Although inbreeding is a valuable breeding technique and one that can be combined with selection to improve response when h2 is small or with crossbreeding to produce animals and plants that farmers grow for market, unplanned and uncontrolled inbreeding often leads to inbreeding depression-decreases in growth rate, fecundity, and survival. The problems that are produced by uncontrolled inbreeding are usually accompanied by loss of alleles via genetic drift.
When a farmer or hatchery manager chooses a management programme, either he elects to improve productivity by utilizing selection, crossbreeding, inbreeding, or a combination of these programmes; or he decides to forego genetic improvements and will not use any breeding programme. If a farmer uses a breeding programme, it is inevitable that he will produce inbred fish, and the level of inbreeding will increase over time. Additionally, genetic drift will alter gene frequencies. However, inbreeding and genetic drift are not as important under these circumstances as they are when no breeding programme will be utilized. The reasons why inbreeding and genetic drift are not as important under these circumstances, as well as methods used to minimize inbreeding during selection, will be discussed in Chapter 8.
When no breeding programme is used to improve the population or to produce genetically improved fish, the only genetic goals should be: to prevent or minimize inbreeding, as well as to prevent genetic drift from reducing genetic variance and to minimize the loss of alleles. When a breeding programme is used, genetic changes are planned and desired because they will lead to improved growth rate, etc. When no breeding programme is conducted, genetic changes are unplanned and random, and those caused by inbreeding and genetic drift can ruin the population.
Consequently, when a farmer or hatchery manager does not incorporate a breeding programme into his management plan, it is advisable to try and prevent inbreeding from reaching levels that depress productivity and profits and to prevent genetic drift from robbing the population of potentially valuable alleles.
This chapter will describe ways to prevent inbreeding from accumulating to levels that cause inbreeding depression when farmers and hatchery managers do not use selection or other breeding programmes, both when fish can be marked and identified and when fish are not marked. Since most farmers and hatchery managers do not mark fish, this usually means that Ne must be managed to minimize inbreeding. The management of Ne to prevent genetic drift from robbing the population of valuable alleles will also be described.
Managing Ne to prevent inbreeding- and genetic drift-related problems means managing Ne at a pre-determined size every generation. Maintaining Ne at a constant size is difficult, because Ne can decline due to diseases, poor spawning season, etc. If Ne declines, the population goes through what is called a “bottleneck.” Bottlenecks accelerate the accumulation of inbreeding and magnify genetic drift. Preventing bottlenecks, especially during acquisition of the population, may be the most important aspect of brood stock management.
Finally, breeding techniques and brood stock management plans that can be used to increase Ne or that can be used to produce the same results with smaller Ne's will be described.
Recommended minimum Ne's that must be maintained by fish farmers or hatchery managers to prevent inbreeding from accumulating to levels that produce inbreeding depression and to prevent genetic drift from robbing the population of genetic variance will be discussed in Chapter 8.
The first step in managing a hatchery population to prevent inbreeding depression is to decide what level of inbreeding causes problems. Unfortunately, there is no answer to this seemingly simple question.
There have been relatively few inbreeding studies with fish. Some of those that have been conducted were done on hatchery fish which were probably already inbred. Even if a major study were to be conducted for an important species, such as common carp, Cyprinus carpio, or Nile tilapia, the inbreeding values that cause inbreeding depression and the level at which inbreeding depression become economically significant might not be the same for all hatchery populations of that species. Studies with other animals have shown that any level of inbreeding can cause inbreeding depression, but the level at which it becomes significant varies from study to study and is often different for different phenotypes. Consequently, no universally undesirable value of F will ever exist for fish. It will be different for different species and for different populations within a species, and it will also be different for different phenotypes.
Because no universally undesirable value of F will ever exist, farmers and hatchery managers have to make intelligent “guesstimates” about what levels of inbreeding they want to avoid. The inbreeding study with rainbow trout that was illustrated in Figures 6 and 7 (pages 18 and 19) showed that inbreeding depression became a serious problem when F≥18%. However, F = 12.5% also produced some inbreeding depression. The effects of F <12.5% were not evaluated, so the effects of mild levels are not known. Most inbreeding studies with fish have examined the effects of F≥25% (F = 25% is one generation of brother-sister matings).
Because there have been so few inbreeding studies in fish, because the effects of mild levels have not been investigated, and because no universally undesirable value of F is likely to be found, farmers and hatchery managers must decide what level of risk they are willing to accept. Those who want little risk should try to prevent inbreeding from exceeding 5%. Those who are willing to accept more risk should try to prevent inbreeding from exceeding 10%. In this manual, “risk” is defined as potential problems due to inbreeding and genetic drift; low levels of risk (smaller levels of inbreeding are desired) require more management, while high levels of risk (larger levels of inbreeding are acceptable) require less management.
These inbreeding values are not carved in stone. They are simply suggested values for populations where there is no selection to improve growth rate or other production phenotypes. Farmers and hatchery managers can substitute any value they choose. Small levels of inbreeding are more difficult and more costly to prevent, but efforts to prevent small levels will produce populations with fewer genetic problems. Large levels require less management and are less expensive, but choosing such levels may mean that the population has to be replaced when inbreeding depression rears its ugly head.
If each fish receives an individual mark, tag, or brand, pedigrees can be developed, which means that individual inbreeding values can be determined. If all fish are marked, inbreeding can be prevented in small populations. The way this is accomplished is: pedigrees are created, and relatives are not allowed to mate. One way to help ensure this is to construct a table of covariance values for all brood fish, as was described in Chapter 3 (Table 1; page 35). If the CovBI value for two brood fish is 0.0, those fish are allowed to mate, because the offspring that will be produced will have F = 0%.
If a farmer wants to allow some inbreeding but wants to keep it below a certain level, he can use the table of covariance values to determine the matings that will produce inbreeding values within his desired range (0% to the level that has been chosen). To do this, the farmer allows all matings where CovBI≤2 (maximum desired level of inbreeding). For example, if a farmer wants to keep F ≤5%, he allows all matings where CovBI ranges from 0.0 to 0.10, and prevents those where CovBI>0.10.
If a farmer marks his fish and maintains pedigrees, he can use the information in Figure 23 (page 57) to determine which matings will enable him to prevent undesired levels of inbreeding. Some types of consanguineous matings produce moderate amounts of inbreeding, while others produce virtually no inbreeding. If very low levels of inbreeding are desired, a farmer can restrict consanguineous matings to those less related than first cousins. If second cousins are mated generation after generation, inbreeding will never exceed 2%. For practical purposes, a regular inbreeding programme of second cousin matings is an effective way to prevent inbreeding depression. Unfortunately, a regular inbreeding programme of second cousin matings is fairly complicated.
If fish are not marked, individual inbreeding values cannot be determined, so a farmer must try to prevent the average inbreeding value from exceeding his desired level. This means that the farmer must manage his population's Ne.
