Decision analysis of whether cloning the most elite Special Forces dogs is a profitable improvement over standard selection procedures. Unless training is extremely cheap or heritability is extremely low, dog cloning is hypothetically profitable. finished certainty : possible importance : 3

Cloning is widely used in animal & plant breeding despite steep costs due to its advantages; more unusual recent applications include creating entire polo horse teams and reported trials of cloning in elite police/Special Forces war dogs. Given the cost of dog cloning, however, can this ever make more sense than standard screening methods for selecting from working dog breeds, or would the increase in successful dog training be too low under all reasonable models to turn a profit? I model the question as one of expected cost per dog with the trait of successfully passing training, success in training being a dichotomous liability threshold with a polygenic genetic architecture; given the extreme level of selection possible in selecting the best among already-elite Special Forces dogs and a range of heritabilities, this predicts clones’ success probabilities. To approximate the relevant parameters, I look at some reported training costs and success rates for regular dog candidates, broad dog heritabilities, and the few current dog cloning case studies reported in the media. Since none of the relevant parameters are known with confidence, I run the cost-benefit equation for many hypothetical scenarios, and find that in a large fraction of them covering most plausible values, dog cloning would improve training yields enough to be profitable (in addition to its other advantages). As further illustration of the use-case of screening for an extreme outcome based on a partial predictor, I consider the question of whether height PGSes could be used to screen the US population for people of NBA height, which turns out to be reasonably doable with current & future PGSes.

Military and police dogs are specially trained for their jobs. Only some dogs are up to the task, but like training seeing-eye guide dogs, it’s difficult to know in advance and many dogs will wash out of training as expensive failures, with even fewer being able to handle the extreme life of a Special Forces dog; then they may get injured on the job, develop hip dysplasia or cancer, cutting short their career, and leading to perennial shortages. This is despite the best efforts of the (mostly European) breeders who raise the Malinois, German Shepherd, Belgian Shepherd, and Labradors preferred for war dogs.

The 7 Tomorrow Dogs/Toppies cloned in 2007.

In 2014, Bloomberg reported on an interesting aspect of Sooam Biotech, the famous South Korean dog cloning company: they were cloning a Special Forces dog. If it’s hard to be a K9, it’s even harder to be a SF dog, able to jump out of airplanes (they have special parachute harnesses), go on raids, carry cameras with them, even (reportedly) wear little doggie hoods with infrared camera goggles for night work; so valuable and specialized are such dogs that special $20,000 animatronic dog models like the “K9 Hero-Trauma” are sold to train medics how to treat injuries like gunshot wounds or amputations. If you have a successful SF dog… maybe the clone will be much more likely to succeed than a random puppy picked from one of the usual breeders, and you can make as many clones as necessary long after the original has gone to Dog Heaven.

Clones of elite individuals are increasingly common in agriculture; plants, like the myriads of apple varieties, have always been propagated clonally, but cloning of cattle has made major commercial inroads —not just cloning of cattle for beef or cows for milk, but also clones of rodeo bulls (the logical extension of the highly successful selective breeding for rodeo bulls). A striking example of this approach is the world polo champion Adolfo Cambiaso, who is so enthusiastic about the benefits of horse cloning that he has cloned his prized polo horse not once but >10 times, and has rode entire teams of clones to repeated victory. On the other hand, dog clones are still extremely expensive (~$100,000) and prices have not yet come down to the ~$10,000–$20,000 of cattle.

There may be cheaper alternatives to improving SF dog yield: training is probably well-refined and can’t be watered down without risking lives, but that leaves a place for improvement of what is trained, the selection into training—better prediction of SF potential means fewer dogs washing out means less total money spent to produce a successful SF dog. The predictions don’t work well, but the descriptions of screening suggest there’s a lot of room for improvement: the research literature supports the generalization that dog and cat behavioral measurements are not all that predictive. They may be badly designed or testing the wrong things, or there may be inherent noise which can be fixed by doing multiple measurements. (Even something as apparently mechanical as offering catnip to a cat can have different results from occasion to occasion and may have rater-specific effects, perhaps because—“set and setting”—the cat is fearful and distrusts the person offering the catnip that day, with the anxiety shutting down any response or play.) Many described measurements in the literature measure a dog once, on one day, by one person, for example, measuring aggressiveness by taking away food and seeing if the dog snaps at the person, and that’s the whole test. Such a test will be hindered by day-to-day variation (perhaps he is stressed that day), different levels of liking for that particular food, disliking of the person taking the food, sheer randomness in the particular split-second decision of whether the dog decides to express their aggression—likely would be much stabler and predictive if they were done multiple times in multiple ways by multiple people etc (although such extended testing would increase the cost of testing). Of course, that would take more time and would cost a lot more, and it’s unclear the increase in predictions is worth it.

However, ranking for selection is easier than prediction of all datapoints: only the ordering matters, and only the ordering in a particular region (near the threshold) matters. When considered in a real-world context, such predictive improvements do not need to be all that large (a point long made by psychometricians & industrial psychologists eg Taylor & Russell 1939/Schmidt et al 1979/Lubinski & Humphreys 1996); counterintuitively, a score or test which correlates, say, r=0.10 with an outcome, which in many areas of science would be dismissed as a trivial correlation of no interest, can be quite useful in screening & should not be dismissed as ‘small’—and the rarer the outcome, the larger the benefit. In the case of dog cloning, our ‘score’ is the extent to which a donor’s performance predicts the performance of its clones, through their shared genes.

Both approaches could wind up being expensive and there’s no a priori answer about which one would be more cost-effective. To a certain extent, they are also mutually exclusive approaches: dog cloning is so expensive that unless it results in high probability of success, it probably won’t be cost-effective at all, and if the probability is sufficiently high, then testing is no longer useful (because you would save money by simply trying to train all clones), so better testing is unlikely to then pay for itself. Testing to gain information is only profitable in a certain intermediate region of probabilities & costs/benefits.

