Population Size of a Colony With a Large Gender Disparity

Question

This is my first post on this site, so please bear with me.

I am working on a series of stories about an interstellar colony with a large gender disparity. Namely the initial population was made up of 120 mature males and 1080 mature females. In an effort to provide genetic diversity tens of thousands of fertilized frozen eggs were included on the ships, all of them female. As a result every female colonist is expected to have at least 12 children during their adult years. Of these pregnancies 9 of the children have to be implanted female embryos. The other 3+ children would be conceived naturally, with those pregnancies being interspersed with those of the implanted ones. This in turn makes the birth ratio of roughly 1 male per 8 births.

The percentage of children who survive to adulthood is 94% female and 99.9% male (males are too precious to allow them to take any risks). Furthermore due to the colonial nature of the planet life expectancy is lower than would be expected considering their advanced medical technology. Therefore I set the death rate to 12.5 out of every 1000 colonists per earth year.

To add even more complexity the ships returned 54 earth years later with a second wave of colonists. That wave had the exact same makeup as the first.

Whilst I have found a number of calculators and articles on exponential growth rate none of them seem to take gender ratios into account. They all seem to assume that there are an equal number of males to females, which is definitely not the case here.

The short story I am currently writing takes place 207 earth years after the initial colonization and I need to get an idea of the planets population size at that point in time. Even a rough estimate (within a few thousand) would do.

Thank you all very much for your time, consideration and aid. I hope that you have a wonderful day.

Arkham

Edits:

Many people have asked why the rush to populate the planet so quickly. The answer is that archaeological evidence was found showing that an attempted alien invasion of earth took place in the year 400 CE and that another invasion could take place at any time. This secret has lead the world governments (in the form of the Grand Alliance) to begin a massive colonization effort, first within the Solar System and then to another star system. After all all of humanity was located in one place and the governments wanted to get all of their eggs out of one basket.

This particular star system has multiple planets which are much easier to terraform than Mars. As a result the Alliance government has decided to colonize all of them quickly. This effort in turn will need a fairly sizeable population base, hence the forced breeding process.

Many have also suggested that 12 children per woman is unrealistic and that women would be overwhelmed. For this I am drawing from my own family history. On my mothers side of the family my grandmother was one of 12 children and my grandfather was one of 13 (it would have been 14 but one died in infancy). Note that this took place in the 1920s in rural Virginia USA and my grandparents told me repeatedly that large families like theirs was the norm and not the exception when they were growing up.

In addition the older children helped to raise the younger ones. I will never forget my grand uncle telling my mother at my grandfather’s funeral that my grandfather had been like a second father to him. In my own immediate family my brother was 10 years older than I was and he often took care of me and my sister when our parents were busy.

Finally all of the wives in the group marriages would not be the same age. Since men can sire children their entire adult lives they can father children well into their old age. Both the oldest wives and the youngest ones (who have not yet started having children themselves) would help with the raising of the children of those of childbearing age. Both my aunt and my grandmother would watch me and my sister when we were young. This would be a similar situation.

This arrangement would not be a happy one for the males either. By the end of the second generation men will have lost their human rights and be viewed as property, first by their mothers and later their wives. Men would have little or no say as to who they marry and would be “sold” to their wives in the form of a dowry. Of course their mother would get a cut of later dowrys even after the males are married off. Of course the male wouldn’t see any of the money.

In fact the males would not even have a room of their own, rotating from household to household at an interval agreed upon in the marriage contracts. They would then stay in their wife’s room while staying in that household.

Some have pointed out that the colonists would eventually run out of frozen embryos. This would not be the case since the embryos would be split in a process known as artificial twinning. This process, currently used in livestock rearing, essentially makes clones by splitting embryos. While this process is currently limited to 4 to 6 splits depending on the species involved the process should be better understood by the 22nd century when the first colony ship is launched.

While this does not answer every questions asked thus far I hope that it helps to clarify things and shed light on my thinking process. Thank you all once again for your aid in this matter and have a great day.

Arkham

My final solution:

I'm sorry for taking so long to get back to this question, but I have been working on rewriting Ash's code for various scenarios (Thank you again Ash!). Then after running the numbers I had to think of a way to make things fit into the stories without leaving plot holes large enough to fly a star-ship through.

After taking everyone’s suggestions into account this is what I was able to come up with:

First of all I decided that there would be no new births for the first 5 years while the colony is first becoming established. That should allow them to get the basic farms up and running as well as find clay (and build kilns) for bricks and calcium carbonate for mortar / concrete, etc. While one story brick houses might be primitive by their standards they would be enough to meet basic housing needs once the colony grows beyond the size that the initial colonist's prefab aluminum / titanium dwellings can hold.