Two important decisions must be made before a farmer or hatchery manager can manage Ne to prevent inbreeding from exceeding the desired maximum level: The first is to decide what the maximum inbreeding value will be. As was described earlier in this chapter, F = 5% is proposed for conservative farmers and hatchery managers who want to take little risk, while F = 10% is proposed for those who are willing to accept more risk. However, each farmer or hatchery manager is free to choose his level of risk and to customize the maximum level of inbreeding for his population.
The second decision a farmer or hatchery manager must make is to determine the number of generations that will be incorporated into the work plan before exceeding the level of inbreeding that has been chosen. In this exercise, a generation is the replacement of brood fish by their offspring, and generations are not allowed to overlap (the mixing of generations).
Once these two decisions have been made, two simple procedures are used to determine the Ne that is needed to achieve a farmer's goal:
Step 1: Once the desired maximum level of inbreeding and the number of generations that will be incorporated into the work plan have been determined, the amount of inbreeding per generation that is needed to produce the maximum level in that number of generations must be determined. The only sensible way Ne can be managed to achieve such a goal is to maintain a constant Ne, which will produce a constant amount of inbreeding. The reasons for this are: the math needed to determine the Ne's is far simpler, and it is far easier to try and maintain a constant Ne than a fluctuating one. The formula needed to determine this value is:
Step 2: Once the inbreeding per generation has been determined, the Ne that is needed to produce that level of inbreeding can be calculated by using the following formula:
|
For example, if a farmer decides that he wants to keep inbreeding from exceeding 5% and he does not want inbreeding to reach 5% until he produces the 10th generation, the Ne that is needed can be determined as follows:
| Step 1. Calculate the inbreeding per generation that will produce F = 5% (0.05) after 10 generations: |
 |
 |
F/generation = 0.005 |
| Thus, if F = 0.005/generation, it will reach 5% (0.05) when the 10th generation is produced. |
| Step 2. Calculate the Ne per generation that will produce F = 0.005/generation: |
 |
 |
 |
 |
| Ne=100 |
The farmer can achieve his goal of preventing inbreeding from exceeding 5% until he produces the 10th generation if he maintains an Ne = 100 for all 10 generations. If Ne = 100 for nine of the 10 generations but drops below 100 for a single generation, he will not be able to achieve his goal.
It is important to note that this procedure determines a minimum Ne, not the number brood fish that must spawned. The two are usually not the same. The only time they are the same is if a 1:1 sex ratio is used, if spawning success is 100%, and if each mating produces viable offspring. In this occurs, a farmer simply divides Ne by 2 to determine the number of males and females that must be spawned. In this example, a farmer would have to spawn 50 males and 50 females every generation to achieve his goal.
If the farmer uses a skewed sex ratio (usually more females than males), he will need more than 100 brood fish. The exact number he would need will be determined by the rarer sex.
If reproductive success is not 100%, a farmer must save and maintain more brood fish than the Ne that he is trying to achieve. The number of brood fish that must be maintained is determined by the typical spawning success rate and by the percentage of matings that produce viable offspring.
For example, if a farmer wants an Ne = 100, if 75% of the fish spawn, if 95% of those that spawn produce viable offspring, and if survival from the time brood fish are set aside until they are spawned is 70%, the farmer determines the number of brood fish that he needs in the following manner:
Step 1. Determine how many males need to spawned. Ne = 100; it will be assumed that the sex ratio will be equal (1:1), so 50 males and 50 females are needed. Step 2. Determine how many fish are needed if some matings produce no viable offspring. In this example, 95% of the males produce viable offspring, so the number of males that are needed is:
Number of males = 52.63 Since the sex ratio in this example is 1:1, the number of males and number of females that are needed are the same; consequently, the number of females needed = 52.63. Step 3. Determine how many male brood fish are needed if spawning success is <100%. Spawning success is 75%, and 52.63 males will spawn, so the number of male brood fish that will be needed is:
Number of males = 70.17 Since the number of males and females are equal, the number of females needed = 70.17. Step 4. Determine how many fish must be saved and set aside if survival is <100%. Survival from the time fish are set aside until they are spawned is 70%; 70.17 males are needed, so the number that must be set aside is:
Number set aside = 100.24 Since the number of males and females are equal, the number of females needed = 100.24. |
Because you cannot have two-tenths of a brood fish, the number is rounded up to 101. Consequently, in this example, the farmer would need to save 101 male and 101 female brood fish to produce an Ne of 100. The same numbers of males and females are needed in this example, because a 1:1 sex ratio was used and each male and each female were mated only once. If a skewed sex ratio is used or if multiple matings are used, the arithmetic becomes more complicated, but the process that was just described can be used to determine how many brood fish must be used.
Effective breeding numbers that are needed to keep inbreeding from exceeding 1–15% for 1–100 generations are listed in Table 4. These numbers were calculated as described in this section. When calculating the Ne that was needed to achieve a desired level of inbreeding, the number that was determined was often not a whole number. When this occurred, the number was rounded to the next higher whole number. This was done because you cannot have a fraction of a fish, and rounding to the next higher whole number ensured that F would not exceed the desired level. For example, an Ne of 83.3 was rounded up to 84. If the number were rounded down, it would fall below the Ne that was calculated, which would mean that the goal could not be achieved.
As was mentioned earlier, uncontrolled inbreeding and genetic drift are twin evils that occur in closed hatchery populations. Because they are conjoined twins and because both are determined by the population's Ne, it is important to know how to manage and control both. In many cases, managing the population to prevent one of these problems will prevent the other. In cases where this does not occur, a slight alteration in management goals (the desired Ne) will prevent both problems from adversely affecting productivity and profits.
It is not possible to prevent genetic drift. Genetic drift is simply random changes in gene frequency that occur because of sampling error, and the only way to prevent sampling error is to have an infinitely large population which is impossible. In aquaculture, sampling error is choice of brood fish that are allowed to spawn and produce the next generation or the acquisition of fish from another fish farm or the wild. Genetic drift causes problems when the random changes in gene frequency cause some alleles to be lost (the frequency goes to 0.0 or 0%). Once lost, these alleles can be regained only via mutation (which is rare) or by the acquisition of new brood fish. Rare alleles (frequencies <0.01) will be lost more easily than common ones, but common ones can also be lost. The probability of losing an allele is related to its frequency and the population's Ne (Table 2; page 47).
Consequently, a hatchery manager who wants to manage his hatchery population in order to prevent unwanted inbreeding from ruining productivity or profits must also manage the population to prevent genetic drift from robbing the population of genetic variance (loss of alleles).
Managing a population to control genetic drift means that a farmer or hatchery manager has to decide how much genetic drift is acceptable. Since genetic drift cannot be stopped, the question has to be modified. For management purposes, the question becomes: How large does Ne have to be to prevent the loss of alleles?
To answer this question, two decisions must be made. The first is: How valuable are the rare alleles; i.e., what is the frequency of the alleles that will be saved? The second is: What guarantee of saving these alleles is desired? The reason these decisions must be made is because the only way the loss of alleles can be prevented and the only way a 100% guarantee can be given that alleles were not lost via genetic drift is to have an infinitely large population. Hatchery populations are usually small, so the only way to manage them and prevent genetic drift from causing problems is to make a compromise between what is ideal (no changes in gene frequency and no loss of alleles) and what is achievable (determined by the above decisions).