So it’s not absurd to think that dog cloning could work out well for training SF dogs, and I took a closer look.

Benefits The benefits of dog cloning are not limited purely to replicating an elite SF dog. The potential benefits of dog clones include: lower total cost: the primary reason for cloning is that since dog clones are more likely to succeed in training given any reasonable heritability, they may reduce washout costs enough to compensate for the expense of cloning. But the total lifetime cost of a dog goes beyond success or failure in becoming a useful dog. Successful dogs can still learn at different rates, and require more or less intensive intervention by trainers. Dogs can learn multiple roles, so a ‘success’ may only be a partial success, like a dog who is approved for odor detection of bombs or drugs, but can’t be used on patrol or raids. They can have longer or shorter careers, reflecting levels of competence and medical issues (hip dysplasia constantly comes up in war dog discussions as a disabling medical problem, and is highly heritable). Hence, discussing only success/failure in training and the reduction in average training cost will seriously underestimate the benefits of cloning the best: clones of the best SF dogs will train faster, with less effort/time, excel at more roles (more likely to be acceptable for at least one role), be less likely to have crippling medical issues that kill them or end their careers prematurely, and have longer careers in general. greater scalability in dogs: there are only a few dog breeders, and they have only a relative handful of bitches at any time Even if demand spiked in a war and 1,000 more dogs were needed yesterday, they wouldn’t exist—dogs take a certain amount of time to reach sexual maturity, have only so big litters, mating in inbred/narrow pedigrees like German Shepherds/Malinois must be managed carefully to avoid exacerbating existing genetic issues (and eating the seed corn), training takes a while (Ritland notes that the US Navy takes delivery of 2-year-old dog candidates), and so on. In reading about US war dogs, a perennial theme noted by Hammerstrom 2005 is that a war happens (WWII, Vietnam, War on Terror), war dogs become incredibly useful to frontline troops, and dog supply simply cannot keep up. Use of cloning can break part of the bottleneck by enabling surrogacy in female dogs of other breeds which are not scarce, and by enabling unlimited reproduction of a particular dog. (This doesn’t require cloning, since one could create the necessary embryos with standard IVF, but since the IVF/surrogacy is necessary, why not use cloning as well?) This option is highly valuable and justifies dog cloning on its own; and because this option is available, militaries can more steeply reduce war dog numbers during peacetime as no ‘reserve’ is necessary. greater scalability in facilities: another bottleneck might be not the number of dogs, but the infrastructure for housing/training/testing the dogs. There might be only so many dog kennels and experienced dog trainers at any point, and increasing the number could take a while. (You probably want the trainers and program management to have SF dog handler experience themselves, but it might take decades for a recruit to become an experienced trainer.) So given the inelastic throughput, here it would be valuable to improve the quality of inputs, which will increase the total yield, simply because it means less dilution or waste of scarce fixed housing/training/testing slots on dogs less likely to succeed. greater predictability: Response to Training: yield might be increased simply by the inherent homogeneity of clones allowing improved training by greater experience, rather than any increased genetic merit. One of the reasons Adolfo Cambiaso gives for investing so heavily in clones of a single polo horse is that he has learned from his long experience with the donor horse how best to train them: each new clone can be given personalized training which he knows it’ll respond best to, because he’s trained many clones before them. If there is some consistent weakness the clones are prone to, he can start addressing it before it even shows up. He also has gained long experience with their injury propensities, preferences, and other behavior, instead of starting from scratch with each new colt. Their similarity avoids the need for learning or wasted pedagogy. Dogs presumably vary as much as horses do, and training of clones could benefit from this sort of homogeneity. (Since dog trainers will have never encountered clones before, and identical twin dogs are vanishingly rare, there’s no way to know how useful this would be in practice until large numbers of dog clones have been trained by individual trainers.)

Reduced Variance for Experimentation or Analysis: statistical power scales poorly with increasing variance; relatively small increases in noise can require much larger n to overcome. The most efficient experiments are within-subject experiments, which avoid comparisons between individuals, but these are often impossible—one could not test improvements in puppy rearing, for example, or most training program changes. This is true of many things in humans as well; for this reason, experiments with identical twins are highly efficient (in the Lanarkshire milk experiment, a sample of n>10,000 children could have been replaced with n~300). Identical twins are remarkably powerful even in the absence of randomization for inferring causation (Turkheimer & Harden 2014) and by controlling for all genetics (which in human research, debunks a large fraction of all correlational research in psychology/sociology), make correlational analyses much more likely to deliver useful causal insights. As dog identical twins hardly exist, this has hitherto been entirely unavailable a research design for dog researchers, but clones change that.

Reduced Variance For Process Control: given the choice between a small group of clones and a much larger group of regular dogs, such that they have ostensibly identical average costs & the same number of expected successes, which should a breeder or trainer prefer? The small group of clones, of course. The large group will, by the law of small numbers, have larger absolute fluctuations due to randomness, especially with a base rate like 1%. It’ll be ‘feast or famine’. Sometimes there will be considerably more, sometimes considerably less in absolute numbers. This will complicate planning greatly, stress facilities/trainers, risk delivering too few (or too many) dogs each year, and so on. Switching to clones with a higher base rate will make the overall process more controllable and predictable, and this is worth something. use in selective breeding: The major use of cloning in cattle is for accelerating breeding programs, and not for their immediate marginal increase in meat or milk yield. While dog breeding is not nearly as sophisticated, the benefits of cloning may also be larger for the long-term improvement in the breed than for its immediate benefits in each cloned dog: clones can improve Estimates Of Genetic Merit by providing the most accurate possible heritability estimates (genetically identical individuals reared in different environments), and correcting individual estimates of traits, which is vital for planning any kind of breeding or selection program

by providing the most accurate possible heritability estimates (genetically identical individuals reared in different environments), and correcting individual estimates of traits, which is vital for planning any kind of breeding or selection program a clone can have a Greater Genetic Potential than the average SF dog if intensive selection is done among SF dogs: if the best SF dog is selected for cloning, it’ll have a higher genetic potential than the default calculation of a truncated normal+regression toward the mean on a random SF dog would imply.

