Alrighty, I've done a lot of searching, and information on this topic is scant, but I did manage to piece together a bit of a guide on how to control spawns.

FIRST: Go to your Game.ini file. In single player, you can find this at:

SteamApps\common\ARK\ShooterGame\Saved\Config\WindowsNoEditor

For servers, your server control panel might have the option to modify it directly.

To edit spawns, add a line with the following:
DinoSpawnWeightMultipliers=(DinoNameTag="[DINOTAG]",SpawnWeightMultiplier=0.1,OverrideSpawnLimitPercentage=True,SpawnLimitPercentage=1)

What each variable does

To my knowledge:

• DinoTag is a unique name for each dino. These are NOT their entity IDs! I have a list of them below.
  
• SpawnWeight is how likely a dinosaur is to spawn (so if you have 5 dinos and each one is at 0.1, each one has an equal weight)
  
• SpawnLimitPercentage affects the max population. Setting this lower means the cap is a portion of the 'natural limit.' It's a multiplier: 0.6 means its population is 60% of what it'd normally be.
  
• OverrideSpawnLimitPercentag I believe just means it uses the listed limit and not the global limit. If it's set to 'false' then the SpawnLimitPercentage value is not used, just weight.

You also only need 1 line per spawn you want to modify! If a dino doesn't have a line of code for their spawn, it'll just use the defaults.

As I said, information on this all is pretty scant. SpawnWeight I believe has the most drastic effect on spawns--it more affects the dinosaur's 'rarity'. SpawnLimit meanwhile controls their population. If something's too populous but you want it to stay common, reduce the limit. If something's too common and it needs to be more rare, reduce the weight.

This of course works for raising spawns as well.

So for instance, to turn down the population of mantas a bit, you could use:
DinoSpawnWeightMultipliers=(DinoNameTag="Manta",SpawnWeightMultiplier=0.1,OverrideSpawnLimitPercentage=True,SpawnLimitPercentage=0.6)

Updated 26 September 2016 with more accurate tags + Scorched Earth dinos

A dino tag is NOT the blueprint path/entity ID. (e.g., the BP path for an anklyo calls it an 'anklyo', while its tag is just 'anky'). These are dinstinct, shorthand names for each dino.

The most recent and accurate list of tags appears to be available at the following link:
http://ark.gamepedia.com/Creature_IDs

Check the 4th column, or see below:

[Dino Name] - [Dino Tag]

• Allosaurus - Allo
  
• Alpha Carno - Elite Carno
  
• Alpha Deathworm - Deathworm
  
• Alpha Fire Wyvern - Wyvern
  
• Alpha Mosasaurus - Mosasaur
  
• Alpha Raptor - Elite Raptor
  
• Alpha Rex - Elite Rex
  
• Angler - Angler
  
• Ankylosaurus - Anky
  
• Araneo - Spider
  
• Archaeopteryx -Archa
  
• Argentavis - Argent
  
• Arthropluera - Arthro
  
• Beelzebufo - Toad
  
• BunnyDodo - Dodo
  
• BunnyOviraptor - Ovi
  
• Brontosaurus - Bronto
  
• Broodmother Lysrix - N/A*
  
• Carbonemys -Turtle
  
• Carnotaurus - Carno
  
• Castoroides - Beaver
  
• Coelacanth - Coel
  
• Compsognathus - Compy
  
• Deathworm - Deathworm
  
• Dilophosaur - Dilo
  
• Dimetrodon - Dimetro
  
• Dimorphodon - Dimorph
  
• Diplodocus - Diplo
  
• Direbear - Direbear
  
• Direwolf - Direwolf
  
• Dodo - Dodo
  
• DodoRex - DodoRex**
  
• Doedicurus - Doed
  
• Dragon - N/A*
  
• Dung Beetle - Bettle
  
• Dunkleosteus - Dunkle
  
• Eurypterid - Euryp
  
• Gallimimus - Galli
  
• Giganotosaurus - Gigant
  
• Gigantopithecus - Bigfoot
  
• Ichthyosaurus - Dolphin
  
• Human (Male) - N/A*
  
• Human (Female) - N/A*
  
• Jerboa - Jerboa
  
• Jug Bug - Jugbug
  
• Oil Jug Bug - Jugbug
  
• Water Jug Bug - Jugbug
  
• Kairuku - Kairu
  
• Leech - Leech
  
• Diseased Leech - Leech
  
• Lymantria - Moth
  
• Lystrosaurus - Lystro
  
• Mammoth - Mammoth
  
• Manta - Manta
  
• Manticore - Manticore*
  
• Mantis - Mantis
  
• Megaloceros - Stag
  
• Megalodon - Mega
  
• Meganeura - Dragonfly
  
• Megapithecus - N/A*
  
• Mesopithecus - Monkey
  
• Morellatops - Camelsaurus
  
• Mosasaurus - Mosasaur
  
• Onychonycteris - Bat
  
• Oviraptor - Ovi
  
• Pachycephalosaurus - Pachy
  
• Paraceratherium - Paracer
  
• Parasaurolophus - Para
  
• Pelagornis - Pela
  
• Phiomia - Phiomia
  
• Piranha - Piranha
  
• Plesiosaur - Plesiosaur
  
• Procoptodon - Kangaroo
  
• Pteranodon - Ptera
  
• Pulmonoscorpius - Scorpion
  
• Quetzalcoatlus - Quetz
  
• Raptor - Raptor
  
• Rock Elemental - RockElemental
  
• Rubble Golem - RockElemental
  
• Sabertooth - Sabertooth
  
• Sabertooth Salmon - Salmon
  
• Sarcosuchus - Sarco
  
• Skeletal Brontosaurus - Bronto**
  
• Skeletal Stegosaurus - Stego**
  
• Skeletal Triceratops - Trike**
  
• Spinosaur - Spino
  
• Stegosaurus - Stego
  
• Tapejara - Tapejara
  
• Terror Bird - TerrorBird
  
• Thorny Dragon - SpineyLizard
  
• Super Turkey - N/A**
  
• Titanoboa - TitanBoa
  
• Titanomyrma - Ant
  
• Titanomyrma - Ant
  
• Titanosaur - Titan
  
• Triceratops - Trike
  
• Trilobite - Trilobite
  
• Tyrannosaurus Rex - Rex
  
• Vulture - Vulture
  
• Wyvern - Wyvern
  
• Fire Wyvern - Wyvern
  
• Lightning Wyvern - Wyvern
  
• Poison Wyvern - Wyvern
  
• Woolly Rhino - Rhino
  
• Yeti - Bigfoot
  
• Zomdodo - Dodo**

*either a boss or not something you can encounter in the wild
**only spawns during certain events
Creatures that share a dino tag with a variant are italicized

One other small thing: If you use Ark Server Launcher, after you add in a line to the config file manually, you can load your ini file from your server into ASL. It'll update the dino spawns list so you can now modify that variable you added from the GUI. Nifty!

If anyone has any updated or more accurate information, please share and I'll update the guide.

Also,
credit to Lupen for the image of the Dunkle horde.