Population biologists generally assume that if a gene has more than one allele and if the frequency of two alleles are ≥0.01, the gene is polymorphic, which means that for management purposes two or more alleles exist for that gene in the population. Alleles whose frequencies are <0.01 do not contribute to polymorphism. This does not mean they are unimportant; they do contribute to genetic variance, but they are often considered too rare to manage for practical biological conservation.
Consequently, a farmer or hatchery manager who wants to preserve as much genetic variance as possible and wants to accept little risk would choose to save alleles whose frequencies are 0.01. Farmers who feel that rare alleles are not that important for farming purposes would choose to save more common alleles. They might choose to save alleles whose frequencies are, say, 0.05. Alleles that are rarer than 0.05 are probably not that important in fish farming. If they were, domestication selection would have increased their frequency dramatically.
The frequency that is chosen is determined by the farmer's or hatchery manager's goals. There is no single correct value. However, hatchery managers who are raising fish that will be stocked in lakes and rivers should try and preserve as much genetic variation as possible and should try and prevent any changes in the genetic make-up of the population. This means saving alleles whose frequencies are 0.01–0.001. Farmers who raise food fish do not need to be as zealous. If they wish to conserve the population's genetic variance, they only need to save alleles whose frequencies are 0.05-0.01; however, many fish farmers should not even worry about the effects of genetic drift.
As was mentioned earlier, it is not possible to manage an Ne to produce a 100% guarantee of saving an allele, so practical workable guarantees must be chosen. In biology, two values are routinely used: 95% and 99%. These values come from statistics: when biologists evaluate experiments statistically, they typically use 0.01 and 0.05 as probability levels. The guarantee of saving an allele is: 1.0 - the probability of losing the allele.
A final decision must be made before the Ne can be managed to prevent the loss of rare alleles: How many generations will be incorporated into the management plan; i.e., how many generations will be produced until the guarantee of keeping the alleles is lowered to the desired level?
Once these decisions have been made, the Ne that is needed to prevent genetic drift from robbing the population of rare alleles is determined by using the following formula:
P = (1.0 - q)2Ne
where: P is the probability of losing the allele in a single random sample (the fish that mate to produce the next generation or the transfer of fish from one hatchery to another); and q is the frequency of the rare allele that is to be saved (q = 0.01 or 0.05 or whatever value is chosen).
Table 4. Effective breeding numbers needed per generation to produce various levels of inbreeding after 1–100 generations. Effective breeding numbers were rounded up.
| No. generations | Maximum level of inbreeding desired | ||||||||||||||
| 1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 11% | 12% | 13% | 14% | 15% | |
| 1 | 50 | 25 | 17 | 13 | 10 | 9 | 8 | 7 | 6 | 5 | 5 | 5 | 4 | 4 | 4 |
| 2 | 100 | 50 | 34 | 25 | 20 | 17 | 15 | 13 | 12 | 10 | 10 | 9 | 8 | 8 | 7 |
| 3 | 150 | 75 | 50 | 38 | 30 | 25 | 22 | 19 | 17 | 15 | 14 | 14 | 12 | 11 | 10 |
| 4 | 200 | 100 | 67 | 50 | 40 | 34 | 29 | 25 | 23 | 20 | 19 | 17 | 16 | 15 | 14 |
| 5 | 250 | 125 | 84 | 63 | 50 | 42 | 36 | 32 | 28 | 25 | 23 | 21 | 20 | 18 | 17 |
| 6 | 300 | 150 | 100 | 75 | 60 | 50 | 43 | 38 | 34 | 30 | 28 | 25 | 24 | 22 | 20 |
| 7 | 350 | 175 | 117 | 88 | 70 | 59 | 50 | 43 | 39 | 35 | 32 | 30 | 27 | 25 | 24 |
| 8 | 400 | 200 | 134 | 100 | 80 | 67 | 58 | 50 | 45 | 40 | 37 | 34 | 31 | 29 | 27 |
| 9 | 450 | 225 | 150 | 113 | 90 | 75 | 65 | 57 | 50 | 45 | 41 | 38 | 35 | 33 | 30 |
| 10 | 500 | 250 | 167 | 125 | 100 | 84 | 72 | 63 | 56 | 50 | 46 | 42 | 39 | 36 | 34 |
| 15 | 750 | 375 | 250 | 188 | 150 | 125 | 108 | 94 | 84 | 75 | 69 | 63 | 58 | 54 | 50 |
| 20 | 1000 | 500 | 334 | 250 | 200 | 167 | 143 | 125 | 112 | 100 | 91 | 84 | 77 | 72 | 67 |
| 25 | 1250 | 625 | 417 | 313 | 250 | 209 | 179 | 157 | 139 | 125 | 114 | 105 | 97 | 90 | 84 |
| 30 | 1500 | 750 | 500 | 375 | 300 | 250 | 215 | 188 | 167 | 150 | 137 | 125 | 116 | 108 | 100 |
| 35 | 1750 | 875 | 584 | 438 | 350 | 292 | 250 | 219 | 195 | 175 | 160 | 146 | 135 | 125 | 117 |
| 40 | 2000 | 1000 | 667 | 500 | 400 | 334 | 286 | 250 | 223 | 200 | 182 | 167 | 154 | 143 | 134 |
| 45 | 2250 | 1125 | 750 | 563 | 450 | 375 | 322 | 282 | 250 | 225 | 205 | 186 | 174 | 161 | 150 |
| 50 | 2500 | 1250 | 834 | 625 | 500 | 417 | 358 | 313 | 278 | 250 | 228 | 209 | 193 | 179 | 167 |
| 55 | 2750 | 1375 | 917 | 688 | 550 | 459 | 393 | 344 | 306 | 275 | 250 | 230 | 212 | 197 | 184 |
| 60 | 3000 | 1500 | 1000 | 750 | 600 | 500 | 429 | 375 | 334 | 300 | 273 | 250 | 231 | 215 | 200 |
| 65 | 3250 | 1625 | 1084 | 813 | 650 | 542 | 465 | 407 | 362 | 325 | 296 | 271 | 250 | 233 | 217 |
| 70 | 3500 | 1750 | 1167 | 875 | 700 | 584 | 500 | 438 | 389 | 350 | 319 | 292 | 270 | 250 | 234 |
| 75 | 3750 | 1875 | 1250 | 938 | 750 | 625 | 536 | 469 | 417 | 375 | 341 | 313 | 289 | 268 | 250 |
| 80 | 4000 | 2000 | 1334 | 1000 | 800 | 667 | 572 | 500 | 445 | 400 | 346 | 334 | 308 | 286 | 267 |
| 85 | 4250 | 2125 | 1417 | 1063 | 850 | 709 | 608 | 532 | 473 | 425 | 387 | 355 | 327 | 304 | 284 |
| 90 | 4500 | 2250 | 1500 | 1125 | 900 | 750 | 643 | 563 | 500 | 450 | 410 | 375 | 347 | 322 | 300 |
| 95 | 4750 | 2375 | 1584 | 1188 | 950 | 792 | 679 | 594 | 528 | 475 | 432 | 396 | 366 | 340 | 317 |
| 100 | 5000 | 2500 | 1667 | 1250 | 1000 | 834 | 715 | 625 | 556 | 500 | 455 | 417 | 385 | 358 | 334 |
Table 2 (page 47) lists the Ne's that are needed to produce various probabilities of losing alleles whose frequencies are 0.001-0.5 after a single generation of genetic drift. Table 2 shows that the probability of losing an allele is inversely related to its frequency: the smaller the frequency, the more likely it is that the allele will be lost via genetic drift. For example, if the frequency of an allele is 0.5, an Ne of only 10 is needed to produce a probability of 1 × 10-6 (0.000001) of losing the allele after a single generation of drift; but if the frequency of an allele is 0.001, an Ne of 6,880 is required to produce that level of probability. In Table 2, no probability is listed for each allelic frequency, once the probability of losing it reaches 1 × 10-6. At that level of probability, the odds of losing the allele via drift approaches zero (the guarantee of saving it becomes 99.9999%).
