Chapter 5. Avoidance of inbreeding
Avoidance of inbreeding is often considered as a synonym for the genetic management of zoo populations. This is not surprising as inbreeding depression can occur as early as in the second generation - due to sibling or parent-offspring matings - after the population was founded [see Chapter 1]. The maintenance of sufficient levels of genetic variation, however, is the main objective of genetic management [Lacy et al., 1995]. Dividing populations into isolated subpopulations (and thus increasing the rate of inbreeding) would, theoretically, aid in accomplishing this objective as it reduces the overall loss of alleles [Kimura and Crow, 1964; Lacy, 1987; Chapter 3].
Management strategies which tolerate certain levels of inbreeding may be preferred for practical reasons. For example, in cases that exchanges of unrelated animals between in situ and ex situ populations or translocations between fragmented natural populations are limited. However, a management strategy which tolerates inbreeding involves the risk that the cost of inbreeding depression may overrule the profit of inbreeding through loss of entire genomes. Thus, (early) detection of inbreeding depression is important in management of small populations of endangered species. This implies that studies on tolerance c.q. sensitivity for inbreeding depression are required for each individual species or even local population prior to developing management strategies. Practical and ethical reasons make it unlikely that breeding experiments to determine sensitivity to inbreeding depression could involve endangered species. Therefore, information on tolerated levels of inbreeding need to be derived from comparative studies and population genetic theory. In this, it is important to compare populations that have similar histories. Additional information on breeding strategies can be derived from mating structure and natural dispersal patterns.
Sex-biased natural dispersal of sub-adult or young individuals has been observed in several primate species [Pusey and Packer, 1987; Smuts et al. 1987]. Social structure patterns tend to have been more extensively studied in primates than in any other taxa, but studies are certainly not totally restricted to this taxonomic order. Eisenberg [1981] and Templeton [1987] assume that avoidance of inbreeding occurs in most mammalian species. Differences in dispersal distances between females and males may also effectively result in avoidance of inbreeding as for example in the black bear, Ursus americanus, [Rogers, 1987]. Dispersal is not necessarily a mechanism itself to avoid inbreeding but may be the result of ecological and/or social factors [Shields, 1987]. However, dispersal will influence the genetic structure of a population and, therefore, its sensitivity to inbreeding depression. Dispersal patterns result in avoidance of full-sib matings but they do not exclude inbreeding within a population or even within a social group. Spatial distribution of social groups and dispersal distances determine to what extent the level of inbreeding increases over generations. Furthermore, parent-offspring matings in social groups are not excluded as for example breeding males may mate with their daughters while male offspring disperse. Behavioural, ecological and genetical studies are required to determine the effectiveness of dispersal patterns and avoidance of inbreeding within social groups. For example, de Ruiter et al. [1994] showed that genetic relatedness among males in natural social groups of long-tailed macaques, Macaca fascicularis, is lower than among females. This is the result of male dispersal in this species.
Given the various examples of sex-biased dispersal and the costs of inbreeding [see Chapter 1], avoidance of inbreeding may be considered as a basic guideline in genetic management of small populations of (endangered) animal species.
Maximal Avoidance of Inbreeding
Computerized studbook programs such as SPARKS [Scobie and Flesness, 1989] and ZRBOOK [Princée, 1989a] provide routines - based on algorithms as described by Quaas [1976] and Henderson [1976] - to compute inbreeding coefficients. Furthermore, additional programs like GENES [Lacy, 1994] can compute tables of inbreeding coefficients of hypothetical offspring for all possible mating combinations in the population within minutes. This enables studbook managers to decide on preferred breeding combinations within a population in order to avoid or to minimize inbreeding. But, the process of decision making has not necessarily been made easier by using these computer tools. This especially accounts for studbook populations with complex pedigree patterns. For example, formation of some breeding pairs from unrelated individuals may result in severe inbreeding in the remaining breeding combinations while the alternative maybe an overall mild inbreeding in all combinations. This type of time-consuming management is basically the result of lack of genetic management in a studbook populations in the past. It will be important to use breeding schemes which minimizes inbreeding in any ex situ population to be established in the future (or recently has been established) in order to prevent this time-consuming genetic management.
Wright [1921] presented breeding schemes which maximizes avoidance of inbreeding and maximally slow down the process of inbreeding once all individuals in a population are related. These Maximal Avoidance of Inbreeding (MAI) schemes do not require computation of inbreeding coefficients. Flesness [1977] describes how the maximal avoidance of inbreeding, based on the models of Wright [1921], can be applied to management of zoo populations composed of breeding pairs. The MAI scheme, however, can also be applied in management of species which are maintained in herds and colonies. Princée [1986] presented a simple MAI scheme to manage free-ranging herds of rare breeds of sheep. Young rams are moved from the herd each generation and replace older rams in other herds as determined by the MAI scheme. This model only presumes that the original founders are unrelated and does not require information on parentages within breeding units as long as the MAI scheme is followed. These breeding schemes may, therefore, be applied in management of endangered species that need to be maintained in social demes [see Chapter 1 ].
