How do I tune the incidence of gene expression in my fictitious population?

Premise

When designing new species, or even creating alternate reality scenarios, I often find myself desiring some trait(s) to be shared among some group, but with various degree of probability. The story may sets requirements about prevalence, sex and heritability. The constraints may be quantitative (e.g. probability $$p$$ of incidence) or qualitative (e.g. traits $$T_1$$ and $$T_2$$ are mutually exclusive).

Generally I resort to genetics for plausible explanations and try to arrange a fitting scenario, but being unfamiliar with the matter, this is a tedious process.

For illustration purposes, some type of constraints I find myself facing are:

• trait W has some probability $$p$$ to occur given that the mother has it with certain probability, but no information is available about the father and the general prevalence among males is $$p_m$$.
• trait X should only be observed in females, but may be passed on to the next generation silently by males
• trait Y is not systematic, but if one individual has it, then it must follow that their sibling have it too
• trait Z is rare, but if both parents have it, their children are very likely to have it too.
• etc.

Again, these are just illustrations to give a general idea of the constraints that stories might impose. These constraints might play important roles in explaining the hierarchical or cultural relationships between different members of the group, reliance on the trait as a survival strategy or consequences of reproduction with individuals from other groups.

Often the precise probability desired is not a hard constraint. In other words clipping probabilities to simple values like (0%, 25%, 50%, 75%, 100%) might be enough if that simplifies the design process.

Question

What methodology could one follow, once the general constraints have been laid out (quantitative and qualitative) to attribute the desired traits to the population's genotype?

Another way of phrasing the question (from my naive point of view): if you were presented with a list of experimental observation about some (set of) trait(s) and asked to provide a genetic model to fit the observation, what methodology would you follow?

Important note

To limit the scope of this question, I am only referring to intermediate timespan constraints: heredity may be part of the constraints but mutations and natural selection can be considered to happen on timescales irrelevant to the story. The question of whether the trait gives competitive advantage or not should therefore not be relevant.

• You seem to have the mindset and the ability with math required to understand genetic theory well. Perhaps just a pointer in the right direction will help make the process fun rather than tedious. – The Square-Cube Law Nov 9 '18 at 23:40
• True. A set of links to useful references would be valid. That said, I think it would be nice if the accepted answer could be useful to people with limited grasp of genetics. E.g. I just learned about "cross-overs" and never used that as a degree of freedom yet. – Alexis Nov 9 '18 at 23:45

There are six basic patterns of inheritance of single gene traits found in humans. These patterns depend primarily on the location of the gene (which chromosome it is found on) and the alleles' effects with one or two copies. I will describe each of these six patterns. I am refraining from describing the results of all possible Punnett Squares for the sake of brevity, but if you want to work out the specifics for each case that is the tool to use.

Autosomal dominant: An autosome refers to all chromosomes in the nucleus that are not sex chromosomes (X and Y). A dominant allele is one which has a phenotypic or observable effect when an individual has at least one copy of it. This means that an individual with an autosomal dominant phenotype could either have one or two copies of the allele while an individual who does not show the phenotype must possess no copies of it. For an individual to inherit this phenotype at least one of the parents must also have this phenotype.

Autosomal recessive: An autosomal recessive allele is one which only influences the phenotype of the individual when both copies of the gene are this allele. An individual with an autosomal recessive phenotype always has two copies of this allele. These traits can skip generations, meaning two individuals who do not have the phenotype but both have one copy will have a child with the phenotype 1/4 of the time.

X-linked Dominant: An X-linked gene is one that is found on the X chromosome. Because females have 2 X chromosomes and males have only 1 this results in different inheritance patterns and phenotypes between the sexes. A dominant allele will create a phenotype in both males and females. A male with this trait will always pass it on to his daughters, but will never pass it on to his sons. A female with this trait will pass it on to half or all of their offspring depending on whether they themselves have one or two copies. This trait will be more prevalent in females than in males because females will be more likely to have at least one X chromosome with this allele.

X-linked Recessive: A recessive allele on the X chromosome will affect more males than females. This is because males only have one X chromosome so a single copy of the recessive allele will be sufficient to create a phenotype. Females with two X chromosomes will require two copies of the allele to present the phenotype. Males will never pass this trait to their sons, and they will only pass one copy to their daughters which is not sufficient for the phenotype to present. Females with this trait and therefore two copies of the allele will always pass it on to their sons, while females without the trait but with one copy will pass it on to their sons half the time.

Y-linked: As humans typically only have up to one copy of the Y chromosome all alleles on the Y chromosome can be thought of as dominant. Females cannot present Y-linked phenotypes as they do not have Y chromosomes. A male with this allele will always pass on this phenotype to his male offspring.

Mitochondrial: Humans actually have a small additional genome outside of the nucleus in their mitochondria. This mitochondrial genome is only inherited from the mother via the egg and not from the father. As a result, mitochondrial alleles can also be thought of as entirely dominant. Males do not pass on their mitochondrial DNA to their offspring but females always do. Male and female offspring will have exactly the same mitochondrial DNA as their mother.

These are the basics. In reality, most human traits are the result of many genes acting in concert and are referred to as complex traits. Each individual allele is inherited according to the above principles, but since many alleles affect the traits it is difficult to determine the effect of each individual one. Most traits are also heavily influenced by their environment. This leads to the concept of penetrance which is the idea that even for single allele traits the presence of a phenotype and its strength can be a stochastic distribution for reasons not always well understood.