In addition after everyone's input I dropped the initial number of children from 12 to 9 (2 natural, 7 implanted) then slowly decreased over the next 3 generations as follows:

2nd Generation 7 (2 natural, 5 implanted)

3rd Generation 6 (2 natural, 4 implanted)

4th Generation 5 (2 natural, 3 implanted)

There was no 5th generation of implanted since they ran out of embryos even though I upped the number of embryos in both waves to 100,000 each.

Note: Each generation was considered to be 25 earth years long.

After this point 3 natural births per woman were expected. Any births less then 3 per female causes the colony to shrink fairly rapidly due to the mortality rate.

The second wave of colonization in the 54th year after the first was set up as a separate community over 100 kilometres from the nearest established settlement. This was done at the new colonists request due to differing “customs.” Close enough to interact by air and via communications, but far enough away (at first at least) for the new colonists to adjust. This second “colony” used the same model as the first. Their numbers were just calculated for 153 earth years as opposed to 207. That population was simply added to the initial colony's population to get the total population.

Here are some quick early population totals for the colony (in earth years):

Year 1: 1,200

Year 6: 2,236

Year 10: 3,204

Year 15 : 4,974

Year 20: 6,624

Year 25: 7,296

Year 30: 8,966

Taking everyone’s input into account this should be a much more reasonable rate of growth for the early colony while still allowing for fast overall growth.

---

Initial colony numbers after 207 earth years:

Total 1,450,891

Infants 168,954

Children 237,493

Teens 200,892

Young Adults 332,063

Adults 353,629

Seniors 157,860

Males 742,073

Females 708,818

---

“Second” colony numbers after 153 earth years:

Total 779,788

Infants 88,944

Children 135,453

Teens 118,528

Young Adults 177,205

Adults 194,641

Seniors 65,017

Males 385,670

Females 394,118

---

Combined Totals:

Total 2,230,679

Infants 257,898

Children 372,946

Teens 319,509

Young Adults 509,268

Adults 548,270

Seniors 222,877

Males 1,127,743

Females 1,102,936

Finally I wanted to thank everyone for their help and guidance in answering this question. While I'm pretty good with the astronomy aspects I'm not that great at population growth calculations. Thank you all for making the new guy feel welcome.

P.S. If any of you are interested in the system this is based on here is a link to a computer animation I did in late 2013 - early 2014 (Yeah I've been working on these stories a LONG time). Please note that this was before they actually started detecting planets in the system and thus while the information presented was calculated using Kepler's laws and the like all of the data is fictional. In case you are wondering the planet in question is "Coopers World." Oh and If you want to read all of the data as it flashes on the screen remember that the pause button is your friend. :)

https://www.youtube.com/watch?v=0ujx2ASqgAg

Answer 1

354 Thousand https://godbolt.org/z/zoPYsz

If you bring 10,000 embryos on the first ship, and 10,000 on the second ship, you'll run out in the 25th year, and 58th year.

I modified your death rate so that when people hit 70 years old it shot up to 10% per year. As otherwise we had hundreds of 100 year olds.

That link allows you to change the values and they should update the simulation in the output window. I'm sorry its in C++, its the only language I know really well.

• Total 354,102
• Infants 39,882
• Children 53,934
• Teens 49,704
• YoungAdults 79,456
• Adults 91,140
• Seniors 39,986
• Males 181,138
• Females 172,964

In the year 207, there are 16 males and 13 females turning 100 years old. There are 8300 babies born that year.

The year 58 had 6135 females and 1152 males born. Birth rates dropped for the next 100 years, until the year 131, (7600 births).

What would really happen?

Each woman has 12 direct children, the father, grandma, and grandfather are spread to thin to help (they'd have to help raise: 96 children, 240 children, and 9216 children respectively). This is just too much.

They're going to revolt

I'm not a woman so I'm not 100% sure on this, but I have a sneaking suspicion they don't like being used as baby factories and forced to raise 12 kids (essentially alone - remember the "husband" has 8 other women in his polycule). The first generation might be optimistic, but mental health would be a real issue, there'd be anger and resentment, but the second generation, born in the first few years and about to be implanted on their 18th birthday will not share that optimism, and you'll have a suffragette movement around about year 20.

... If a woman refuses to be a baby factory are we really going impregnate her against her will?

There's a whole bunch of LGBT issues also not considered here.