The schemes which have been described by Wright [1921] refer to groups of 2, 4, 8 and 16 individuals. The MAI scheme presented in this section is a more generalized extension of Wright's schemes. The term breeding unit is used in this general MAI model as it reflects the independency of group composition and social structure. These breeding units are composed of one maternal and one paternal bloodline regardless whether the unit refers to a pair, herd or colony. The model will be illustrated with an example of a population composed of eight breeding units. This example can be compared with the 'octuple third cousins' scheme of Wright [1921]. Guidelines to start MAI management for a population are:
- The population starts with unrelated animals that belong to generation group zero.
- The number of breeding units in the population should be a power of two (8 breeding units=23).
- Each breeding unit is assigned a number (1 - 8 in this example).
- Bloodlines (e.g. A,B,C,D) are assigned to maternal and paternal lines in each initial breeding unit. Group 1 consists of lines A and B, group 2 of lines C and D, and so on .
- Offspring inherit the maternal and paternal bloodlines. For example, offspring that are born in group 1 will have bloodlines AB.
- Offspring that belong to one sex (males in this example) are moved from their Natal group each generation to another group. The breeding group to which offspring is moved (the Host group) is determined as follows:
and
where Natal is the number of the natal group; Host is the number of the host group; G is the number of generations since the population was started; and Nb is the number of breeding groups.
Figures 17 and 18 present the MAI model, as described previously, for generations one and two, respectively. Circles in these figures represent breeding groups. Arrows indicate transfers from natal to host groups. Maternal and parental lines in the breeding unit are shown, as characters of the alphabet, near these boxes. Bloodlines of male offspring are shown near the arrows.
The MAI model will be illustrated by 'following' breeding group 1. This group starts with lines A and B. Male offspring of the first generation (bloodlines AB) are moved, according equation 20, to group 2. Male offspring of group 8 (bloodlines OP) are combined with female offspring of group 1. Male offspring of the second generation in group 1 (lines ABOP) cannot be combined with female offspring in group 2 (lines ABCD), as they are cousins. According MAI equation 20, males of group 1 will be combined with females of group 3 (lines CDEF). Inbreeding can be avoided in the third generation by bi-directional breeding combinations between groups 1 and 5, 2 and 6, 3 and 7, 4 and 8.
Avoidance of inbreeding is not longer possible after the third generation. All offspring in the fourth generation have bloodlines ABCDEFGHIJKLMNOP. Exchanges of offspring in the fourth generation are according the schemes for the first generation. The same cycle of steps between groups (i.e 1,2,4) are repeated continuously. Inbreeding coefficients will increase gradually and equally for all offspring after the fourth generation, when the MAI scheme is continued.
A power of 2 is the keyword in the MAI model that is presented in this section. This model cannot be applied to populations that consist of breeding groups which numbers are not equal to powers of 2. The number of generations (G), starting at generation 1, during which inbreeding can be avoided can be calculated by the following equations:
where Nb is the number of breeding groups. For example, inbreeding will occur after generation 5 in a population that is composed of 32 breeding units. I would like to call these exchange steps between generations the MAI cycle. Maximal avoidance can be seen as a sequence of MAI cycles (MAI sequence).
Variation in MAI Models
The MAI model, that has been described above, is a simple low-intensity genetic management model that allows one to calculate exchange schemes for groups in each generation. It basically uses a cycle of steps which represents powers of 2 in ascending order (i.e. 1, 2, 4). This cycle is repeated continuously. Note that MAI can be started using different cycles of exchange steps e.g. 4, 2, 1 or 2, 1, 4. The following rules have to be taken in account:
- Each "step" must equal a power of 2;
- A "step" cannot be larger than 2(MAI cycle - 1) (see Equation 23).
- All steps between 1 and the maximum step must occur in the MAI cycle.
- Each step may occur only once during a MAI cycle.
- The MAI cycle can not be changed in midcycle. Variations in the MAI cycle may be required to adapt this model to management that already has started with avoidance of inbreeding schemes that differ from the cycle calculated from equations 22 and 23 .
Maximal Avoidance of Inbreeding models have to be considered as guidelines for genetic management rather than rules. Histories of populations, the number of breeding groups and reproductive success in individual groups determine the extent to which MAI can be applied. Population managers' creativity will always be essential for further application of this model.
MAI models and social structure
Since MAI schemes do not require information on parentages within breeding units, they can be applied in breeding management regardless of mating system. Exchange steps in the MAI scheme could refer to natural dispersal patterns with respect to gender (and age). Management of harem groups involves replacement of male breeders and removal of male offspring. Since generally only one male per harem can be placed in another harem, a "surplus" of young males will exist. In this context, surplus refers to available space and not to genetic importance. It maybe required, however, that each individual should have the opportunity to breed in order to increase effective population size in small populations. A solution for management of harem species can be found in establishing male groups.
