Charles suffered from numerous disabilities and congenital defects. His autopsy report is a staggering read. It states that after his death Charles had no blood, a heart the size of a peppercorn, corroded lungs, a head full of water, rotten and gangrenous intestines and had only a single testicle that was as black as coal. While not all of these can be blamed on inbreeding pituitary hormone deficiency and distal renal tubular acidosis could explain several of these conditions both are caused by recessive alleles.
However, it is very rare to have both. Mice used in lab experiments are often inbred, as the similar genetic structures enable experiments to be repeated. Controlling outcomes is also the motivation for inbreeding in the farming industry, with cows being bred to increase milk yields and sheep are careful selected to produce more wool. There is evidence that suggests inbreeding certain animals can have more of a negative impact than a positive one.
The two largest populations of koalas in Australia could cease to exist by just one disease, due to them being so so heavily inbred, scientists have warned. A study, headed by Dr David Balding , examined inbreeding in pedigree dogs. Like the animals bred for farming, particular traits are encouraged in pedigree dogs, including their height and the quality of their fur. The study found that a large proportion of pedigree dogs suffered from conditions caused by recessive alleles such as heart disease, deafness and abnormal development of their hip joints.
The problem is more alarming than it might seem on the surface. The reproductive patterns of Pyemotes boylei, a type of mite, are built around inbreeding. The mother mite keeps her eggs inside her until they reach maturity and the first wave to hatch is male. The degree to which rejected relatives subsequently inbreed is likely to be critical to inclusive fitness calculations.
Conceptual models that assume reciprocal inbreeding avoidance [ 24 — 26 ] or the availability of optimally related kin [ 28 ] would have limited applicability or predictive ability when the inclusive fitness benefits of inbreeding versus avoiding inbreeding are conditional upon the subsequent mating decisions of rejected relatives. Nevertheless, multiple studies have attempted to apply quantitative predictions derived from existing models of biparental inbreeding [ 24 — 27 ] to empirical systems [ 31 — 34 ].
Here we show that these predictions are unlikely to be accurate when highly restrictive assumptions are violated. We then extend this model in three ways. First, we relax the assumption that focal individuals are outbred. Second, we relax the assumption that the rejected relatives of focal individuals will subsequently outbreed.
We discuss how our model relates to empirical and theoretical research on biparental inbreeding, and to the broader context of inclusive fitness theory. We thereby highlight new avenues of research for biparental inbreeding theory, including understanding family dynamics and ultimately a more predictive evolutionary theory of inbreeding strategy. In the most basic model, males can mate with any number of females during a reproductive bout to increase their reproductive success, but females can only mate with one male and produce n offspring, which is assumed constant for all females and reproductive bouts.
Mates can be unrelated and produce outbred offspring, or be related by some degree and produce correspondingly inbred offspring. All other potential mates of M1 and F1 are assumed to be unrelated to both M1 and F1. Following inbreeding avoidance by one focal individual M1 or F1 , the other focal individual is therefore assumed to outbreed [ 24 — 26 ].
In contrast, if F1 inbreeds with M1 , she cannot also outbreed. Females F1 and F2 produce n offspring. The focal male M1 is related by r M1,F1 to the focal female F1.
Whether or not M1 inbreeds or avoids inbreeding with F1 does not affect his opportunity to outbreed with an unrelated female F2. Parker [ 24 , 25 ] calculated the inclusive fitness consequences of inbreeding versus avoiding inbreeding for M1 and F1. Areas where neither sex, both sexes, and males only benefit from inbreeding are shown in white, grey, and black, respectively. The intersections between black and white areas and black and grey areas respectively demarcate the thresholds below which M1 and F1 benefit by inbreeding [ 24 , 25 ].
From the perspective of F1 , the inclusive fitness gain from inbreeding with M1 versus avoiding inbreeding can be calculated similarly [ 24 , 25 ]. Inbreeding with M1 is therefore beneficial for F1 if, 2 Fig 2 shows that the threshold of inbreeding depression below which inbreeding benefits F1 is symmetrical to that for M1.