However, proper brood stock management requires medium- to long-range planning, which means a farmer or hatchery manager must know how large the Ne must be to prevent the loss of alleles after 3 or 5 or 25 generations, depending on management goals. Minimum constant Ne's that are needed to produce 95% and 99% guarantees of keeping alleles whose frequencies are 0.1, 0.05, 0.01, 0.005, and 0.001 are listed in Table 5. The method that was used to calculate the values in Table 5 is outlined in Table 6.
The values listed in Table 5 show that fairly small Ne's are needed to save alleles whose frequencies are ≥0.05, while fairly large Ne's are required to save alleles whose frequencies are ≤0.005. This is why most farmers and hatchery managers should try and save alleles whose frequencies are 0.01–0.05. However, hatchery managers and farmers who have large farms, who culture a species which requires thousands of brood fish, or who spawn wild fish could try and save alleles whose frequencies are ≤0.01. The frequency of the allele that a farmer or hatchery manager wants to save is determined by the species that is cultured, the size of the farm, and the management goals.
The 95% and 99% guarantees apply for all alleles of a given frequency (e.g., 0.01 or 0.05). This means if 100 alleles have that frequency, 95% or 99% will be saved, but 5% or 1% will be lost.
Table 5. Effective breeding numbers needed per generation for 1–100 generations to produce 95% and 99% guarantees of saving alleles whose frequencies (f) are 0.1–0.001. The guarantee of saving an allele is: 1.0 and -probability of losing it. Effective breeding numbers were rounded up.
| No. generations | f = 0.1 | f = 0.05 | f = 0.01 | f = 0.005 | f = 0.001 | |||||
| 95% | 99% | 95% | 99% | 95% | 99% | 95% | 99% | 95% | 99% | |
| 1 | 15 | 22 | 30 | 45 | 150 | 230 | 299 | 460 | 1498 | 2302 |
| 2 | 18 | 26 | 36 | 52 | 183 | 264 | 367 | 529 | 1838 | 2647 |
| 3 | 20 | 28 | 40 | 56 | 203 | 284 | 407 | 569 | 2038 | 2847 |
| 4 | 21 | 29 | 43 | 59 | 218 | 298 | 436 | 598 | 2181 | 2993 |
| 5 | 22 | 30 | 45 | 61 | 229 | 309 | 458 | 620 | 2292 | 3104 |
| 6 | 23 | 31 | 47 | 63 | 238 | 319 | 476 | 638 | 2382 | 3195 |
| 7 | 24 | 32 | 48 | 64 | 245 | 326 | 491 | 654 | 2459 | 3272 |
| 8 | 24 | 32 | 50 | 66 | 252 | 333 | 505 | 667 | 2526 | 3339 |
| 9 | 25 | 33 | 51 | 67 | 258 | 339 | 516 | 679 | 2584 | 3398 |
| 10 | 26 | 33 | 52 | 68 | 263 | 344 | 527 | 689 | 2637 | 3450 |
| 15 | 27 | 35 | 56 | 72 | 283 | 364 | 567 | 730 | 2839 | 3653 |
| 20 | 29 | 37 | 59 | 75 | 297 | 378 | 596 | 758 | 2983 | 3797 |
| 25 | 30 | 38 | 61 | 77 | 308 | 390 | 618 | 780 | 3094 | 3908 |
| 30 | 31 | 38 | 63 | 78 | 318 | 399 | 636 | 799 | 3185 | 3999 |
| 35 | 31 | 39 | 64 | 80 | 325 | 406 | 651 | 814 | 3262 | 4076 |
| 40 | 32 | 40 | 65 | 81 | 332 | 413 | 665 | 827 | 3329 | 4143 |
| 45 | 33 | 40 | 67 | 82 | 338 | 419 | 677 | 839 | 3388 | 4202 |
| 50 | 33 | 41 | 68 | 83 | 343 | 424 | 687 | 850 | 3440 | 4255 |
| 55 | 34 | 41 | 69 | 84 | 348 | 429 | 697 | 859 | 3488 | 4302 |
| 60 | 34 | 42 | 69 | 85 | 352 | 433 | 705 | 868 | 3531 | 4346 |
| 65 | 34 | 42 | 70 | 86 | 356 | 437 | 713 | 876 | 3571 | 4386 |
| 70 | 35 | 42 | 71 | 87 | 360 | 441 | 721 | 883 | 3608 | 4423 |
| 75 | 35 | 43 | 72 | 87 | 363 | 444 | 727 | 890 | 3643 | 4457 |
| 80 | 35 | 43 | 72 | 88 | 366 | 447 | 734 | 896 | 3675 | 4489 |
| 85 | 36 | 43 | 73 | 88 | 369 | 450 | 740 | 903 | 3705 | 4520 |
| 90 | 36 | 44 | 73 | 89 | 372 | 453 | 746 | 908 | 3734 | 4548 |
| 95 | 36 | 44 | 74 | 90 | 375 | 456 | 751 | 914 | 3761 | 4575 |
| 100 | 36 | 44 | 74 | 90 | 377 | 458 | 756 | 919 | 3786 | 4601 |
Table 6. Method used to determine effective breeding numbers that are listed in Table 5.
Given: You want to save alleles whose frequencies are 0.01 (q), and you want a 95% guarantee of saving the allele (P = 0.05) after 10 generations (when the 10th generation is produced). What constant Ne is needed to achieve this goal?
Step 1: Calculate the guarantee per generation that is needed to produce a 95% guarantee after 10 generations:
0.95 = (guarantee/generation)10
guarantee/generation = (0.95)1/10
guarantee/generation = 0.994883803
(0.95)1/10 can be determined by using the “yx” button on a hand-held calculator.