... And starve

Farming is going to be a real issue, take year 15 as an example:

There will be:

• Infants 2682
• Children 6749
• Teens 853 (13 and 14 year old)
• Adults 984 (90 males and 894 females)

Those 900 woman are going to be fully occupied nursing 3 infants each, and yelling discipline at 7 misbehaving children. Assuming all the men are farmers, they're going to need to grow food for 11,000 people, 122 mouths to feed each. With current American tech they can hit 166 mouths fed per farmer. You've regressed tech for this (for the infant mortality figure), so I've got to assume farming has as well. In postwar american, 1 Farmer feeds 73 people. Putting the tweens and children in the field may put starvation off a bit, but they need to be in school, otherwise you're society is going to regress very quickly, and you'll be illiterate within a few generations.

Edit: actually that 1 in 73 assumes theres people refining fuel, making fertilizers and pesticides, making replacmenet parts, and spitting out new machinery at an exponential rate. That's not going to happen as everyone is busy making babies or growing food. You'll regress to 1930s level farm output, which is 1 farmer per 4 mouths.

... and die of exposure

The growth rate in the number of buildings is also extreme.

Each male in the first 60 years has to build 80 houses in their lifetime (one for each of his partners daughters), each house has to hold a family of up to 14 (most 13, but the males need to live somewhere too). That's a lot to build, remember he's making his own nails, cutting his own logs, etc, all while farming food for 122 people.

So slow the implantation down

Embryos can be stored for a while, so no need to implant them ASAP. Changing the requirements to 3 natural children, and 3 embryos (so 6 children total per woman) the population at year 207 is 345,000.

I wrote a calculator for this:

https://godbolt.org/z/zoPYsz

The panel on the left is C++ code, the pannel on the right is the output.

Just change the numbers on the left (eg what years do women have children), and the log will update on the right.

Here's the source if the link goes dead (C++17)

#include <vector>
#include <set>
#include <iostream>
#include <numeric>

int main()
{
    // There are 0 children aged 0 to 17 on the first ship
    std::vector<size_t> males(18,0);
    std::vector<size_t> females(18,0);

    // Our initial colonists
    males.push_back(120);
    females.push_back(1080);

    auto survivalRateMaleChild = 0.99;
    auto survivalRateFemaleChild = 0.94;
    auto survivalRateEveryone = (1000.0 - 12.0) / 1000.0;

    auto simulatedYears = 207;

    // What years of her life does a given woman have children?
    std::set<int> randomChildAt = {19, 25, 35};
    std::set<int> femaleChildAt = {21, 22, 23, 24, 26, 27, 28, 29, 30};
    
    // Finite number of embryos
    auto embryos = 10000;

    for (auto year = 0; year < simulatedYears; year++)
    {
        // Calculate our births

        size_t newMales = 0;
        size_t newFemales = 0;

        if (embryos > 0)
        {
            for (auto i : femaleChildAt)
            {
                if (i >= females.size()) continue;
                newFemales += females[i];
            }
        }
        embryos -= newFemales;

        if (embryos < 0 && newFemales)
        {
            std::cout << "Run out of embryos\n";
        }

        for (auto i : randomChildAt)
        {
            if (i >= females.size()) continue;
            newFemales += females[i] / 2;
            newMales += females[i] / 2;
        }

        males.insert(males.begin(), newMales);
        females.insert(females.begin(), newFemales);

        // Kill off our infant mortality children (they all die at age 5)
        males[5] *= survivalRateMaleChild;
        females[5] *= survivalRateFemaleChild;

        // Kill of our random death rate. Child infant mortality is
        // calcualted seperately, we don't want to double kill them.
        for (auto age = 18; age < females.size(); age++)
        {
            females[age] *= survivalRateEveryone;
            males[age] *= survivalRateEveryone;
        }

        // Kill of our seniors, 10% die per year
        for (auto age = 70; age < females.size(); age++)
        {
            females[age] *= 0.90;
            males[age] *= 0.90;
        }

        // Add the second ship, which is full of 18 year olds.
        if (year == 57)
        {
            males[18] += 120;
            females[18] += 1080;
            embryos += 10000;
        }