This zone is greatest given small r M1,F1 values and decreases to zero as r M1,F1 approaches 1 self-fertilisation. Waser et al. Clearly, in order to calculate appropriate thresholds for inbreeding avoidance or preference Ineqs. In particular, it is not always appreciated that the relevant r M1,F1 values depend on the degree to which focal individuals are themselves inbred. The alternative implicit assumption, that all focal individuals are outbred, is unlikely to be valid in populations where biparental inbreeding might occur.
The inclusive fitness consequences of inbreeding versus avoiding inbreeding therefore need to be considered for focal individuals that are themselves inbred to some degree, by defining r M1,F1 appropriately. If focal individuals are themselves inbred, then two homologous alleles have a non-zero probability of occurring identical-by-descent within an individual.
Substituting Eq 3 into Ineq. Increasing f M1 increases the right hand side of Ineq. We limit our model to one additional relative M2 , rather than many differently related individuals for tractability. Our current aim is simply to demonstrate that an additional relative can affect inbreeding depression thresholds defining inbreeding strategies, not to predict evolutionary outcomes that might arise given realistic relatedness distributions within populations; we therefore do not assume that a focal population comprises only three relatives, or that this situation will persist over evolutionary time see Discussion.
The right hand side of Ineq. Inbreeding with M1 instead of M2 increases the inclusive fitness of F1 if, 8 The left hand side of Ineq. We use these scenarios as examples to illustrate why the existence of additional related potential mates is important for predicting the evolution of inbreeding strategy, not to make specific quantitative predictions for any particular species.
Furthermore, the three focal individuals considered in each scenario are not assumed to be the only individuals within a focal population, nor are their relatedness combinations assumed to be representative of the full relatedness structure of a larger population. Our objective here is simply to show that the presence of a related potential mate affects inclusive fitness calculations. Scenario 1 illustrates a case in which all three focal individuals are equally related.
Scenario 2 introduces an example in which relatedness differs among all three focal individuals. For simplicity, our illustrative scenarios assume that focal individuals are outbred, but this is not a condition of Ineqs. Solving Ineq. Therefore, assuming there are no additional costs of inbreeding, M1 will never benefit from avoiding inbreeding if F1 subsequently inbreeds with an equally close relative of both M1 and F1.
From Ineq. We now provide such a function, and thereby provide a systematic analysis of Ineqs. The fitness of offspring produced by M1 and F1 can therefore be defined as, 9 By substituting Eq 9 into Ineq. Our example scenario 3 therefore illustrates that the presence of a related M2 can affect the threshold slopes below which inbreeding is beneficial for a focal M1 and F1 , potentially increasing the predicted zone of sexual conflict over inbreeding.
Moving away from the three simple illustrative scenarios, a more systematic analysis of inbreeding depression thresholds can be obtained using Ineqs.
Each panel shows a single constant combination of f M2,F1 and f M1,M2 values. Inbreeding depression thresholds y-axis shown on a natural log scale illustrate the values below which M1 and F1 have higher inclusive fitness by inbreeding instead of avoiding inbreeding.
The kinship between M1 and F1 f M1,F1 increases along the x-axis of all plots. Negative threshold values are mathematically possible for some parameter combinations, but are biologically unrealistic because they require that offspring fitness increases monotonically with inbreeding.
Where negative thresholds would be required, inbreeding is therefore assumed to never be beneficial. For simplicity, these examples assume focal individuals are outbred.
Although Fig 4 assumes that focal individuals are outbred, inspection of Ineqs. These patterns remain similar when a linear i. The effects of coefficients of kinship and inbreeding on inbreeding depression thresholds are therefore likely to be robust to different functions relating inbreeding to offspring fitness.