EDIT: To address the specific examples you gave in your question and generally on the plausibility of inheritance patterns that don't neatly fit into the above categories it's important to recognize that genetics is incredibly complex and is full of weird phenomena and bizarre exceptions. With enough knowledge and thinking you can probably justify just about anything you can imagine, but that doesn't mean that whatever you come up with is actually likely to ever occur. I'll take a shot at providing an explanation for each of the examples you gave.

trait W has some probability $$p$$ to occur given that the mother has it with certain probability, but no information is available about the father and the general prevalence among males is $$p_m$$.

As far as I can tell there are no difficulties with this scenario. It could describe any of the automosomal, X-linked, or mitochondrial examples patterns above. If you'd like to calculate the actual probabilities the fundamental equation at the heart of human genetics is the Hardy-Weinberg Principle.

trait X should only be observed in females, but may be passed on to the next generation silently by males

If this trait is related to being female in some way this is trivial. Males can pass on predispositions for breast cancer for instance but are unlikely to present it themselves. However, if this is a general trait that would be expected to be observed in both males and females it is difficult to justify why it would not present in males. Some possibilities might involve X-inactivation or genomic imprinting.

trait Y is not systematic, but if one individual has it, then it must follow that their sibling have it too

The genes that one individual inherits will always be independent of those their siblings inherit. While generally, we say sibling share 50% of their DNA, that's only an average. In reality, siblings can share as little as 0% and as much as 100% of their DNA although either extreme is quite unlikely. The only genetic way to ensure that all offspring of a set of parents will have a trait is if the trait is recessive and both parents have it. Another explanation could, however, be environmental. If, for instance, a mother exposes all of her children to the same odd prenatal environment that could cause all of them to possess a similar trait.

trait Z is rare, but if both parents have it, their children are very likely to have it too.

This trait would fit nicely into an autosomal recessive pattern of inheritance.

• Wait so my Y chromosome is essentially the same as my father's and by induction the same as all my male ancestors? – Alexis Nov 10 '18 at 0:36
• Does your last paragraph implies that as far as bottom-up WB is concerned, one should not worry about realistic genotypes, because there will always be a realistic explanation for whatever feature that the story requires? – Alexis Nov 10 '18 at 0:39
• @Alexis Yes, your Y chromosome is passed down through your paternal lineage unaltered except by mutation (with the exception of the Pseudoautosomal region). My last paragraph was not intended to imply that anything is possible. Multigenic traits, environmental effects, and incomplete penetrance allow you to justify what might be called cryptic inheritance patterns where the inheritance appears random and doesn't fit any of the above patterns well. However, it can't really be used to justify strange inheritance rules such as sibling inheritance of trait Y in your example above. – Mike Nichols Nov 10 '18 at 0:50
• If I can abuse of your help, is example Y actually an impossible constraint, or simply one that would need more that the complex traits you described? And in the former case, could you describe in your answer the reasoning behind it? – Alexis Nov 10 '18 at 1:16
• @Alexis The human Y chromosome is capable of recombining some genes with the X. It is transmitted from father mostly, but not fully unaltered. – The Square-Cube Law Nov 10 '18 at 2:47

You could do it like the father of genetics, Gregor Mendel (pun intended, since he was a catholic priest).

The wiki has this to say about him:

Though farmers had known for millennia that crossbreeding of animals and plants could favor certain desirable traits, Mendel's pea plant experiments conducted between 1856 and 1863 established many of the rules of heredity, now referred to as the laws of Mendelian inheritance.

His laws can be summarized thus:

• Law of segregation: During gamete formation, the alleles for each gene segregate from each other so that each gamete carries only one allele for each gene.

• Law of independent assortment: Genes for different traits can segregate independently during the formation of gametes.

• Law of dominance: Some alleles are dominant while others are recessive; an organism with at least one dominant allele will display the effect of the dominant allele.

You can apply this to the constraints you mentioned:

trait Z is rare, but if both parents have it, their children are very likely to have it too.

What this means, for example, is that the trait is very probably tied to recessive alleles; The more pairs involved, the rarer a trait expression is. For example, I come from a city where (AFAIK and remember) 97.5% of the population has a positive Rh blood factor. There is only one gene for the Rh factor, but there are many different alleles (over 170), with only a minority of them being recessive and giving no expression to the Rh factor.

Hence, your case where children inherit a rare trait could be similar to the Rh negative expression. You can simplify it by considering always only two or three possible alleles, and having both parents have only recessive copies. It's just a matter then of combinatory analysis. If you want numbers different from multiples of 25% for probabilities, work with pairs or trios of genes for a trait.

but mutations (...) can be considered to happen on timescales irrelevant to the story.

Your story, your rules. But mutations are one of the reasons sometimes a child who should by all Math have two recessive genes ends up expressing a dominant trait (the other being misidentified parentage).

Over generations, mutation is a matter of statistics; in a syory, it's a lottery (and plot).

Sometimes your genes are not all that there is to a trait. Some genes need some stimulus to be expressed. For example, you may have the genes for size D cups, but if.you are a man you probably won't have breats that large. That's because those genes express themselves more if you have more strogen and progesterone than testosterone in your blood

So:

trait X should only be observed in females, but may be passed on to the next generation silently by males.

Looks like a gene that is not in the X chromossome, but it requires female hormones to be expressed.

Other examples of stimulus:

• Some people only get red rather than tan with exposure to the the sun, but even if you have the genes for a tan you still need sunlight in order to be tan.

• Many allergies are genetic. Classic example of genes with a trigger.

Sometimes genea interact among themselves as well. Hemoglobine is produced by a series of genes; Porphyria happens when a gene in the chain fails. And the gene for polydactilia will have no expression if you are unlucky enough to be born without hands.