        // Print some stats

        std::cout << 
            "Y: " << year << ". " 
            << newMales << "m and " 
            << newFemales << "f born. Pop: "
            << std::accumulate(males.begin(), males.end(), 0) +
            std::accumulate(females.begin(), females.end(), 0) << "\n";
    }


    std::cout << "At end of simulation: \n";

    size_t total = 0;
    size_t infants = 0;
    size_t children = 0;
    size_t teenages = 0;
    size_t youngAdults = 0;
    size_t adults = 0;
    size_t seniors = 0;
    size_t male = 0;
    size_t female = 0;
    for (auto age = 0; age < 100; age++)
    {
        if (age >= females.size()) continue;
        std::cout << age << " yr olds: " << males[age] << " males and " << females[age] << " females.\n";
    
        auto t = males[age] + females[age];
        
        male += males[age];
        female += females[age];

        if (age < 5) infants += t;
        else if (age < 13) children += t;
        else if (age < 20) teenages += t;
        else if (age < 35) youngAdults += t;
        else if (age < 60) adults += t;
        else seniors += t;

        total += t;
    }

    std::cout << "Total " << total << "\n";
    std::cout << "Infants " << infants << "\n";
    std::cout << "Children " << children << "\n";
    std::cout << "Teens " << teenages << "\n";
    std::cout << "YoungAdults " << youngAdults << "\n";
    std::cout << "Adults " << adults << "\n";
    std::cout << "Seniors " << seniors << "\n";

    std::cout << "Males " << male << "\n";
    std::cout << "Females " << female << "\n";
    return 0;
}