Step 2: Calculate the probability of losing the allele per generation:
Probability of losing the allele/generation = 1.0 - guarantee of saving it /generation
Probability of losing the allele/generation = 1.0 - 0.994883803
Probability of losing the allele/generation = 0.005116196882
Step 3: Calculate the Ne that is needed to produce a P = 0.005116196882 when q = 0.01 (the frequencies of the alleles you are trying to save):
P = (1.0 - q)2Ne
0.005116196882 = (1.0 - 0.01)2Ne
To determine Ne, the formula must be converted to logarithms. This can be done by using the “log” button on a hand-held calculator.
log 0.005116196882 = log(0.99)2Ne
log 0.005116196882 = (2Ne)(log 0.99)
524.89 = 2Ne
262.45 = Ne
Ne is rounded to the next higher whole number, so an Ne of 263 is needed every generation in order to produce a 95% guarantee of saving an allele whose frequency is 0.01 when the 10th generation is produced.
All of the recommendations that were made in the previous section were based on maintaining minimum constant Ne's. Unfortunately, it is difficult to maintain a constant Ne generation after generation. Anyone who has ever managed a population of fish knows all too well that it is difficult to maintain a steady-state population. Many factors conspire to occasionally reduce population size. Sudden drastic decreases in population size are called “bottlenecks.” The genetic effects of bottlenecks can be devastating and can have long-term repercussions.
As was described in Chapter 4, the mean Ne over a series of generations is the harmonic mean, not the simple arithmetic mean. Consequently, the generation with the smallest Ne has a disproportionate influence on the average value. This means that a bottleneck can dramatically lower mean Ne, which in turn will dramatically increase inbreeding and genetic drift.
For example, if a farmer wants to maintain a constant Ne of 100 for 10 generations but experiences a bottleneck of 20 in generation 6, the mean Ne that he produced is:
Ne mean can be determined by using the “1/x” button on a hand-held calculator.
The arithmetic average for this series of Ne's is 92, so mean Ne is 22% smaller than would be expected. If there were two bottlenecks of 20, mean Ne would have dropped to only 55.6.
Bottlenecks can have severe and long-lasting effects on inbreeding, because once inbreeding occurs, it lowers future Ne's, as was described in Chapter 4. The impact that bottlenecks have on average inbreeding depends on the size of the bottleneck and how many there are. A population which is poorly managed and which experiences multiple bottlenecks where the population is reduced to relatively few males and/or females will be quite inbred. On the other hand, a well-managed population that experiences a single bottleneck will be far less affected. A single bottleneck will produce an immediate increase in inbreeding and the average inbreeding may increase for a generation or two (the amount depends on the size of the bottleneck), but if the population is properly managed to minimize inbreeding before and after the bottleneck, the average inbreeding will plateau a few generations after the bottleneck, and the damage due to inbreeding might not be severe.
Figure 32. Effects of bottlenecks on gene frequency. Since genetic drift and the probability of losing alleles are inversely related to effective breeding number (Ne), the size of a bottleneck determines the amount of genetic change. The frequencies of the A and a alleles in the population are both 0.5. As the bottleneck (Ne) becomes smaller, genetic drift alters gene frequency until at an extreme, the frequency of an allele goes to zero.
The effects that bottlenecks can have on genetic drift are far more devastating. The probability of losing an allele is inversely related to Ne, so the odds of losing the allele increase as Ne decreases. Bottlenecks increase the probability dramatically. The effect that a bottleneck can have on gene frequency is illustrated in Figure 32.
For example, if a farmer is trying to maintain a constant Ne of 344 for 10 generations in order to produce a guarantee of 99% for keeping an allele whose frequency is 0.01 (Table 5) and there is a bottleneck of 25 in generation 8, the probability of losing the allele when the 10th generation is produced is determined as follows:
Step 1. The probability of losing the allele each generation must be determined.
Step 2. The guarantee of keeping the allele each generation must be determined (1.0 - probability of losing the allele).
The probabilities of losing the allele and the guarantees of keeping the allele for all 10 generations are:
| Ne | Step 1: Probability of losing allele | Step 2: Guarantee of keeping allele | |
| (P = (1.0 - q)2Ne) | (1.0 - P) | ||
| 344 P = (0.99)2(344) | = 0.0009931477 | 0.999006852 | |
| 344 P = (0.99)2(344) | = 0.0009931477 | 0.999006852 | |
| 344 P = (0.99)2(344) | = 0.0009931477 | 0.999006852 | |
| 344 P = (0.99)2(344) | = 0.0009931477 | 0.999006852 | |
| 344 P = (0.99)2(344) | = 0.0009931477 | 0.999006852 | |
| 344 P = (0.99)2(344) | = 0.0009931477 | 0.999006852 | |
| 344 P = (0.99)2(344) | = 0.0009931477 | 0.999006852 | |
| 25 P = (0.99)2(25) | = 0.605006067 | 0.394993932 | |
| 344 P = (0.99)2(344) | = 0.0009931477 | 0.999006852 | |
| 344 P = (0.99)2(344) | = 0.0009931477 | 0.999006852 | |
Step 3. The guarantee of keeping the allele for 10 generations must be determined. It is the product of the guarantee of keeping the allele for each generation; i.e., the guarantees for each generation are multiplied to determine the guarantee after the 10th generation is produced:
| Guarantee after 10 generations | = | (0.999006852)(0.999006852)(0.999006852)(0.999006852) (0.999006852)(0.999006852)(0.999006852)(0.394993932) (0.999006852)(0.999006852) |
| Guarantee after 10 generations | = | 0.3915 |
Step 4. The probability of losing the allele after 10 generations must be determined. It is 1.0 - the guarantee of keeping the allele:
Probability of losing allele = 1.0 - Guarantee of keeping allele
Probability of losing allele = 1.0 - 0.3915
Probability of losing allele = 0.6085
The bottleneck of 25 at generation 8 increased the probability of losing the allele in the 10th generation from 0.01 (which was the goal) to 0.6085.
The overall effect of a single bottleneck on genetic drift is far more severe than it is on average inbreeding, and its occurrence can prevent a farmer or hatchery manager from achieving his goals, even if he has done an outstanding job for many generations. This is because once an allele is lost, it can be recovered only by mutation or the introduction of new brood stock. Consequently, prevention of bottlenecks should be the major brood stock management goal if the genetic goal is to minimize the detrimental effects of inbreeding and genetic drift.
Since inbreeding and genetic drift are controlled by the population's Ne, it should be obvious that managing Ne is the most effective way to control or to prevent these twin problems from ruining productivity and profits. Minimum constant Ne's need to be maintained to prevent inbreeding from exceeding desired levels or to produce desired guarantees of keeping alleles with certain frequencies.
However, there are some management techniques that can be used to “artificially” increase Ne or to manage the brood fish to “stretch” generations. These techniques lengthen the time frame before inbreeding and genetic drift cause problems. By incorporating some of these management techniques, smaller numbers of brood fish can be used; smaller Ne's can be used; or the brood fish that are spawned can be managed more effectively to prevent genetic degradation of a population.
