Resource Gathered Settler / Native / Asian Resources per Sec Dutch Settler Resources per Sec Coureur Resources per Sec[1] Settler Wagon Resources per Sec Pilgrim Building Equivalent Villagers Equivalent Dutch Villagers[2]
Berries 0.67 ---- 0.83[3] 1.34 0.70 Bank 4.6 4.0
Coin (Mine) 0.60 0.69 0.74[4] 1.20 0.65 Bank with "Tulip Speculation" 5.3 4.6
Coin (Plantation) 0.50 ---- 0.63 1.00 0.55 Factory (select resource below) 9.2 8.0
Coin (Rice Paddy) 0.34 ---- 0.43 0.68 0.37 Upgraded factory (+30% selected res.)[5] 11.9 10.4
Crates 8.00 ---- 10.00 20.00[6] 8.00
Export (gather passively if tasked to a resource)[7] 0.03 ---- 0.04 0.06 0.03 Factory Set To: Coin
Farm (Mill) 0.67[8] ---- 0.84 1.34 0.70
Farm (Native Farm) 0.50 ---- 0.63 1.00 0.55 Resources gathered per sec for calculating villager second costs
Farm (Rice Paddy) 0.50 ---- 0.63 1.00 0.55 Resource Resource Type Base Rate / Sec + % Rate Rate / Sec
Fishing (coin) - Canoe, Tlaloc Canoe, Marathan Catamaran, War Canoe 0.17 ---- ---- ---- ----  
Coin Gather Rate Mining 0.60 0% 0.60
Fishing (coin) - Fishing Ship, Caravel, Galley, Fune, War Junk 0.50[9] ---- ---- ---- ---- Food Gather Rate Berries / Cherries 0.67 0% 0.67
Wood Gather Rate Tree 0.50 0% 0.50
Fishing (food) - Canoe, Tlaloc Canoe, War Canoe, Marathan Catamaran 0.22 ---- ---- ---- ---- Fishing - Whaling (canoe, etc.) Berries / Cherries Coin
Fishing - Whaling (fishing boat) Farm Food
Fishing (food) - Fishing Ship, Caravel, Galley, Fune, War Junk 0.67 ---- ---- ---- ---- Mining Fishing (canoe, etc.) Tree Wood
Mining - Dutch Fishing (fishing boat) Mango Grove
Herdables - Europeans (sheep, cow, etc.) 2.00 ---- 2.50 4.00 2.20 Plantation Hunting
Herdables - Fulling Mills (British - 300%) 6.00 ---- ---- ---- ---- Rice Paddy Mill
Herdables - Natives (sheep, cow, etc.) 1.25 ---- ---- ---- ---- Rice Paddy
Herdables - Fulling Mills (Iroquois - 300%) 3.75 ---- ---- ---- ----
Hunting 0.84[10] ---- 1.04[11] 1.70[12] 0.88
Trade (Export) 0.03 ---- 0.04[13] 0.06 0.03
Tree / Grove (Wood) 0.50 ---- 0.62[14] 1.00 0.55
Animal Decay Rate 0.75 ---- ---- ---- ----
Auto Building Gather Rate Resources per Sec Coureur 25%
Bank 2.75 Settler Wagon 200%
Bank with "Tulip Speculation" 3.16
Factory (all resources) 5.50
Upgraded factory (30% all resources)[15] 7.15
Villager seconds available while constantly creating villagers can be calculated by using the following formula.
   
The formula below was for AoK: For a vs. villager start, the formula is:[16]  
an = T(n2 + (n(5-n))/2) an = T(n2 + (n([5+sv]-n))/2)  
   
an  = number of villager seconds when the n villager was created (assumes constant villager production)  
n = total number of villagers created (does not include starting villagers)  
sv = number of starting villagers  
T = Villager training time (25 settlers, 29 Coureur, etc.)  
   
  Villager Type Settler / Villager Configure Reduction in Res Gather 0% 0%
  Villager Train Points (T) 25 Effect of Reduction to Export Bonus 0% 5%
  Number of starting villagers (sv) 5 Export Generated (Export / Sec) 0.03 10%
  Number of villagers created 7 Settler / Villager  
  Total villagers 12 Food gathered Coureur  
  Time to create villagers (min) 2.92[17] 1249.5  
  Villager Seconds Available (an) 1,488 Food after Age-Up  
  Approximate Export Passively Gathered[18] 45 449.5  
   
EXAMPLE 1:  
A ~3:20 minute Discovery (8 villagers created at 25 train points with a start of 6) will have 1,900 villager seconds available upon researching Colonial.  The French, starting with 5 villagers and creating 7 more at 29 seconds apiece comes to 1,726.  The coureur's gather ~25% faster so approximately 2,157 villager seconds are produced in same time.  For example, the extra 431 more villager seconds can produce 216 more wood.  Walking to the resource, building buildings, etc. must also be taken into consideration when calculating total resources with a certain amount of villager seconds available (Coureurs are also 0.5 faster).  
   
EXAMPLE 2:  
The British start with 6 villagers (25 second spawn time) and a 300 food crate.  In order to click the age up button at 2:30 (age at 4:00), a total of 6 villagers can be created at the TC in approximately 2:30.  It actually takes a few seconds before the first villager can be spawned due to the fact the crates must be collected first.  Therefore, a 4:00 minute Colonial time is impossible but can be very close.  Also, the British will spawn a villager by building a house with the first wood.  This is almost like an extra starting villager but difficult to calculate with many unknown variables.  
               