Year by year running log of births and population

Y: 0. 0m and 0f born. Pop: 1185
Y: 1. 533m and 533f born. Pop: 2236
Y: 2. 0m and 0f born. Pop: 2221
Y: 3. 0m and 1041f born. Pop: 3247
Y: 4. 0m and 1028f born. Pop: 4260
Y: 5. 0m and 1015f born. Pop: 5260
Y: 6. 0m and 1002f born. Pop: 6209
Y: 7. 494m and 494f born. Pop: 7183
Y: 8. 0m and 977f born. Pop: 8083
Y: 9. 0m and 965f born. Pop: 8972
Y: 10. 0m and 953f born. Pop: 9850
Y: 11. 0m and 941f born. Pop: 10716
Y: 12. 0m and 929f born. Pop: 11596
Y: 13. 0m and 0f born. Pop: 11523
Y: 14. 0m and 0f born. Pop: 11452
Y: 15. 0m and 0f born. Pop: 11381
Y: 16. 0m and 0f born. Pop: 11311
Y: 17. 436m and 436f born. Pop: 12114
Y: 18. 0m and 0f born. Pop: 12101
Y: 19. 0m and 0f born. Pop: 12075
Y: 20. 0m and 0f born. Pop: 12050
Y: 21. 244m and 244f born. Pop: 12502
Y: 22. 0m and 0f born. Pop: 12422
Y: 23. 477m and 953f born. Pop: 13793
Y: 24. 471m and 941f born. Pop: 15134
Run out of embryos
Y: 25. 465m and 1859f born. Pop: 17375
Y: 26. 458m and 458f born. Pop: 18178
Y: 27. 452m and 452f born. Pop: 18981
Y: 28. 447m and 447f born. Pop: 19700
Y: 29. 884m and 884f born. Pop: 21284
Y: 30. 872m and 872f born. Pop: 22778
Y: 31. 862m and 862f born. Pop: 24336
Y: 32. 850m and 850f born. Pop: 25870
Y: 33. 208m and 208f born. Pop: 26123
Y: 34. 414m and 414f born. Pop: 26766
Y: 35. 410m and 410f born. Pop: 27391
Y: 36. 404m and 404f born. Pop: 28005
Y: 37. 796m and 796f born. Pop: 29405
Y: 38. 394m and 394f born. Pop: 30047
Y: 39. 389m and 389f born. Pop: 30660
Y: 40. 384m and 384f born. Pop: 31263
Y: 41. 490m and 490f born. Pop: 32061
Y: 42. 374m and 374f born. Pop: 32593
Y: 43. 803m and 803f born. Pop: 33984
Y: 44. 796m and 796f born. Pop: 35349
Y: 45. 1213m and 1213f born. Pop: 37536
Y: 46. 565m and 565f born. Pop: 38408
Y: 47. 660m and 660f born. Pop: 39463
Y: 48. 551m and 551f born. Pop: 40248
Y: 49. 809m and 809f born. Pop: 41531
Y: 50. 798m and 798f born. Pop: 42743
Y: 51. 1186m and 1186f born. Pop: 44722
Y: 52. 582m and 582f born. Pop: 45491
Y: 53. 445m and 445f born. Pop: 45991
Y: 54. 378m and 378f born. Pop: 46338
Y: 55. 562m and 562f born. Pop: 47047
Y: 56. 554m and 554f born. Pop: 47708
Y: 57. 818m and 818f born. Pop: 50134
Y: 58. 541m and 4677f born. Pop: 54932
Run out of embryos
Y: 59. 1152m and 6135f born. Pop: 61797
Y: 60. 701m and 701f born. Pop: 62763
Y: 61. 1095m and 1095f born. Pop: 64500
Y: 62. 507m and 507f born. Pop: 65036
Y: 63. 871m and 871f born. Pop: 66047
Y: 64. 694m and 694f born. Pop: 66606
Y: 65. 1545m and 1545f born. Pop: 69192
Y: 66. 744m and 744f born. Pop: 70142
Y: 67. 830m and 830f born. Pop: 71293
Y: 68. 725m and 725f born. Pop: 72199
Y: 69. 784m and 784f born. Pop: 73214
Y: 70. 856m and 856f born. Pop: 74303
Y: 71. 1209m and 1209f born. Pop: 76098
Y: 72. 653m and 653f born. Pop: 76780
Y: 73. 779m and 779f born. Pop: 77663
Y: 74. 550m and 550f born. Pop: 78045
Y: 75. 1182m and 1182f born. Pop: 79646
Y: 76. 733m and 733f born. Pop: 80237
Y: 77. 1058m and 1058f born. Pop: 81416
Y: 78. 2528m and 2528f born. Pop: 85495
Y: 79. 3300m and 3300f born. Pop: 91098
Y: 80. 777m and 777f born. Pop: 91590
Y: 81. 1193m and 1193f born. Pop: 92929
Y: 82. 675m and 675f born. Pop: 93190
Y: 83. 991m and 991f born. Pop: 93984
Y: 84. 2514m and 2514f born. Pop: 97801
Y: 85. 3625m and 3625f born. Pop: 104035
Y: 86. 935m and 935f born. Pop: 104873
Y: 87. 1289m and 1289f born. Pop: 106431
Y: 88. 761m and 761f born. Pop: 106942
Y: 89. 892m and 892f born. Pop: 107606
Y: 90. 825m and 825f born. Pop: 108071
Y: 91. 1419m and 1419f born. Pop: 109902
Y: 92. 818m and 818f born. Pop: 110519
Y: 93. 1014m and 1014f born. Pop: 111492
Y: 94. 2322m and 2322f born. Pop: 115018
Y: 95. 3188m and 3188f born. Pop: 120184
Y: 96. 959m and 959f born. Pop: 120792
Y: 97. 1408m and 1408f born. Pop: 122265
Y: 98. 1623m and 1623f born. Pop: 124147
Y: 99. 2168m and 2168f born. Pop: 126967
Y: 100. 847m and 847f born. Pop: 127044
Y: 101. 1628m and 1628f born. Pop: 128796
Y: 102. 897m and 897f born. Pop: 128979
Y: 103. 1212m and 1212f born. Pop: 129751
Y: 104. 2498m and 2498f born. Pop: 133069
Y: 105. 3360m and 3360f born. Pop: 138194
Y: 106. 1076m and 1076f born. Pop: 138709