This assumption may be unrealistic; if M1 inbreeds with F1 , his opportunity to mate with F2 might decrease Fig 1A. Inequality Eq 12 shows that the magnitude of inbreeding depression below which inbreeding with F1 benefits M1 decreases as c increases from zero. The indirect cost to M1 equals the opportunity cost to M2 n c 2 multiplied by r M1,M2.
Extending our model that includes M2 Ineq. Including an opportunity cost in scenario 1 therefore decreases the inbreeding depression threshold below which M1 benefits by inbreeding with F1 versus inbreeding avoidance. Rearranging Ineq. The fitness costs associated with inbreeding, primarily inbreeding depression in resulting offspring, have caused a widespread assumption among animal ecologists that inbreeding avoidance must be adaptive [ 10 , 21 , 22 ].
Meanwhile, empirical studies have reported a lack of inbreeding avoidance [ 34 , 42 — 47 ], or even an apparent preference for inbreeding [ 48 — 52 ], causing a mismatch between expectations and data [ 27 ]. This mismatch is partially resolved by basic conceptual models of biparental inbreeding that imply that the inclusive fitness benefit of inbreeding might cause inbreeding tolerance or preference to be adaptive even given inbreeding depression in offspring fitness, and that predict sexual conflict over inbreeding [ 24 — 28 ].
Consequently, the zone of sexual conflict, and thus the sexually antagonistic selection that drives coevolving mating traits [ 53 ], will depend on the distributions of inbreeding and relatedness among potential mates, and on how these potential mates interact to determine inbreeding versus inbreeding avoidance among relatives.
His model assumes that optimally related mates are always available, and that sexual conflict is resolved in favour of females, with negligible male opportunity cost and linear inbreeding depression. In such cases, the combined inclusive fitness effects of pair-wise social interactions for focal individuals cannot simply be added up. In contexts other than biparental inbreeding, the complicating effect of non-additivity has long been recognised [ 56 ], and there is growing consensus that social interactions are likely to have non-additive effects on inclusive fitness [ 55 ].
In the context of biparental inbreeding, additive inclusive fitness effects are widely assumed [ 24 — 28 ], but are unlikely to be biologically realistic. To develop a comprehensive theory of inbreeding, it is therefore necessary to move beyond pair-wise interactions between potential mates and consider inbreeding conflict in the broader context of populations characterised by complex and non-additive interactions among realistic distributions of relatives. Non-additive inclusive fitness effects are likely prevalent in both plant and animal populations in which biparental inbreeding occurs.
Most models that focus on plants consider the fitness costs and benefits of self-fertilisation versus outcrossing, but assume that non-selfing individuals inevitably outbreed with no opportunity to cross with a non-self relative but see [ 57 ]; [ 11 — 16 ].
As in animal populations, when biparental inbreeding and inbreeding depression occur in plants [ 58 — 60 ], inbreeding conflict is expected, though very few studies have considered how such conflict might be resolved [ 61 ]. Our extension was minimal; to keep the model tractable while making our conceptual point, we only allowed three individuals to be related e.
In natural populations, multiple potential mates of both sexes might be related to each other to different degrees. A more comprehensive theory of biparental inbreeding that incorporates realistic variation in relatedness arising from any mating system and potential feedbacks between relatedness and inclusive fitness is likely needed to make useful quantitative predictions.
The complexity inherent in modelling multiple interacting individuals that are related to different degrees due to internally consistent ancestry means that further extensions to simple algebraic models will quickly become intractable. Below we show how our model of inbreeding among more than two relatives creates novel predictions regarding inbreeding conflict among nuclear family members, and outline key steps towards predictive evolutionary models of inbreeding strategies.
The dynamics of interactions among nuclear family members, including mating strategies, are of major interest in evolutionary and behavioural ecology [ 62 — 65 ]. Relaxing the assumption of additive inclusive fitness effects may alter predictions regarding within-family sexual conflict over inbreeding.