than the average SF dog if intensive selection is done among SF dogs: if the best SF dog is selected for cloning, it’ll have a higher genetic potential than the default calculation of a truncated normal+regression toward the mean on a random SF dog would imply. elite clones can be Heavily Used In Breeding Programs in allowing particular individuals to keep contributing genetically long after the original has become infertile or died, or contribute far more (as mentioned before, female dogs are highly limited in reproductive fecundity compared to males, but they could be cloned & born via surrogacy). For example, the first cloned dog, Snuppy, died in 2015, but is survived by 3 clones of himself.2, and the record for number of clones appears to be the 49 clones of the world’s tiniest dog, Miracle Milly. Value of Information: dog cloning may or may not be worthwhile, but if it is, the total returns from cloning hundreds of dogs per year indefinitely (plus the additional benefits) could be large. It would be valuable to know if it would work. Since I have not found any SF/military-specific heritabilities reported in the scientific literature (and the SF dog programs generally seem genetically unsophisticated so there may not be any private or classified ones either), the only way to know is to try it out experimentally. The clones’ realized performance would also provide additional valuable information as it would estimate heritability, which would be useful for the regular kinds of breeding & selection as well—because they give an idea of how much one can predict a dog’s performance based on known relatives, and how fast a breeding program can/should proceed. And since, to be profitable, the success rate of clones need to be >=9% (which is highly likely, see later), this is reasonably easy to estimate: a sample of ~50 clones would give a reasonably precise estimate as to the success rate and enable better decision-making as to whether to keep pursuing cloning (in which case more information will come in and firm up the decision) or drop it as a dead end due to too high costs and/or low heritability. (By the same logic, one could treat choice of donor itself as a multi-armed bandit problem to optimize the selection, since with success rates likely >50%, the necessary sample sizes will be not unreasonable and will be reached as clone use ramps up—like in South Korea, which has at least 42 clone dogs deployed in 2019 and appear to be increasing clone use as they claim great increases in success rates, decreases in costs, and net savings, implying substantial heritability.)

Modeling the SF selection problem South Korea How could we estimate the benefit of cloning? Given an active dog cloning program like Sooam and sufficient experience, it can be estimated directly. Choi et al 2014 reports that normally-bred detector dogs have a training success rate of 30% vs 86% for cloned dogs; the 30% appears to be based on the drug detection program, and the 86% is based on their sample of 7 of which 6 passed (ie 67=0.86) Oh et al 2018 notes as a followup …the Toppy [clones] had the exact same genetic information as the elite drug sniffing dog, whereas the control dogs were the offspring of sniffer dogs. Surprisingly, all seven Toppy were selected with high scores, in contrast with the control group, of which three of the seven trained dogs were selected (Choi et al. 2014). In the 6 months after the seven Toppy clones were added to airport security, the drug detection rate increased sixfold, at the same time saving the budget for selecting elite dogs. Thus, outstanding abilities can be passed on to the next generation by cloning identical dogs that inherit identical genetic material. A 2017 Korea Bizwire provides a partial cost-benefit analysis in a press release: Cloning and deployment of special forces dogs began in 2012 as part of an initiative by the Rural Development Administration (RDA), in an effort to slash spending on police dog training. Special forces dogs come at a high price. For every dog, an estimated 1.3 billion won ($112,554) is spent on training them for multiple purposes such as human rescue, explosive detection and custom service. Despite the price, only 3 out of 10 dogs [30%] make it through the exhaustive training process to serve on police forces. Clone dogs, on the other hand, have a much higher pass rate of 80%, bringing down the training costs to 46 million won ($39,775). Compared to regular dogs, they offer savings of 65%. “Sharing a competent and well-trained dog is no longer impossible, thanks to cloning”, said Im Gi-soon, a chief animal biotechnologist at the National Institute of Animal Science (NIAS). It’s unclear if this 80% estimate is merely re-reporting Choi et al 2014, but if training each costs 3⋅112,55410 = ~$33,000, so going from 30% to 80% success rate means the clones have a training cost which is 39,775112,554 = 35% that of the regular dogs or $72,000. The costs here clearly exclude cloning, but as Viagen is able to offer consumer dog cloning at $50,000 and Sooam has the advantage of experience & much greater scale (in addition to any patriotic discounts), the SK police could be getting a substantially lower price. But if they pay the full $50,000 anyway, then they are still reducing the total cost to (33,000+50,000)⋅108=103,750, saving $8,804. And at the $15k which may be the Viagen marginal cost, they would save $52,554. However, one might doubt these numbers or how applicable they are, and they appear to exclude the substantial cost of cloning, rendering the cost-benefit incomplete. A 2019 newspaper article states: According to the Animal and Plant Quarantine Agency, 42 of its 51 [82%] sniffer dogs were cloned from parent animals as of April, indicating such cloned detection dogs are already making significant contributions to the country’s quarantine activities. The number of cloned dogs first outpaced their naturally born counterparts in 2014, the agency said. Of the active cloned dogs, 39 are currently deployed at Incheon International Airport, the country’s main gateway…While the average cost of raising one detection dog is over 100 million won (US$85,600), it is less than half that when utilising cloned puppies, they said. The lower price here may refer to lower levels of selectivity: “detection dog” vs “training them for multiple purposes”. But the wording implies this refers to total costs, since it states “raising” rather than just “training”, which usually means a total cost from the beginning. So if training each candidate dog costs the implied $25,680 and the success rates continue to be 30% vs 80%, and the clones have a per-success cost half that of normal dogs, then the implied amortized cloning cost would appear to be ~$8,560 (85,600⋅0.5=10⋅(25,680+8,560)8). Cost-benefit in selection problems How would we approach this problem from first principles? A SF dog is highly selected among candidate dogs, and it is either an acceptable SF dog or not. Being a SF dog requires a package of traits, ranging from physical health to courage to finely-controlled aggression (attacking if the handler orders, immediately stopping when counter-ordered), which sum up to an overall quality: somewhat poorer health can be made up by better smelling skills, say. So a natural approach is to treat it as a logistic model, or more specifically, a liability threshold model (“Ch25, Threshold Characters”, Lynch & Walsh 1998): if a bunch of random variables all sum up to a certain high score, the dog becomes SF, otherwise, it is a normal dog. These random variables can be split into genetic variables, and everything else, ‘environmental’ variables. Then the benefit of cloning can be estimated based on how much the genetic variables contribute to a high score, how high the genetic variables of a cloned SF dog might be (remembering that they are highly selected and thus imply regression to the mean), and this provides an estimate for increased probability that the clones will achieve a high score too. This is effectively an extreme case of truncation selection where a single individual is used as the ‘parent’ of the ‘next generation’. (This is not a bivariate maximum, because the clone is different from the selected donor individual, and is a draw from a new distribution.) Once the probability a clone will succeed versus a random candidate dog is calculated, then one can get the cost of screening candidate dogs for a SF dog versus cloning+screening clone dogs for a SF dog. So we need to know: how difficult it is for a regular SF dog candidate to succeed, and what the implied threshold for a ‘SF score’ is of a random SF dog, and of a elite SF dog if possible, how much less difficult it is for a cloned SF dog candidate to succeed, for the implied boost in their average scores the cost of training a regular SF dog candidate the cost of cloning an elite SF dog the heritability of SF success, or failing that, dog traits in general as a prior The answers seem to be: <1% of breeder puppies may eventually make it to successful SF deployment; most selection happens in the 2 years before handover from the breeder to the military, and failure rates are substantially lower during the military training. For more conventional military or police use, success rates are much higher, and from puppy to deployment, probably more something like 25%. Of successful SF dogs, the SF cloning pilots appear to be choosing from dogs in the top 1% or higher of SF dogs. the post-handover cost of training per SF dog is likely >$50,000, with total lifetime cost being higher; conventional military/police dogs are again much less stringently selected/trained and thus cost much less, perhaps as low as $20,000. dog cloning costs have dropped steeply since the first cloned dog in 2005 (in large part thanks to consumer demand for pet cloning), with 2019 list prices at <$50,000 and marginal costs possibly as low as $16,000 (so cloning at scale could cost only >$16,000)