Y: 107. 1549m and 1549f born. Pop: 140200
Y: 108. 875m and 875f born. Pop: 140326
Y: 109. 1118m and 1118f born. Pop: 140784
Y: 110. 1650m and 1650f born. Pop: 142267
Y: 111. 2638m and 2638f born. Pop: 145891
Y: 112. 1043m and 1043f born. Pop: 146277
Y: 113. 1408m and 1408f born. Pop: 147364
Y: 114. 2338m and 2338f born. Pop: 150270
Y: 115. 3084m and 3084f born. Pop: 154552
Y: 116. 1078m and 1078f born. Pop: 154738
Y: 117. 1695m and 1695f born. Pop: 156234
Y: 118. 1340m and 1340f born. Pop: 157007
Y: 119. 1793m and 1793f born. Pop: 158581
Y: 120. 2322m and 2322f born. Pop: 161157
Y: 121. 3470m and 3470f born. Pop: 166111
Y: 122. 1167m and 1167f born. Pop: 166396
Y: 123. 1637m and 1637f born. Pop: 167614
Y: 124. 2118m and 2118f born. Pop: 169794
Y: 125. 2797m and 2797f born. Pop: 173291
Y: 126. 1160m and 1160f born. Pop: 173447
Y: 127. 1934m and 1934f born. Pop: 175290
Y: 128. 1087m and 1087f born. Pop: 175195
Y: 129. 1406m and 1406f born. Pop: 175387
Y: 130. 2693m and 2693f born. Pop: 178162
Y: 131. 3842m and 3842f born. Pop: 183353
Y: 132. 1293m and 1293f born. Pop: 183435
Y: 133. 1831m and 1831f born. Pop: 184628
Y: 134. 2052m and 2052f born. Pop: 186271
Y: 135. 2704m and 2704f born. Pop: 189062
Y: 136. 1512m and 1512f born. Pop: 189424
Y: 137. 2511m and 2511f born. Pop: 191965
Y: 138. 1392m and 1392f born. Pop: 192236
Y: 139. 1875m and 1875f born. Pop: 193417
Y: 140. 2999m and 2999f born. Pop: 196814
Y: 141. 4172m and 4172f born. Pop: 202595
Y: 142. 1395m and 1395f born. Pop: 202764
Y: 143. 2052m and 2052f born. Pop: 204309
Y: 144. 1866m and 1866f born. Pop: 205478
Y: 145. 2463m and 2463f born. Pop: 207728
Y: 146. 2138m and 2138f born. Pop: 209263
Y: 147. 3357m and 3357f born. Pop: 213413
Y: 148. 1382m and 1382f born. Pop: 213376
Y: 149. 1868m and 1868f born. Pop: 214041
Y: 150. 3015m and 3015f born. Pop: 217020
Y: 151. 4115m and 4115f born. Pop: 222220
Y: 152. 1489m and 1489f born. Pop: 222131
Y: 153. 2299m and 2299f born. Pop: 223795
Y: 154. 1903m and 1903f born. Pop: 224499
Y: 155. 2511m and 2511f born. Pop: 226080
Y: 156. 2713m and 2713f born. Pop: 228055
Y: 157. 4096m and 4096f born. Pop: 232993
Y: 158. 1624m and 1624f born. Pop: 232977
Y: 159. 2253m and 2253f born. Pop: 234239
Y: 160. 3044m and 3044f born. Pop: 237092
Y: 161. 4118m and 4118f born. Pop: 242053
Y: 162. 1717m and 1717f born. Pop: 242162
Y: 163. 2737m and 2737f born. Pop: 244489
Y: 164. 1853m and 1853f born. Pop: 244869
Y: 165. 2455m and 2455f born. Pop: 246181
Y: 166. 3272m and 3272f born. Pop: 249116
Y: 167. 4766m and 4766f born. Pop: 255204
Y: 168. 1710m and 1710f born. Pop: 255074
Y: 169. 2417m and 2417f born. Pop: 256290
Y: 170. 2948m and 2948f born. Pop: 258612
Y: 171. 3954m and 3954f born. Pop: 262866
Y: 172. 2159m and 2159f born. Pop: 263481
Y: 173. 3430m and 3430f born. Pop: 266861
Y: 174. 1981m and 1981f born. Pop: 267155
Y: 175. 2650m and 2650f born. Pop: 268513
Y: 176. 3658m and 3658f born. Pop: 271891
Y: 177. 5205m and 5205f born. Pop: 278496
Y: 178. 1900m and 1900f born. Pop: 278446
Y: 179. 2783m and 2783f born. Pop: 280252
Y: 180. 2907m and 2907f born. Pop: 282257
Y: 181. 3885m and 3885f born. Pop: 286016
Y: 182. 2745m and 2745f born. Pop: 287447
Y: 183. 4266m and 4266f born. Pop: 292152
Y: 184. 2058m and 2058f born. Pop: 292271
Y: 185. 2785m and 2785f born. Pop: 293619
Y: 186. 3933m and 3933f born. Pop: 297289
Y: 187. 5492m and 5492f born. Pop: 304145
Y: 188. 2072m and 2072f born. Pop: 304075
Y: 189. 3138m and 3138f born. Pop: 306233
Y: 190. 2855m and 2855f born. Pop: 307707
Y: 191. 3804m and 3804f born. Pop: 310799
Y: 192. 3404m and 3404f born. Pop: 313075
Y: 193. 5150m and 5150f born. Pop: 319083
Y: 194. 2245m and 2245f born. Pop: 319144
Y: 195. 3091m and 3091f born. Pop: 320760
Y: 196. 4080m and 4080f born. Pop: 324370
Y: 197. 5624m and 5624f born. Pop: 331087
Y: 198. 2435m and 2435f born. Pop: 331364
Y: 199. 3769m and 3769f born. Pop: 334521
Y: 200. 2872m and 2872f born. Pop: 335699
Y: 201. 3833m and 3833f born. Pop: 338495
Y: 202. 4051m and 4051f born. Pop: 341704
Y: 203. 5973m and 5973f born. Pop: 348982
Y: 204. 2394m and 2394f born. Pop: 348960
Y: 205. 3370m and 3370f born. Pop: 350811
Y: 206. 4153m and 4153f born. Pop: 354227