The simplest and least expensive technique that can be used to increase the time frame until inbreeding- and genetic drift-related problems cause trouble is to stretch the generation interval. This is not always possible, since some fish die when they spawn. But when it is possible, this technique is very effective. In this manual, a generation is defined as the replacement of brood fish by their offspring. Generations are not allowed to overlap. The definition of “generation” does not contain a specific time frame in terms of years. So if the normal time it takes for a fish to go from egg to brood fish and then for that fish to spawn and be discarded so that it can be replaced by its offspring is 2 years, the generation interval for that species is 2 years. If the time interval for another species is 4 years, the generation interval for that species is 4 years.
But these time intervals can be stretched if brood fish are allowed to spawn for an extra year or two before they are replaced by their offspring. The longer a generation can be stretched, the longer it will take for inbreeding-and genetic drift-related problems to become evident.
For example, let's assume that the generation interval for the species a farmer cultures is 2 years. Let's also assume that he wants to keep inbreeding below 5% for 10 generations (20 years). To do this, he needs an Ne of 100 per generation (Table 4). However, if he can stretch the generation interval so that it doubles to 4 years, he can use an Ne of only 50 to produce the same amount of inbreeding (5%) at the end of 20 years, because he will produce only five generations during this time span. Consequently, a farmer can maintain and spawn fewer fish by stretching the generations.
The major constraint with this type of brood stock management is survival. If survival of brood fish declines during this “extra” period, Ne of the population will decline. However, if survival of brood fish is not adversely affected by the extra stretched interval, this technique is an easy way of controlling inbreeding. One way of compensating for mortalities is to maintain additional brood fish and to use them to replace those that die.
Most farmers or hatchery managers use what is called “random mating” when they spawn their fish. Random mating is a breeding protocol where fish are mated without regard to phenotypic value. The only time random mating is not used is when selective breeding or crossbreeding programmes are implemented to improve growth rate or other phenotypes.
The Ne of a population can be “artificially” increased by using a breeding programme called “pedigreed mating.” Pedigreed mating differs from random mating in that each female leaves one daughter and each male leaves one son to be used as brood fish in the following generation. In actuality, each male and each female can leave more than one descendant, but all fish must leave the same number. This means that a male that spawns with five females will leave the same number of sons as a male that spawns with only one female. They will leave unequal numbers of daughters, but they will leave the same number of sons. The sons and daughters that become brood fish in the following generation must be chosen randomly from each family. No fish can be chosen because it has a specific phenotype or is a certain weight; if that is done, some form of selection is occurring.
When pedigreed mating is used, the Ne of the population increases because the genetic variance is artificially increased by ensuring that each brood fish is represented in the next generation. When pedigreed mating is used, Ne is determined by using the following formula:
if there are more males,
or
If there are more females.
If equal numbers of males and females are spawned, either formula can be used.
For example, if a farmer spawns 50 females and 30 males using random mating, his Ne is:
Ne = 75
If he uses pedigreed mating, the Ne increases to:
Ne= 133.3
Pedigreed mating increased Ne by 77.8% in the above example, and the inbreeding that would be produced would decline from 0.67% to 0.38%.
The only difficulty in using pedigreed mating is that you have to be able to mark the fish or be able to grow each family in an isolated pond or tank so that individual families can be identified.
There are several practical ways that spawning can be modified in order to increase Ne and thus reduce inbreeding and the effects of genetic drift.
— One way to reduce inbreeding and the effects of genetic drift is to spawn more fish than are needed. Most farmers and hatchery managers have been trained to be efficient, and this means spawning the fewest number of fish that will enable them to meet production goals. Farmers in particular want to be efficient so that they spend less money raising their crop. Furthermore, one way hatchery managers at public hatcheries are evaluated is cost per fingerling. But this philosophy is at odds with the control of inbreeding and genetic drift.
This problem is especially acute in aquaculture, because the fecundity of some species of fish is so great that it is often possible to spawn one or two females and males and produce the number of fingerlings that are needed for grow-out. But the ability to spawn relatively few fish must be moderated if inbreeding and genetic drift are to be controlled.
The best way to manage a population is to determine what Ne is needed to prevent inbreeding- and genetic drift-related problems under the time frame that has been chosen and then spawn the number of brood fish that will enable the farmer to produce that Ne. The farmer should spawn many more fish than he normally would and simply keep a small and equal random sample of eggs or fingerlings from each spawn. He can sell the surplus eggs or fish to other farmers. If he cannot sell the surplus fish, they should be discarded. This might seem wasteful, but this practice improves the genetics of the population.
— An easy way to increase Ne and thus reduce the rate of inbreeding and genetic drift is to spawn a more equal sex ratio. Most farmers and hatchery managers use skewed sex ratios when they spawn their fish. This is done because one male can usually be used to fertilize eggs from several females. This enables aquaculturists to use and maintain fewer males, which lowers production costs.
This may be a great idea in terms of efficiency, but it is a bad idea if you want to manage and control the genetic quality of the population. When a skewed sex ratio is used, the rarer sex has a disproportionate influence on the size of Ne.
The impact that a skewed sex ratio has on inbreeding can be seen in the following formula:
where: number of males and number of females are the numbers that produce viable offspring. The effect that a skewed sex ratio has on inbreeding is more pronounced when the total breeding population is small. For example, if a farmer spawns 100 females and 10 males he produces the following amount of inbreeding:
F=0.01375
If he moderates the sex ratio and uses 100 females and 40 males the inbreeding becomes:
F=0.004375
The addition of 30 males reduced inbreeding per generation from 1.38% to 0.44%.
The impact that skewed sex ratios have on inbreeding even means that smaller populations can produce less inbreeding. For example, a population with 50 males and 50 females produces less inbreeding than one with 20 males and 200 females (0.5% vs 0.69%) even though it is less than half as large.
The inbreeding that is produced by various combinations of males and females is shown in Table 7. The inbreeding values in that table show that if the number of one sex is held constant, increasing the other sex produces diminishing returns; i.e., the reduction in inbreeding becomes less and less despite substantial increases in the commoner sex. For example, if a farmer spawns 10 males and 100 females, F = 1.38%; if he spawns 10 males and 250 females, F = 1.30%. Table 7 clearly shows that the best way to reduce inbreeding is to increase the number of males and females and to spawn a sex ratio that is as close to 1:1 as possible.