Liability threshold model This requires us to estimate two things: the threshold and the heritability on the liability scale. For common police dogs and other working dogs, training appears to be not that hard, and estimates of 30–50% are seen. This gives a threshold of 50%, or in standard deviations, 0SD. A SF dog is much more selective, and the only specific estimate given is <1% by Mike Ritland, which in standard deviations, means each dog would be >=2.33SD, and the actual mean created by this selection effect is +2.66SD. (If this is confusing imagine a threshold like 50%: is the mean of everyone over 50% equal to 50%? No, it has to be higher, and the mean of everyone >=0SD/>=50% is actually more like 0.8SD/75%—not 0SD/50%!—and we need to use the truncated normal distribution to get it right.) The clone of the SF dog shares only genetics with it, it doesn’t benefit from the unique luck and environment that the original did which helped it achieve it success, so it will regress to the mean. If genetics determined 100% of the outcome, then the clones would always be +2.66SD just like the donor, and hence make the 1%/+2.33SD cutoff 100% of the time, as they have the same genetic potential and zero environmental input (although that is extremely unlikely a scenario, due to measurement error in the testing if nothing else). While if genetics contributed 0% to the outcome and did not matter, then the clones will make the 1% cutoff just as often as if they were a random dog sampled from their breeders ie. 1%. And in between, in between. Under a more plausible case like genetics determining 50% of the variability (a common level of heritability for better-studied human traits), then that is equivalent to a perfect genetic predictor correlating r=0.7; the r, remember, is equivalent to ‘for each 1 SD increase in the independent variable, expect +r SDs in the dependent variable’, so since the clone donor is +2.66SD, the clones will only be 2.66⋅0.7=1.86 SD above the mean. If the clones are distributed around a mean of +1.86SD thanks to their genes, what’s the probability they will then reach up to a total of +2.33SD (the threshold) with help from the environment & luck? Half the variance is used up, and the environment has to contribute another 2.33−1.86 = +0.47SD, despite causing differences of only 0.7SD on average. In that case, the clones will have ~26% chance of being successful—which is a remarkable 26x greater than a random dog, but also far from guaranteed. But one can do better, since it is not necessary to select a random SF dog (with their implied average of +2.66SD) but one can select the best SF dog and clone this elite specimen instead. Multi-stage selection is always more efficient than single-stage selection, particularly when we are interested in extremes/tails, due to the ‘thin tails’ of the normal distribution. At any time there are thousands of SF dogs worldwide, and more in retirement (and perhaps more if tissue samples have been preserved from earlier generations), so the gain from an additional selection step is potentially large (especially when we consider tail effects), and since only 1 dog is necessary for cloning, why settle for anything less than the best? If one can select at least the best SF dog out of 1000 , then the new ‘threshold’ is +4.26SD and the expectation for our elite dog is +4.47SD, and likewise, the clones at 50% heritability would be +3.16SD, which is considerably above the original SF threshold of 2.33SD, and now fully 88% of the clones would be expected to succeed at SF training. Source code defining the truncated normal distribution, the cloning process, and a Monte Carlo implementation : ## exact mean for the truncated normal distribution: truncNormMean <- function (a, mu= 0 , sigma= 1 , b= Inf ) { phi <- dnorm erf <- function (x) 2 * pnorm (x * sqrt ( 2 )) - 1 Phi <- function (x) { 0.5 * ( 1 + erf (x / sqrt ( 2 ))) } Z <- function (beta, alpha) { Phi (beta) - Phi (alpha) } alpha = (a - mu) / sigma; beta = (b - mu) / sigma return ( ( phi (alpha) - phi (beta)) / Z (beta, alpha) ) } ## If we select the top percentile, the cutoff is +2.32SD, but the mean is higher, +2.66SD: qnorm ( 0.99 ) # [1] 2.32634787 truncNormMean ( qnorm ( 0.99 )) # [1] 2.66521422 truncNormMean ( qnorm ( 1 -0.01 ^ 2 )) # [1] 3.95847967 cloningBoost <- function ( successP= 0.01 , preThreshold= 0.01 , heritability= 0.5 , verbose= FALSE ) { threshold <- qnorm ( 1 - preThreshold) successThreshold <- qnorm ( 1 - successP) originalMean <- truncNormMean (threshold) cloneMean <- 0 + ( sqrt (heritability) * originalMean) ## regress to mean regression <- originalMean - cloneMean cloneP <- pnorm (cloneMean - successThreshold, sd= sqrt ( 1 - heritability)) if (verbose) { print ( round ( digits= 3 , c (threshold, successThreshold, originalMean, cloneMean, regression, cloneP))) } return (cloneP) } ## Alternative Monte Carlo implementation to check: cloningBoostMC <- function ( successP= 0.01 , preThreshold= 0.01 , heritability= 0.5 , verbose= FALSE , iters1= 10000000 , iters2= 1000 ) { threshold <- qnorm ( 1 - preThreshold) successThreshold <- qnorm ( 1 - successP) r <- sqrt ( heritability) r_env <- sqrt ( 1 - heritability) ## NOTE : this is a brute-force approach chosen for simplicity. If runtime is ## a concern, one can sample from the extremes directly using the beta-transform trick: ## https://www.gwern.net/Order-statistics#sampling-gompertz-distribution-extremes population <- rnorm (iters1, mean= 0 , sd= 1 ) eliteDonors <- population[population >= threshold] clones <- as.vector ( sapply (eliteDonors, function (d) { rnorm (iters2, ## sample _n_ clones per donor ## regress back to mean for true genetic mean: mean= d * r, ## left-over non-genetic variance affecting clones: sd= r_env) })) successes <- clones >= successThreshold cloneP <- mean (successes) if (verbose) { library (skimr) print ( skim (population)); print ( skim (eliteDonors)); print ( skim (successes)) } return (cloneP) } ## Varying heritabilities, 0-1: cloningBoost ( successP= 0.01 , heritability= 1.0 , verbose= TRUE ) # [1] 2.326 2.326 2.665 2.665 0.000 1.000 # [1] 1 cloningBoost ( successP= 0.01 , heritability= 0.8 , verbose= TRUE ) # [1] 2.326 2.326 2.665 2.384 0.281 0.551 # [1] 0.551145688 cloningBoost ( successP= 0.01 , heritability= 0.5 , verbose= TRUE ) # [1] 2.326 2.326 2.665 1.885 0.781 0.266 # [1] 0.266071352 cloningBoost ( successP= 0.01 , heritability= 0.2 , verbose= TRUE ) # [1] 2.326 2.326 2.665 1.192 1.473 0.102 # [1] 0.102340263 cloningBoost ( successP= 0.01 , heritability= 0.0 , verbose= TRUE ) # [1] 2.326 2.326 2.665 0.000 2.665 0.010 # [1] 0.01 ## Enriched selection by selecting elites rather than random: cloningBoost ( successP= 0.01 , preThreshold= 0.01 * ( 1 / 1000 ), heritability= 0.5 , verbose= TRUE ) # [1] 4.265 2.326 4.479 3.167 1.312 0.883 # [1] 0.882736927 For insight, we can look at how final success probability increases with different heritabilities/_r_s, in the single-step selection scenario (corresponding to a random selection of SF dogs for cloning) and for the double-step selection (selecting a top 1% SF dog for cloning): ## Plotting the increase in subsequent probability given various correlations: df1 <- data.frame ( PriorP= numeric (), R= numeric (), Success.Rate= numeric ()) for (p in c ( 0.01 , seq ( 0.05 , 0.95 , by= 0.05 ), 0.99 )) { for (r in seq ( 0 , 1 , by= 0.01 )) { df1 <- rbind (df1, data.frame ( PriorP= p, R= r, Success.Rate= cloningBoost ( successP= p, heritability= r ^ 2 ))) } } library (ggplot2); library (gridExtra) p1 <- qplot (R, Success.Rate, color= as.ordered (PriorP), data= df1) + geom_line () + theme ( legend.title= element_blank ()) p2 <- qplot (R, log (Success.Rate), color= as.ordered (PriorP), data= df1) + geom_line () + theme ( legend.title= element_blank ()) grid.arrange (p1, p2, ncol= 1 ) ## Double-step selection: df2 <- data.frame ( PriorP= numeric (), R= numeric (), Success.Rate= numeric ()) for (p in c ( 0.01 , seq ( 0.05 , 0.95 , by= 0.05 ), 0.99 )) { for (r in seq ( 0.01 , 1 , by= 0.01 )) { df2 <- rbind (df2, data.frame ( PriorP= p, preThreshold= p * 0.01 , R= r, Success.Rate= cloningBoost ( successP= p, preThreshold= p * 0.01 , heritability= r ^ 2 ))) } } library (ggplot2); library (gridExtra) p1 <- qplot (R, Success.Rate, color= as.ordered (PriorP), data= df2) + geom_line () + theme ( legend.title= element_blank ()) p2 <- qplot (R, log (Success.Rate), color= as.ordered (PriorP), data= df2) + geom_line () + theme ( legend.title= element_blank ()) grid.arrange (p1, p2, ncol= 1 ) How the probability of post-selection success increases given a prior base rate and a predictor of r power for