And breakdown of those alive at year 207:

0 yr olds: 4153 males and 4153 females.
1 yr olds: 3370 males and 3370 females.
2 yr olds: 2394 males and 2394 females.
3 yr olds: 5973 males and 5973 females.
4 yr olds: 4051 males and 4051 females.
5 yr olds: 3794 males and 3603 females.
6 yr olds: 2843 males and 2699 females.
7 yr olds: 3731 males and 3542 females.
8 yr olds: 2410 males and 2288 females.
9 yr olds: 5567 males and 5286 females.
10 yr olds: 4039 males and 3835 females.
11 yr olds: 3060 males and 2905 females.
12 yr olds: 2222 males and 2110 females.
13 yr olds: 5098 males and 4841 females.
14 yr olds: 3369 males and 3199 females.
15 yr olds: 3765 males and 3575 females.
16 yr olds: 2826 males and 2683 females.
17 yr olds: 3106 males and 2949 females.
18 yr olds: 2026 males and 1923 females.
19 yr olds: 5306 males and 5038 females.
20 yr olds: 3753 males and 3564 females.
21 yr olds: 2625 males and 2491 females.
22 yr olds: 1915 males and 1818 females.
23 yr olds: 3925 males and 3727 females.
24 yr olds: 2493 males and 2368 females.
25 yr olds: 3488 males and 3311 females.
26 yr olds: 2576 males and 2447 females.
27 yr olds: 2437 males and 2313 females.
28 yr olds: 1642 males and 1559 females.
29 yr olds: 4451 males and 4228 females.
30 yr olds: 3090 males and 2933 females.
31 yr olds: 2209 males and 2097 females.
32 yr olds: 1629 males and 1547 females.
33 yr olds: 2792 males and 2651 females.
34 yr olds: 1732 males and 1645 females.
35 yr olds: 3140 males and 2983 females.
36 yr olds: 2311 males and 2195 females.
37 yr olds: 1870 males and 1775 females.
38 yr olds: 1303 males and 1237 females.
39 yr olds: 3609 males and 3425 females.
40 yr olds: 2444 males and 2319 females.
41 yr olds: 1808 males and 1715 females.
42 yr olds: 1346 males and 1277 females.
43 yr olds: 1967 males and 1869 females.
44 yr olds: 1215 males and 1152 females.
45 yr olds: 2895 males and 2747 females.
46 yr olds: 2112 males and 2005 females.
47 yr olds: 1541 males and 1461 females.
48 yr olds: 1092 males and 1037 females.
49 yr olds: 2740 males and 2603 females.
50 yr olds: 1789 males and 1698 females.
51 yr olds: 1633 males and 1552 females.
52 yr olds: 1220 males and 1158 females.
53 yr olds: 1459 males and 1384 females.
54 yr olds: 928 males and 881 females.
55 yr olds: 2559 males and 2429 females.
56 yr olds: 1847 males and 1755 females.
57 yr olds: 1125 males and 1066 females.
58 yr olds: 818 males and 776 females.
59 yr olds: 1985 males and 1885 females.
60 yr olds: 1241 males and 1177 females.
61 yr olds: 1416 males and 1345 females.
62 yr olds: 1056 males and 1000 females.
63 yr olds: 1147 males and 1090 females.
64 yr olds: 766 males and 725 females.
65 yr olds: 2297 males and 2178 females.
66 yr olds: 1626 males and 1543 females.
67 yr olds: 997 males and 945 females.
68 yr olds: 725 males and 687 females.
69 yr olds: 1306 males and 1240 females.
70 yr olds: 693 males and 657 females.
71 yr olds: 1111 males and 1055 females.
72 yr olds: 745 males and 709 females.
73 yr olds: 592 males and 559 females.
74 yr olds: 365 males and 346 females.
75 yr olds: 990 males and 939 females.
76 yr olds: 612 males and 583 females.
77 yr olds: 278 males and 263 females.
78 yr olds: 189 males and 177 females.
79 yr olds: 304 males and 289 females.
80 yr olds: 157 males and 149 females.
81 yr olds: 351 males and 332 females.
82 yr olds: 232 males and 221 females.
83 yr olds: 156 males and 148 females.
84 yr olds: 95 males and 90 females.
85 yr olds: 270 males and 256 females.
86 yr olds: 156 males and 149 females.
87 yr olds: 105 males and 99 females.
88 yr olds: 67 males and 63 females.
89 yr olds: 76 males and 72 females.
90 yr olds: 39 males and 36 females.
91 yr olds: 115 males and 108 females.
92 yr olds: 73 males and 70 females.
93 yr olds: 36 males and 34 females.
94 yr olds: 20 males and 19 females.
95 yr olds: 56 males and 54 females.
96 yr olds: 27 males and 27 females.
97 yr olds: 13 males and 12 females.
98 yr olds: 6 males and 5 females.
99 yr olds: 16 males and 13 females.