Table 7. Percent inbreeding that is produced each generation in a population with random mating among various numbers of males and females. Inbreeding values were rounded to the nearest hundredth.
| No. females | No. males | |||||||||||||||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 20 | 25 | 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | ∞ | |
| 1 | 25.00 | 18.75 | 16.67 | 15.62 | 15.00 | 14.58 | 14.29 | 14.06 | 13.89 | 13.75 | 13.12 | 13.00 | 12.75 | 12.67 | 12.62 | 12.60 | 12.58 | 12.57 | 12.56 | 12.56 | 12.55 | 12.50 |
| 2 | 18.75 | 12.50 | 10.42 | 9.38 | 8.75 | 8.33 | 8.04 | 7.81 | 7.64 | 7.50 | 6.88 | 6.75 | 6.50 | 6.42 | 6.38 | 6.35 | 6.33 | 6.32 | 6.31 | 6.31 | 6.30 | 6.25 |
| 3 | 16.67 | 10.42 | 8.33 | 7.29 | 6.67 | 6.25 | 5.95 | 5.73 | 5.56 | 5.42 | 4.79 | 4.67 | 4.42 | 4.33 | 4.29 | 4.27 | 4.25 | 4.24 | 4.23 | 4.22 | 4.22 | 4.17 |
| 4 | 15.62 | 9.38 | 7.29 | 6.25 | 5.62 | 5.21 | 4.91 | 4.69 | 4.51 | 4.38 | 3.75 | 3.62 | 3.38 | 3.29 | 3.25 | 3.22 | 3.21 | 3.20 | 3.19 | 3.18 | 3.18 | 3.12 |
| 5 | 15.00 | 8.75 | 6.67 | 5.62 | 5.00 | 4.58 | 4.29 | 4.06 | 3.89 | 3.75 | 3.12 | 3.00 | 2.75 | 2.67 | 2.62 | 2.60 | 2.58 | 2.57 | 2.56 | 2.56 | 2.55 | 2.50 |
| 6 | 14.58 | 8.33 | 6.25 | 5.21 | 4.58 | 4.17 | 3.87 | 3.65 | 3.47 | 3.33 | 2.71 | 2.58 | 2.33 | 2.25 | 2.21 | 2.18 | 2.17 | 2.15 | 2.15 | 2.14 | 2.13 | 2.08 |
| 7 | 14.29 | 8.04 | 5.95 | 4.91 | 4.29 | 3.87 | 3.57 | 3.35 | 3.17 | 3.04 | 2.41 | 2.29 | 2.04 | 1.95 | 1.91 | 1.89 | 1.87 | 1.86 | 1.85 | 1.84 | 1.84 | 1.79 |
| 8 | 14.06 | 7.81 | 5.73 | 4.69 | 4.06 | 3.65 | 3.35 | 3.12 | 2.95 | 2.81 | 2.19 | 2.06 | 1.81 | 1.73 | 1.69 | 1.66 | 1.65 | 1.63 | 1.62 | 1.62 | 1.61 | 1.56 |
| 9 | 13.89 | 7.64 | 5.56 | 4.51 | 3.89 | 3.47 | 3.17 | 2.95 | 2.78 | 2.64 | 2.01 | 1.89 | 1.64 | 1.56 | 1.51 | 1.49 | 1.47 | 1.46 | 1.45 | 1.44 | 1.44 | 1.39 |
| 10 | 13.75 | 7.50 | 5.42 | 4.38 | 3.75 | 3.33 | 3.04 | 2.81 | 2.64 | 2.50 | 1.88 | 1.75 | 1.50 | 1.42 | 1.38 | 1.35 | 1.33 | 1.32 | 1.31 | 1.31 | 1.30 | 1.25 |
| 20 | 13.12 | 6.88 | 4.79 | 3.75 | 3.12 | 2.71 | 2.41 | 2.19 | 2.01 | 1.88 | 1.25 | 1.12 | 0.88 | 0.79 | 0.75 | 0.72 | 0.71 | 0.70 | 0.69 | 0.68 | 0.68 | 0.62 |
| 25 | 13.00 | 6.75 | 4.67 | 3.62 | 3.00 | 2.58 | 2.29 | 2.06 | 1.89 | 1.75 | 1.12 | 1.00 | 0.75 | 0.67 | 0.62 | 0.60 | 0.58 | 0.57 | 0.56 | 0.56 | 0.55 | 0.50 |
| 50 | 12.75 | 6.50 | 4.42 | 3.38 | 2.75 | 2.33 | 2.04 | 1.81 | 1.64 | 1.50 | 0.88 | 0.75 | 0.50 | 0.42 | 0.38 | 0.35 | 0.33 | 0.32 | 0.31 | 0.31 | 0.30 | 0.25 |
| 75 | 12.67 | 6.42 | 4.33 | 3.29 | 2.67 | 2.25 | 1.95 | 1.73 | 1.56 | 1.42 | 0.79 | 0.67 | 0.42 | 0.33 | 0.29 | 0.27 | 0.25 | 0.24 | 0.23 | 0.22 | 0.22 | 0.17 |
| 100 | 12.62 | 6.38 | 4.29 | 3.25 | 2.62 | 2.21 | 1.91 | 1.69 | 1.51 | 1.38 | 0.75 | 0.62 | 0.38 | 0.29 | 0.25 | 0.22 | 0.21 | 0.20 | 0.19 | 0.18 | 0.18 | 0.12 |
| 125 | 12.60 | 6.35 | 4.27 | 3.22 | 2.60 | 2.18 | 1.89 | 1.66 | 1.49 | 1.35 | 0.72 | 0.60 | 0.35 | 0.27 | 0.22 | 0.20 | 0.18 | 0.17 | 0.16 | 0.16 | 0.15 | 0.10 |
| 150 | 12.58 | 6.33 | 4.25 | 3.21 | 2.58 | 2.17 | 1.87 | 1.65 | 1.47 | 1.33 | 0.71 | 0.58 | 0.33 | 0.25 | 0.21 | 0.18 | 0.17 | 0.15 | 0.15 | 0.14 | 0.13 | 0.08 |
| 175 | 12.57 | 6.32 | 4.24 | 3.20 | 2.57 | 2.15 | 1.86 | 1.63 | 1.46 | 1.32 | 0.70 | 0.57 | 0.32 | 0.24 | 0.20 | 0.17 | 0.15 | 0.14 | 0.13 | 0.13 | 0.12 | 0.07 |
| 200 | 12.56 | 6.31 | 4.23 | 3.19 | 2.56 | 2.15 | 1.85 | 1.62 | 1.45 | 1.31 | 0.69 | 0.56 | 0.31 | 0.23 | 0.19 | 0.16 | 0.15 | 0.13 | 0.12 | 0.12 | 0.11 | 0.06 |
| 225 | 12.56 | 6.31 | 4.22 | 3.18 | 2.56 | 2.14 | 1.84 | 1.62 | 1.44 | 1.31 | 0.68 | 0.56 | 0.31 | 0.22 | 0.18 | 0.16 | 0.14 | 0.13 | 0.12 | 0.11 | 0.11 | 0.06 |
| 250 | 12.55 | 6.30 | 4.22 | 3.18 | 2.55 | 2.13 | 1.84 | 1.61 | 1.44 | 1.30 | 0.68 | 0.55 | 0.30 | 0.22 | 0.18 | 0.15 | 0.13 | 0.12 | 0.11 | 0.11 | 0.10 | 0.05 |
| ∞ | 12.50 | 6.25 | 4.17 | 3.12 | 2.50 | 2.08 | 1.79 | 1.56 | 1.39 | 1.25 | 0.62 | 0.50 | 0.25 | 0.17 | 0.12 | 0.10 | 0.08 | 0.07 | 0.06 | 0.06 | 0.05 | 0.00 |
Source: Tave, D. 1990. Effective breeding number and broodstock management: I. How to minimize inbreeding. Pages 27–38 in R.O. Smitherman and D. Tave, eds. Proceedings Auburn Symposium on Fisheries and Aquaculture. Alabama Agricultural Experiment Station, Auburn University, Alabama, USA.