single-step selection; absolute probabilities, and log-transformed. Likewise, but with an additional selection step prior to cloning to further select the best one. Cost-benefit Does cloning minimize loss? My cost-benefit below takes the cost per final dog without cloning, computes the implied per-dog-candidate cost, and then computes the increased success rate for a given threshold+heritability, and sees if the expected cloning+training cost is less than the original total cost. dogCloningCB <- function (successP, heritability, totalTrainingCost, marginalCloningCost, verbose= FALSE ) { normalLoss <- totalTrainingCost marginalTrainingCost <- totalTrainingCost / ( 1 / successP) cloningP <- cloningBoost ( successP= successP, heritability= heritability) cloningLoss <- (( 1 / cloningP) * (marginalTrainingCost + marginalCloningCost)) if (verbose) { return ( list ( Boost= cloningP, Cost.normal= normalLoss, Cost.marginal= marginalTrainingCost, Cost.clone= cloningLoss, Profitable= normalLoss > cloningLoss, Profit= normalLoss - cloningLoss)) } return (normalLoss - cloningLoss) } ## Example: 30% success rate, 50% heritability, $85k per-dog training cost, $15k per-clone cost dogCloningCB ( 0.30 , 0.5 , 85600 , 15000 , verbose= TRUE ) # $Boost # [1] 0.972797623 # # $Cost.normal # [1] 85600 # # $Cost.marginal # [1] 25680 # # $Cost.clone # [1] 41817.5364 # # $Profitable # [1] TRUE # # $Profit # [1] 43782.4636 Scenarios As the key heritability trait is almost completely unknown and heritabilities of dog behavioral traits are all over the map and seem to suffer from severe measurement error issues, we might as well consider a wide range of scenarios to get an idea of what it would take. For success/threshold, we continue with 1%; for heritability, we’ll consider the most plausible range, 0–90%; for training cost, we’ll do the full $50k–$283k range since while it’s unclear what these numbers mean, treating them as a total per-dog cost is being conservative and makes it harder for cloning to be profitable, and for cloning costs we’ll consider the Vangemert case up to Viagen’s list price of $50k (since there doesn’t seem to be any good reason to pay twice as much to Sooam). scenarios <- expand.grid ( SuccessP= 0.01 , Heritability= seq ( 0 , 0.9 , by= 0.10 ), trainingCost= seq ( 50000 , 283000 , by= 10000 ), cloningCost= seq ( 15000 , 50000 , by= 10000 )) scenarios $ Profit <- round ( unlist ( Map (dogCloningCB, scenarios[, 1 ], scenarios[, 2 ], scenarios[, 3 ], scenarios[, 4 ]))) ## Plot relationships among profitable scenarios: scenariosProfitable <- scenarios[scenarios $ Profit > 0 ,] library (ggplot2); library (gridExtra) p1 <- qplot (cloningCost, Profit, color= Heritability, data= scenariosProfitable) + geom_hline ( yintercept= 0 , color= "red" ) p2 <- qplot (trainingCost, Profit, color= Heritability, data= scenariosProfitable) + geom_hline ( yintercept= 0 , color= "red" ) grid.arrange (p1, p2, ncol= 1 ) ## All profitable scenarios: scenariosProfitable # ... The SF dog cloning scenarios showing profit vs possible cloning & training costs, colored by heritabilities. The subset of profitable scenarios for SF dog cloning (typically requiring high heritabilities, and higher training costs / lower cloning costs). Success Probability Heritability Training cost Cloning Cost Profit 0.01 0.6 50000 15000 4333 0.01 0.7 50000 15000 13962 0.01 0.8 50000 15000 21877 0.01 0.9 50000 15000 29015 0.01 0.5 60000 15000 1369 0.01 0.6 60000 15000 14038 0.01 0.7 60000 15000 23729 0.01 0.8 60000 15000 31695 0.01 0.9 60000 15000 38879 0.01 0.5 70000 15000 10993 0.01 0.6 70000 15000 23743 0.01 0.7 70000 15000 33497 0.01 0.8 70000 15000 41514 0.01 0.9 70000 15000 48744 0.01 0.4 80000 15000 2576 0.01 0.5 80000 15000 20617 0.01 0.6 80000 15000 33449 0.01 0.7 80000 15000 43264 0.01 0.8 80000 15000 51332 0.01 0.9 80000 15000 58609 0.01 0.4 90000 15000 12086 0.01 0.5 90000 15000 30242 0.01 0.6 90000 15000 43154 0.01 0.7 90000 15000 53032 0.01 0.8 90000 15000 61151 0.01 0.9 90000 15000 68473 0.01 0.4 100000 15000 21596 0.01 0.5 100000 15000 39866 0.01 0.6 100000 15000 52859 0.01 0.7 100000 15000 62799 0.01 0.8 100000 15000 70970 0.01 0.9 100000 15000 78338 0.01 0.3 110000 15000 2785 0.01 0.4 110000 15000 31106 0.01 0.5 110000 15000 49490 0.01 0.6 110000 15000 62565 0.01 0.7 110000 15000 72567 0.01 0.8 110000 