The magnitude of inbreeding depression below which a son increases his inclusive fitness by inbreeding with his mother is therefore identical to that for his mother, eliminating mother-son conflict. In contrast, father-daughter conflict over inbreeding is not predicted to be eliminated. This is because any alternative mate of a daughter that is related to her father must also be related to her.
Thus, while Waser et al. If a son has high confidence in the identity of both parents, he might benefit from ensuring that his parents continue to breed together to ensure the production of full siblings i. This simple example illustrates that accounting for the alternative mates of relatives will be necessary for any comprehensive theory of family dynamics. While inter-sexual conflict over inbreeding is often emphasised, the evolution of inbreeding strategy might also be affected by interactions between same-sex relatives.
Our model assumed that the inbreeding strategy of any one focal male was not directly affected by the strategies of other males. Specifically, we assumed that when a focal male M1 avoided inbreeding, the other male M2 mated with the focal female F1.
We further assumed that when M1 inbred with F1 , M2 did not interfere. But in reality, M1 and M2 might mutually compete to inbreed with F1 , or might mutually avoid inbreeding. If inbreeding conflict is generally resolved in favour of females, meaning that females are successful at avoiding inbreeding when it benefits them to do so, then there might be little selection for males to attempt inbreeding when there is sexual conflict.
For example, competition between M1 and M2 may affect the inclusive fitness benefits of inbreeding. Details of the mating system are therefore likely to strongly influence the resolution of sexual conflict [ 25 , 68 ].
As an illustrative example, if M1 and M2 are equally related to F1 and inbreeding depression is strong, then M1 and M2 will both benefit from mutual inbreeding avoidance. Both males will lose fitness if either inbreeds with F1 , but each will lose more if he avoids inbreeding with F1 but his male relative inbreeds with F1. The decision for each male to inbreed with F1 or not can be modelled using a game-theoretic framework where payoffs are proportional to the inclusive fitness benefits for different mating situations.
A full game-theoretic model is beyond the scope of this paper, but a simple example illustrates a basic framework. We further assume no opportunity cost of inbreeding i. If both M1 and M2 avoid inbreeding, we assume F1 outbreeds with a different unrelated male. Both M1 and M2 therefore have an indirect fitness benefit of r n r 2.
Inbreeding avoidance is therefore an ESS for M1 i. Interestingly, a mixed strategy, in which inbreeding avoidance is probabilistic, is an ESS for a narrow range of intermediate values. If M1 inbreeds but M2 avoids inbreeding, then M1 will receive a payoff of 21 40 , greater than if both mutually inbreed or avoid inbreeding. In contrast, M2 receives a payoff of only 7 Instead of an absolute inbreeding avoidance, preference, or tolerance strategy, a probabilistic strategy might therefore be predicted in some circumstances.
This basic model makes multiple restrictive assumptions, but it suggests that a game-theoretic approach might be useful for understanding mating conflicts among male relatives. Our models imply that the inclusive fitness costs and benefits of inbreeding versus avoiding inbreeding will vary among individuals depending on their interactions with multiple different relatives of both sexes, and on the degree to which focal individuals are themselves inbred.
Understanding these costs and benefits and their combined consequences for the evolution of inbreeding strategies therefore requires consideration of not only the relatedness of an individual to its potential mate s , but also the relatedness between the individual and the subsequent mates of rejected relatives. How is this higher level of inbreeding affecting our dairy industry? At this point it is hard to say. What does this mean in English? If this occurs in good genes then we see a positive effect.
However, if this happens in bad genes we see negative effects. The fear is that if a new disease emerges there will not be enough diversity in the cattle population to fight it off. The main problem with inbreeding is that we have no control over what genes are passed from parent to offspring, therefore we run the risk of increasing homozygosity at both good and bad genes.
The race to create the best herds has resulted in increasing the inbreeding in all current active sires in the U. What this means is that any bull in the current active sire list of any stud will likely be related to your herd.
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