Miscellaneous Notes:
1 Coureur des bois harvest ~25% faster than a regular settler.  Since the coureur cost 29 train points, 2 less than 31 as expected (25 * 125% = 31.25), a marginally better economy is the result (see calculator below).  The real advantage is using the Coureur villager cards since 3 and 4 are available early.
2 Settler Wagons harvest ~200% faster than a regular settler and only count as 1 settler at a mill or plantation (max limit on mill or plantation is 10).  Therefore, use settler wagons on mills and plantations to maximize space and the amount of mills / plantations required.  
3 1 Train Point = 1 Build Point = 1 Second (in Medium Speed Game)
4 Plantation production goes down with more villagers because they bump into each other while walking around.  A similar effect exists for all resources.  When more villagers are assigned to a resource, the resource is consumed faster, and each villager spends more time walking to the next source.  Therefore, 1 villager per hunt resource harvest faster than all villagers on 1 or 2 resources.  Of course as noted in the Resource Rate Herdables worksheet, the herd will be depleted faster, as carcass rot is increased.
5 It takes 2 seconds to convert the factory from one resource to another.  
6 In order to get a complete list of resource related home city shipments, go to the "Home City Shipments - Natives" Worksheet or "Home City Shipments - European" Worksheet and use the filter buttons located at the top of the spreadsheet and filter either "Wise Woman" or "Manufacturing Plant" respectively.  This will show all available home city shipments for the Wise Woman or Manufacturing Plant (resource related).  The filter can then be refined to civilization by selecting "Yes" under the respective Civilization.
7 The reason native ships (with the exception of the fishing boat), gather slower than the European Caravel / Galley, is because they are ~ 1/4 cheaper and have a larger build limit.  It is fair they gather fish and whale at a reduced rate.  Keep in mind that only 4 ships can gather at any whale and 8 at any fishing location.
8 Native villagers gather food from the farm and herdables slower than their European counterparts on a mill / herdable.  This is balanced by the fact that Native civilizations can obtain farms much earlier economically (travois) than Europeans can obtain Mills.  In addition, villagers on a farm spend more time gathering and less walking than on a mill (bumping into each other).  It is difficult to compare what is actually happening in game.
9 Despite the proto file stating that Native Farms gather slower than Mills, they are actually equal.  A test was performed with 1 villager on a Mill for 1 minute and the food gathered was 30.  The same value was collected for one Native villager on a Farm in a minute time frame.  Therefore, the Europeans spend a lot more time walking around on the Mill.  To further verify this, a Native was placed on a European Mill and a European was placed on a Native Farm, the food collected in both instances was 30,
Native Food Farm in 1 Min 30
Native Food Mill in 1 Min 30
European Food Farm in 1 Min 30
European Food Mill in 1 Min 30[19]
10 A bank, with 2.75 gold resource collection per second is equivalent to approximately 4.6 standard villagers or 4 Dutch villagers on mines with no upgrades.  Since they cost 700 resources, it may be more profitable to invest in villagers initially.  

[1]
NOTE:
Also Coureur Cree
[2]
NOTE:
Dutch villagers gather gold from mines faster, so these buildings are not as effective. 
[3]
NOTE:
Calculated value (+25%) is 0.84.  This is 0.01 worse than anticipated.
[4]
NOTE:
Calculated value (+25%) is 0.75.  This is 0.01 worse than anticipated.
[5]
NOTE:
Includes Factory Cannery (30% Food), Factory Steam Power (30% Gold), and Factory Water Power (30% Wood)
[6]
NOTE:
Calculated value (+200%) is 16.00.  This is 4.00 better than anticipated.
[7]
NOTE:
<Rate type ='Trade'>0.030000</Rate>

After allying with a civilization, the consulate can be configured to generate additional export.  A 5% reduction in all resource generation generates a 35% increase in export.  A 10% reduction boosts export by 65%
[8]
NOTE:
The AOE3 proto file states the Mill gathering rate is 0.67 food per second per villager.  However, due to villager inefficiencies, the actual rate of food gathering is the same as on a farm at 0.5 food per second.  See the in-game testing discussed in the #9 comment below.
[9]
NOTE:
Excessive Taxation increases this amount by 1.5.  Total of 2 gold per second. 
[10]
NOTE:
For example, 10 settlers for 1 minute will collect 504 food while hunting (not including walking time [= 10*0.84*60].
[11]
NOTE:
Calculated value (+25%) is 1.05.  This is 0.01 worse than anticipated.
[12]
NOTE:
Calculated value (+200%) is 1.68.  This is 0.02 better than anticipated.
[13]
NOTE:
Calculated value (+25%) is 0.0375.  This is 0.0025 better  than anticipated.
[14]
NOTE:
Calculated value (+25%) is 0.63.  This is 0.01 worse than anticipated.
[15]
NOTE:
Includes Factory Cannery (30% Food), Factory Steam Power (30% Gold), and Factory Water Power (30% Wood)
[16]
Note:
For example:  If you start with 6 villagers, the formula is:
an = 25(n2 + (n(11-n))/2)
[17]
Note:
Convert this to time by multiplying the decimal by 60 (seconds).  For example, 3.33 would be 3:20
[18]
NOTE:
See the worksheet "Consulate Summary" for more details. 
[19]
NOTE:
Spend a lot of time walking around.  The expected value is 40.2.