it takes to breed up a new army is significant. This perk will not affect you negatively even in that case.
In the long grind between level 50 and 59, where your trimps are not dying and battle takes up a long time, each upgrade roughly increases your clear speed by 5% multiplicatively. And 20 upgrades will multiply your clear speed by roughly 2.8.
Bait
Convenient at the beginning of the game, and slightly useful during the short period in the early mid-game when a significant fraction of your trimps are dying very fast, and your nurseries/venimps haven't completely kicked in yet. Not very useful, and becomes less so with pheromones. But a few levels means you don't have to trap trimps 1 by 1 early game. Becomes completely obsolete in mid-late game, because you can only trap a maximum of 10 times per second due to the fact that the game only runs every 100ms.
Trumps
Useful early game; becomes insignificant really quickly. Not a particularly good perk. Does stack with Carpentry however. Early-game, it is a good idea to get lots of levels in this and then respec out of it later on - you will keep the bonus on all the Territory Bonuses you've gotten so far.
Pheromones
Trimp breeding is linear. This upgrade increases the base speed of breeding. Extremely potent if trimp breeding is a limiting factor. Superb upgrade to get if you suffer a significant down time due to slowness of breeding. Not so useful if you don't.
Packrat
This is a convenience upgrade. The benefit of this is to decrease the relative cost of storage upgrades compared to the amount stored. With no upgrade, it takes 1/4 of the resource to double storage. As such, if you want enough storage for 8 hours of production, you have to wait 1 hour. With 5 levels in this, it takes 1/8 of the resource to double storage. So you only have to wait half an hour if you want storage for 8 hours.
This perk becomes almost useless after AutoStorage is unlocked, so I wouldn't recommend taking it past level 20.
Motivation
Increases your production, useful perk. A great perk before breaking the planet. You should get motivation to around 10-15 in the early game.
Power
Increases your clear speed; kind of like agility. In fact, it does almost the exact thing as agility if trimp breeding is not an issue. Linear increase, however, compared to compounding increase of agility. At higher levels, agility is more useful.
Toughness
Increases your health. Useful upgrade from 1 to 50. Makes it easier to survive one shot from quick attacking enemies, and gives more time for your trimps to breed. Not so useful from 50-59, as you take no damage, and your block value is significantly higher than your hp.
Looting
Useful as a direct multiplier to helium gained (except those from dimension of anger). Not that useful for other things (except maybe a bit of gem and fragments early on). The gain from production quickly makes the gain from looting insignificant.
Unlockable Perks
These perks are initially hidden, but can be unlocked by completing various challenges. For a full list of challenges and how to unlock them, see Challenges
Range
Increases your minimum damage (80%) by 2% to a maximum of 100%. Each upgrade will improve your average damage by 1%, so you should spend 1/5 of what you are spending on power for this upgrade. The maximum levels is 10, which costs 69 Helium in total.
Artisanistry
Reduces the cost of equipment on that level by 5%
Carpentry
It increases your maximum population by 10% compounding. Easily one of the most important perks in the game. You should sink at least half of your helium into carpentry, as it gives you more workers and increases breed speed, loot and production.
Later in the game, you will be unable to buy co-ordination upgrades because you don't have enough trimps; carpentry can help you buy more coordination upgrades and therefore increase health, damage and block.
Meditation
Meditation gives you a boost to production for every 10 minutes you do not change zones, the bonuses can go up to 60 minutes. The maximum you can have is level 7, which gives you 7% every 10 minutes up to a max of 42%. This will likely not have much effect on quick runs and the first half of the zones, as you will clear the zones in less than 10 minutes. It is good for when you have to spend a while away from the game and/or are doing a deep run. It will also help if you are farming maps for a long time.
Resilience
This perk gives a 5% increase to health (compounding). This quickly becomes more effective than toughness after breaking the planet as it compounds.
Anticipation
Anticipation increases damage according to how long your trimps take to breed. The damage increase is 2% per level per second of breed time up to 30 seconds. The maximum level is 10, and it costs 42.6K helium to make out.
This perk has a big impact on how you should play the game, so instead of reducing breed time as much as possible, you should try to make breed time match exactly how long it takes for your trips to die. This way you retain a 100% uptime but also get a good bonus from anticipation. Before zone 70, just try not to buy too many Nurseries, but once you unlock Geneticists, buy as many nurseries as you can and use Geneticists to bring up the breed time. This will mean that you can get lots of health bonus from the Geneticist.
Siphonology
For each level of Siphonology you can get a map bonus from maps 1 below your current level. The maximum level is 3 and costs 399K helium to fully upgrade.
The benefit of siphonology is that it makes it easier to get up to 200% damage bonus on your current zone, by enabling you to complete easier maps for the same rewards. This means you can save fragments by making fewer and/or lower level maps. This can also make it more viable to farm resources while getting the map bonus, as the optimal map farming zone is often a few lower that the current zone.