Paradoxically, increasing the number of the commoner sex may prevent the loss of rare alleles via genetic drift, simply because by spawning more fish a farmer increases the likelihood that one of the brood fish will carry a rare allele. However, increasing the number of the rarer sex will also increase the likelihood of choosing a brood fish with a rare allele, and this approach is better because it will increase Ne significantly.
If the number of brood fish cannot be increased at a hatchery or farm, the only ways Ne can be increased are to switch to pedigreed mating or to moderate the sex ratio so it is closer to 1:1. The improvements in moderating the sex ratio or in switching to pedigreed mating can be assessed by evaluating the effective breeding efficiency (Nb) of the proposed changes. The Nb is the ratio of Ne to the size of the breeding population (N):
The Nb's for random and pedigreed matings over all possible sex ratios are shown in Figure 33. The curves for both types of mating clearly show that sex ratios that are in the 40% male:60% female to 60% male:40% female range are far more effective in maximizing Ne, within the constraints of a fixed population size, than are sex ratios that are more skewed than 60:40.
For example, if a farmer uses random mating, spawns 100 fish, and wants to use a skewed sex ratio, the following sex ratios would produce the following Nb's:
| Sex ratio (female:male) | Nb |
| 90:10 | 36% |
| 80:20 | 64% |
| 70:30 | 84% |
The farmer can then use these Nb's to decide what sex ratio is best in terms of spawning efficiency, fingerling production, and prevention of inbreeding. The Nb's show that he can moderate the skewness of his sex ratio slightly, yet still use a sex ratio which is quite skewed (70:30) and produce far less inbreeding. The inbreeding that is produced by a 70:30 sex ratio is 57% less than that produced by a 90:10 sex ratio. Figure 33 shows that some sex ratios do not have to be moderated to help control inbreeding; a 55:45 sex ratio has an Nb of 99%, so moderating that ratio closer to 50:50 will produce little improvement in terms of inbreeding control.
Figure 33 also shows the benefits that can be derived by switching from random mating to pedigreed mating. If pedigreed mating is used, a farmer can use a skewed sex ratio and still produce a large Nb. For example, if pedigreed mating is used, a 79:21 sex ratio produces an Nb of 102%, which is larger than the Nb that can be produced by a 50:50 sex ratio (100%) with random mating, provided N remains constant. Tremendous gains, in terms of Nb, can be made if a farmer switches from random to pedigreed mating and brings the sex ratio closer to 50:50.
— A final approach to managing Ne is to alter certain hatchery practices if gametes are stripped. When eggs and sperm are stripped, many farmers and hatchery managers pool eggs from several females and then fertilize the eggs either by using pooled milt or by adding milt from several males in a sequential manner. Both techniques will lower Ne from what you think it is. The reasons are: One, if milt is pooled and added, there is competition among the sperm, due to a difference in potency. Some males produce more vigorous sperm, and these sperm cells will fertilize a disproportionate number of eggs. In some cases, most of the eggs will be fertilized by sperm from a single male. Second, if milt is added in a sequential manner, the sperm from the first male will fertilize most of the eggs, while that from the last few males will fertilize comparatively few eggs.
The solutions to both problems are quite simple. Fertilize eggs from each female with sperm from a single male. If you want to have sperm from several males fertilize eggs from each female, subdivide each egg mass and fertilize each lot separately. If this is done, Ne can be accurately determined, because you know which brood fish produced offspring.
Figure 33. Effective breeding efficiency (Nb) over all possible sex ratios for both random mating and pedigreed mating. Effective breeding efficiency is a measure of the efficiency of the sex ratio or mating system in maximizing Ne within the constraints of a fixed population size (N).
Source: Tave, D. 1984. Effective breeding efficiency: An index to quantify the effects that different breeding programs and sex ratios have on inbreeding and genetic drift. Progressive Fish-Culturist 46:262–268.
Unless a farmer is going to conduct a selective breeding programme or use inbreeding to improve the results of selection or crossbreeding, a population should be managed genetically to prevent unwanted inbreeding from causing inbreeding depression and to prevent genetic drift from robbing the population of alleles and genetic variance. If fish can be marked, inbreeding depression can be prevented by creating pedigrees and by preventing consanguineous matings or by preventing matings between relatives more closely related than second cousins.
Marking fish and preventing consanguineous matings will not prevent genetic drift. Managing a population to minimize the effects of genetic drift can be be accomplished only by managing Ne.
When fish are not marked (which will be the case for most hatchery populations), the only way to prevent unwanted inbreeding from accumulating and to prevent the ravages of genetic drift is to manage the population's Ne. When a farmer is not using a breeding programme to improve a population, managing a population's Ne is probably the most important aspect of brood stock management. A population's Ne is one of the most important pieces of information about the population, because Ne is inversely related to both inbreeding and genetic drift. Consequently, managing Ne is a key aspect of fish husbandry.
There is no universal Ne that can be used to manage every population. It must be customized for each population. This chapter outlined the techniques and methods that must be used to determine the Ne that is needed. That number can be determined by answering a series of questions: One, what level of inbreeding will cause problems? Two, what is the frequency of the rare alleles that a farmer wants to save, and what guarantee does he want that the alleles have been saved? Three, how many generations does the farmer want to incorporate into the work plan before that level of inbreeding has been reached and when the guarantee will end?
The levels of inbreeding that cause problems in hatchery populations are not known, so appropriate levels must be determined by a “guesstimate.” Two values were proposed: 5% and 10%. The value chosen depends on how important the population is and what the goals are. Populations that are being cultured for food can use either 5% or 10%. Populations that are being cultured for stocking programmes must use 5%; if possible, lower levels should be used for these populations.
The frequency of the rare alleles that should be saved depends on the population. If the fish are being farmed, the frequency should be 0.05 for most farmers who wish to manage their populations genetically, and 0.01 for those who have the ability and desire to conserve as much genetic variance as possible. If the population is being cultured for stocking programmes the frequency should be no greater than 0.01; if possible, the frequency should be 0.005-0.001. These frequencies are not absolute but are presented as guideline values.
When managing a population's Ne, the major goal is to maintain Ne at a constant level every generation. If Ne drops below the desired value for a single generation, the genetic goals cannot be achieved. Maintaining Ne at the desired level generation after generation may be the most difficult aspect of brood stock management, because Ne can decline for a variety of reasons. Sudden and drastic decreases in Ne are called bottlenecks, and they can cause permanent and irreversible genetic damage.
Finally, there are a number of management techniques that can be used to increase Ne or that can be used to produce the same level of inbreeding but with a smaller number of brood fish: pedigreed mating; stretching generations; bringing the sex ratio closer to a 1:1 ratio; and altering some fertilization techniques when gametes are stripped.
Recommended Ne's, based on the information generated in this chapter, that will enable a farmer or hatchery manager to prevent inbreeding- and genetic drift-related problems are presented in Chapter 8.