Figure 19 shows a MAI model for harem groups that include male groups. Each generation the male breeder of a harem group is replaced by another male according the MAI guidelines as described previously. The "surplus" male offspring are moved to one or multiple male groups. Once the male breeder has produced offspring, he is replaced by a male sibling from one of the male groups. This means that animals in male groups need to be identified on individual or at least on natal group level.
Male or female groups can also be established in management of colonies (multi-male and multi-female groups). For instance, females and female descendants of ring-tailed lemurs, Lemur catta, form the core of a social group, while males transfer frequently [Richard, 1987]. Integration of the concept of male groups in MAI management of species with this type of social organization would involve removal of all young males from the colony at sexual maturity. These males would immediately either be introduced to new colonies or maintained in all male groups. In contrast to the management of harem groups not only one but all males are replaced. MAI management not necessarily involves replacement of males or females in existing breeding groups. Species-specific social organization may require that parental groups are maintained and that offspring are removed from the group to form new breeding groups. MAI guidelines are used to determine which male(s) and female(s) will form a new group. Such type of management is for example implemented in the European Endangered Species Programme (EEP) of African wild dogs, Lycaon pictus.
MAI models in metapopulation management
The MAI model can also be applied to populations that are divided in subpopulations e.g. in situ and ex situ or regionally managed. Figure 20 shows the MAI management of a population that is composed of four subpopulations (A through D). Each subpopulation is composed of four breeding groups (1 through 4). Inbreeding in this population of sixteen breeding groups can be avoided for four generations (Equation 22).
According to the "normal" MAI model, exchanges between groups in different sub-populations would take place during each generation. Logistic considerations, such as co-ordination or costs of transport, might require that exchanges between subpopulations are limited and that they be managed collectively. These requirements can be achieved by nesting different MAI schemes with each scheme acting on a different level. The first level acts between units within a subpopulation and the second between them. The basic guideline of such management is to start MAI cycles of a next level at the moment that MAI cycles of previous levels have been completed. In our example we would start a MAI cycle between units within subpopulations. This cycle would be completed after the second generation. Offspring of the third generation would then migrate between subpopulations to the equivalent group in the appropriate subpopulation. They would migrate to the equivalent group in the next sub-population e.g. A-1 to B-1, B-2 to C-2 etc. (see figure 20). Exchanges between sub-populations A to D occur during generations three and four. The MAI cycle in subpopulations then begins again.
Discussion
Maximal Avoidance of Inbreeding schemes were developed by Wright [1921] to minimize inbreeding in populations which are composed of breeding pairs. This study shows that MAI schemes can also be applied to management of populations which are subdivided in breeding units of any size and composition. Breeding combinations or migration (dispersal) schemes to minimize inbreeding can be computed using equations 20 and 21 for each individual in each generation without needing data on parentages within breeding units (i.e. if MAI is followed). Therefore, this breeding scheme can be implemented in management of species with complex (social) mating structures and in metapopulation management involving in situ populations [see Chapter 1].
Kimura and Crow [1963b] showed that MAI schemes are not the most optimal strategies to minimize increase in homozygosity (by state) in the population [see also Chapter 1]. Increase in homozygosity in circular mating is initially higher during early generations of inbreeding, since half-sib matings are involved, than in MAI. However, homozygosity on the long-term will be lower in circular mating systems than in MAI [see Kimura and Crow, 1963b]. The advantage of circular mating systems in retention of (observed) heterozygosity is limited. For example, the transition point for a population of 32 individuals is approximately at 250 generations, when heterozygosity has already decreased to less than 20 percent of the original level [See Kimura and Crow, 1963b]. Furthermore, rapid inbreeding in circular mating systems increases risks on inbreeding depression in early generations.
The MAI schemes presented in this study assume that initial populations are established from unrelated individuals. This would limit implementation of MAI in the management of zoo populations with prior breeding histories. Ballou and Lacy [1995] and Montgomery et al. [1997] studied effects of management by mean kinship, MAI and random mating on retention of gene diversity and minimizing inbreeding in populations with a prior breeding history. They concluded that management by mean kinship is the optimal strategy in both minimizing inbreeding and retention of gene diversity in such populations. This does not imply that MAI management is not a good strategy to manage populations with a breeding history. The studies of Ballou and Lacy [1995] and Montogomery et al. [1997] ignored breeding histories prior to MAI management. Initial breeding pairs were randomly drawn from the population while management by mean kinship was based on complete pedigree data. Ballou and Lacy [1995] concluded, however, that high levels of gene diversity can be retained and (further) inbreeding be minimized in MAI strategies of populations. Therefore, MAI strategies provide good prospects for management of populations for which historical pedigree data are incomplete.
A serious practical problem of MAI strategies is created by the requirement that the number of breeding units must equal a power of 2. This also implies that MAI can not be continued in cases that one or more breeding units have not reproduced. A solution to this problem is to continue with management by mean kinship whenever pedigree data are available. This will generally refer to populations which are subdivided in breeding pairs. Strategies to replace other types of breeding units, however, require further studies. The results of the study by Ballou and Lacy [1995] indicate that replacement of breeding units by randomly selecting (groups of) individuals from other breeding units can be an option.