15000 80788 0.01 0.9 110000 15000 88202 0.01 0.3 120000 15000 12119 0.01 0.4 120000 15000 40616 0.01 0.5 120000 15000 59114 0.01 0.6 120000 15000 72270 0.01 0.7 120000 15000 82334 0.01 0.8 120000 15000 90607 0.01 0.9 120000 15000 98067 0.01 0.3 130000 15000 21453 0.01 0.4 130000 15000 50126 0.01 0.5 130000 15000 68738 0.01 0.6 130000 15000 81976 0.01 0.7 130000 15000 92102 0.01 0.8 130000 15000 100425 0.01 0.9 130000 15000 107932 0.01 0.3 140000 15000 30787 0.01 0.4 140000 15000 59636 0.01 0.5 140000 15000 78362 0.01 0.6 140000 15000 91681 0.01 0.7 140000 15000 101869 0.01 0.8 140000 15000 110244 0.01 0.9 140000 15000 117796 0.01 0.3 150000 15000 40121 0.01 0.4 150000 15000 69146 0.01 0.5 150000 15000 87987 0.01 0.6 150000 15000 101386 0.01 0.7 150000 15000 111637 0.01 0.8 150000 15000 120062 0.01 0.9 150000 15000 127661 0.01 0.3 160000 15000 49455 0.01 0.4 160000 15000 78656 0.01 0.5 160000 15000 97611 0.01 0.6 160000 15000 111092 0.01 0.7 160000 15000 121404 0.01 0.8 160000 15000 129881 0.01 0.9 160000 15000 137526 0.01 0.2 170000 15000 6819 0.01 0.3 170000 15000 58789 0.01 0.4 170000 15000 88166 0.01 0.5 170000 15000 107235 0.01 0.6 170000 15000 120797 0.01 0.7 170000 15000 131171 0.01 0.8 170000 15000 139699 0.01 0.9 170000 15000 147390 0.01 0.2 180000 15000 15842 0.01 0.3 180000 15000 68123 0.01 0.4 180000 15000 97676 0.01 0.5 180000 15000 116859 0.01 0.6 180000 15000 130502 0.01 0.7 180000 15000 140939 0.01 0.8 180000 15000 149518 0.01 0.9 180000 15000 157255 0.01 0.2 190000 15000 24865 0.01 0.3 190000 15000 77457 0.01 0.4 190000 15000 107186 0.01 0.5 190000 15000 126483 0.01 0.6 190000 15000 140208 0.01 0.7 190000 15000 150706 0.01 0.8 190000 15000 159337 0.01 0.9 190000 15000 167119 0.01 0.2 200000 15000 33887 0.01 0.3 200000 15000 86791 0.01 0.4 200000 15000 116696 0.01 0.5 200000 15000 136107 0.01 0.6 200000 15000 149913 0.01 0.7 200000 15000 160474 0.01 0.8 200000 15000 169155 0.01 0.9 200000 15000 176984 0.01 0.2 210000 15000 42910 0.01 0.3 210000 15000 96125 0.01 0.4 210000 15000 126206 0.01 0.5 210000 15000 145732 0.01 0.6 210000 15000 159619 0.01 0.7 210000 15000 170241 0.01 0.8 210000 15000 178974 0.01 0.9 210000 15000 186849 0.01 0.2 220000 15000 51933 0.01 0.3 220000 15000 105459 0.01 0.4 220000 15000 135716 0.01 0.5 220000 15000 155356 0.01 0.6 220000 15000 169324 0.01 0.7 220000 15000 180009 0.01 0.8 220000 15000 188792 0.01 0.9 220000 15000 196713 0.01 0.2 230000 15000 60956 0.01 0.3 230000 15000 114794 0.01 0.4 230000 15000 145226 0.01 0.5 230000 15000 164980 0.01 0.6 230000 15000 179029 0.01 0.7 230000 15000 189776 0.01 0.8 230000 15000 198611 0.01 0.9 230000 15000 206578 0.01 0.2 240000 15000 69979 0.01 0.3 240000 15000 124128 0.01 0.4 240000 15000 154736 0.01 0.5 240000 15000 174604 0.01 0.6 240000 15000 188735 0.01 0.7 240000 15000 199544 0.01 0.8 240000 15000 208429 0.01 0.9 240000 15000 216442 0.01 0.2 250000 15000 79002 0.01 0.3 250000 15000 133462 0.01 0.4 250000 15000 164246 0.01 0.5 250000 15000 184228 0.01 0.6 250000 15000 198440 0.01 0.7 250000 15000 209311 0.01 0.8 250000 15000 218248 0.01 0.9 250000 15000 226307 0.01 0.2 260000 15000 88025 0.01 0.3 260000 15000 142796 0.01 0.4 260000 15000 173756 0.01 0.5 260000 15000 193852 0.01 0.6 260000 15000 208145 0.01 0.7 260000 15000 219079 0.01 0.8 260000 15000 228067 0.01 0.9 260000 15000 236172 0.01 0.2 270000 15000 97048 0.01 0.3 270000 15000 152130 0.01 0.4 270000 15000 183266 0.01 0.5 270000 15000 203476 0.01 0.6 270000 15000 217851 0.01 0.7 270000 15000 228846 0.01 0.8 270000 15000 237885 0.01 0.9 270000 15000 246036 0.01 0.2 280000 15000 106070 0.01 0.3 280000 15000 161464 0.01 0.4 280000 15000 192776 0.01 0.5 280000 15000 213101 0.01 0.6 280000 15000 227556 0.01 0.7 280000 15000 238614 0.01 0.8 280000 15000 247704 0.01 0.9 280000 15000 255901 0.01 0.8 50000 25000 3733 0.01 0.9 50000 25000 15476 0.01 0.7 60000 25000 478 0.01 0.8 60000 25000 13551 0.01 0.9 60000 25000 25341 0.01 0.7 70000 25000 10246 0.01 0.8 70000 25000 23370 0.01 0.9 70000 25000 35205 0.01 0.6 80000 25000 3986 0.01 0.7 80000 25000 20013 0.01 0.8 80000 25000 33188 0.01 0.9 80000 25000 45070 0.01 0.6 90000 25000 13691 0.01 0.7 90000 25000 29781 0.01 0.8 90000 25000 43007 0.01 0.9 90000 25000 54934 0.01 0.5 100000 25000 2282 0.01 0.6 100000 25000 23397 0.01 0.7 100000 25000 39548 0.01 0.8 100000 25000 52826 0.01 