Answer 2

About 100 billion people. Roughly.

I'm ignoring the difference between the male/female survival rates (which shouldn't exist anyway because males aren't more valuable than females even with a 9/1 gender ratio) and I'm also ignoring the death rate because it's about 1%, and therefore of little consequences. There are 1080 females in the first generation, and they'll each have 12 children, of which 10 of them will be female. Scratch off the 80 females to represent the all the children who won't survive, and we're left with 1000. Assuming the same rate as the initial population, that means that the female population will grow 10x each generation, and the male numbers will be between 1/9 and 1/8 that of the female population. A generation is between 20-30 years, which means that by the time the second colony ship shows up, there's already 100x the population on the planet than the ship, so we get to ignore those entirely, because we're doing a rough estimate. There are 7-9 generations between the landing and 207 years into the future, so by that estimate we have a total population of roughly 100,000,000,000 women and 12,500,000,000 men.

This number may be a tad higher than you expected (and in fact exceeds the current Earth population) but if you make every female required to produce 10 female offspring and let it go for eight generations, this kind of exponential growth is simply what happens. At this point it stops being a colony because its population has simply exceeded Earth's.

Answer 3

Gender ratios do not matter in your scenario.

You have mandated the # of offspring per woman. It does not really matter how many men there are or if there are any; if there are frozen eggs there are certainly frozen sperm. If you want to maximize population growth (it seems you do) dispense with males entirely and make babies with frozen xx sperm. That maximizes genetic diversity. You can have some XY frozen away for when you want your population growth to level off an bring males into the population.

Maybe you are unconcerned about genetic diversity and you want some real males for your story. One or 2 will suffice. One bull can sire thousands of calves. That bull never sees a cow. It is all done artificially, minimizing waste and the need to tote the bull around the world.

Your population will be determined by the number of females. Males are just there. The math: assume 25 year reproductive life for woman. At t+25 years population of females = ((pop of females at time t)+((pop of females at time t)*7/8))*0.875

Males is the same but *1/8.

Answer 4

It doesn't matter, because almost certainly this setup will fail.

As other users have said, a new colony needs A LOT of work, and you can't really automate all of it, especially not for the first years. Think about it the new location might not be good for farming, or might not be good for farming what you have, and you need farming sorted out fast, and remember, almost all the humans are busy, the women with presumably caring for their kids, the men could farm, but there's no way they could farm enough, they don't have the resources, remember the land where they are is pretty unknown. Aside from that who is gonna be teaching and caring, it can't just be the parents, they couldn't do it and if you want the teens to do it, well they wont do a good job because pretty soon your gonna have problems with education. if you have an automated education system, who is gonna do maintenance on any of the systems? You don't have many spare people so soon stuff is gonna break down and you won't have anyone to fix it.

Let's say all that gets figured out somehow. Your colony will grow fast. After just 2-3 generations, you will be having in the hundred thousands, and those people need houses, your gonna need to find a way to make those houses, (remember the humans can't do that)

Let's say you still get that automated. People are eventually gonna want rights, so they will revolt, but against who? that brings another problem, who is controlling this all? In short, I think you need to tweak the numbers a bit, and change how it's structured to get a working colony that CAN grow.

How to fix those

First off, you need to make the growth smaller so the colony can keep up better, 100 kids per guy and 12 kids per gal is a very large number, especially in an unexplored environment, resources wouldn't keep up well, and care would be difficult otherwise, using half that would probably fix both. (edit: It has come to my attention that only 25 kids would be genetic at all for fathers, for a few generations at least, you can't keep splitting them forever, and with growth there wont be enough to spread out to everyone, so that number will increase eventually)

Next, you need to probably need to rethink having males never get into harms way like you say, if you want them to do work that has to get done, they are gonna be in harms way, and if you did step one, then they could get hurt more, and each have a tad higher number than the half you just mad them have.

You can adjust a bit of what I suggest to better fit your liking but I don't think your current setup will work as well as you hope.