0.9 100000 25000 64799 0.01 0.5 110000 25000 11906 0.01 0.6 110000 25000 33102 0.01 0.7 110000 25000 49316 0.01 0.8 110000 25000 62644 0.01 0.9 110000 25000 74664 0.01 0.5 120000 25000 21530 0.01 0.6 120000 25000 42807 0.01 0.7 120000 25000 59083 0.01 0.8 120000 25000 72463 0.01 0.9 120000 25000 84528 0.01 0.4 130000 25000 1124 0.01 0.5 130000 25000 31154 0.01 0.6 130000 25000 52513 0.01 0.7 130000 25000 68851 0.01 0.8 130000 25000 82281 0.01 0.9 130000 25000 94393 0.01 0.4 140000 25000 10634 0.01 0.5 140000 25000 40778 0.01 0.6 140000 25000 62218 0.01 0.7 140000 25000 78618 0.01 0.8 140000 25000 92100 0.01 0.9 140000 25000 104257 0.01 0.4 150000 25000 20144 0.01 0.5 150000 25000 50403 0.01 0.6 150000 25000 71924 0.01 0.7 150000 25000 88386 0.01 0.8 150000 25000 101918 0.01 0.9 150000 25000 114122 0.01 0.4 160000 25000 29654 0.01 0.5 160000 25000 60027 0.01 0.6 160000 25000 81629 0.01 0.7 160000 25000 98153 0.01 0.8 160000 25000 111737 0.01 0.9 160000 25000 123987 0.01 0.4 170000 25000 39164 0.01 0.5 170000 25000 69651 0.01 0.6 170000 25000 91334 0.01 0.7 170000 25000 107921 0.01 0.8 170000 25000 121555 0.01 0.9 170000 25000 133851 0.01 0.3 180000 25000 1530 0.01 0.4 180000 25000 48674 0.01 0.5 180000 25000 79275 0.01 0.6 180000 25000 101040 0.01 0.7 180000 25000 117688 0.01 0.8 180000 25000 131374 0.01 0.9 180000 25000 143716 0.01 0.3 190000 25000 10864 0.01 0.4 190000 25000 58184 0.01 0.5 190000 25000 88899 0.01 0.6 190000 25000 110745 0.01 0.7 190000 25000 127456 0.01 0.8 190000 25000 141193 0.01 0.9 190000 25000 153581 0.01 0.3 200000 25000 20198 0.01 0.4 200000 25000 67694 0.01 0.5 200000 25000 98523 0.01 0.6 200000 25000 120450 0.01 0.7 200000 25000 137223 0.01 0.8 200000 25000 151011 0.01 0.9 200000 25000 163445 0.01 0.3 210000 25000 29532 0.01 0.4 210000 25000 77204 0.01 0.5 210000 25000 108148 0.01 0.6 210000 25000 130156 0.01 0.7 210000 25000 146991 0.01 0.8 210000 25000 160830 0.01 0.9 210000 25000 173310 0.01 0.3 220000 25000 38866 0.01 0.4 220000 25000 86714 0.01 0.5 220000 25000 117772 0.01 0.6 220000 25000 139861 0.01 0.7 220000 25000 156758 0.01 0.8 220000 25000 170648 0.01 0.9 220000 25000 183174 0.01 0.3 230000 25000 48200 0.01 0.4 230000 25000 96224 0.01 0.5 230000 25000 127396 0.01 0.6 230000 25000 149567 0.01 0.7 230000 25000 166526 0.01 0.8 230000 25000 180467 0.01 0.9 230000 25000 193039 0.01 0.3 240000 25000 57534 0.01 0.4 240000 25000 105734 0.01 0.5 240000 25000 137020 0.01 0.6 240000 25000 159272 0.01 0.7 240000 25000 176293 0.01 0.8 240000 25000 190285 0.01 0.9 240000 25000 202904 0.01 0.3 250000 25000 66868 0.01 0.4 250000 25000 115244 0.01 0.5 250000 25000 146644 0.01 0.6 250000 25000 168977 0.01 0.7 250000 25000 186061 0.01 0.8 250000 25000 200104 0.01 0.9 250000 25000 212768 0.01 0.3 260000 25000 76202 0.01 0.4 260000 25000 124754 0.01 0.5 260000 25000 156268 0.01 0.6 260000 25000 178683 0.01 0.7 260000 25000 195828 0.01 0.8 260000 25000 209922 0.01 0.9 260000 25000 222633 0.01 0.3 270000 25000 85536 0.01 0.4 270000 25000 134264 0.01 0.5 270000 25000 165893 0.01 0.6 270000 25000 188388 0.01 0.7 270000 25000 205596 0.01 0.8 270000 25000 219741 0.01 0.9 270000 25000 232497 0.01 0.2 280000 25000 8357 0.01 0.3 280000 25000 94871 0.01 0.4 280000 25000 143774 0.01 0.5 280000 25000 175517 0.01 0.6 280000 25000 198093 0.01 0.7 280000 25000 215363 0.01 0.8 280000 25000 229560 0.01 0.9 280000 25000 242362 0.01 0.9 50000 35000 1937 0.01 0.9 60000 35000 11802 0.01 0.8 70000 35000 5226 0.01 0.9 70000 35000 21666 0.01 0.8 80000 35000 15044 0.01 0.9 80000 35000 31531 0.01 0.7 90000 35000 6530 0.01 0.8 90000 35000 24863 0.01 0.9 90000 35000 41396 0.01 0.7 100000 35000 16298 0.01 0.8 100000 35000 34682 0.01 0.9 100000 35000 51260 0.01 0.6 110000 35000 3639 0.01 0.7 110000 35000 26065 0.01 0.8 110000 35000 44500 0.01 0.9 110000 35000 61125 0.01 0.6 120000 35000 13345 0.01 0.7 120000 35000 35833 0.01 0.8 120000 35000 54319 0.01 0.9 120000 35000 70989 0.01 0.6 130000 35000 23050 0.01 0.7 130000 35000 45600 0.01 0.8 130000 35000 64137 0.01 0.9 130000 35000 80854 0.01 0.5 140000 35000 3195 0.01 0.6 140000 35000 32755 0.01 0.7 140000 35000 55368 0.01 0.8 140000 35000 73956 0.01 0.9 140000 35000 90719 0.01 0.5 150000 35000 12819 0.01 0.6 150000 35000 42461 0.01 0.7 150000 35000 65135 0.01 0.8 150000 35000 83774 0.01 0.9 150000 35000 100583 0.01 0.5 160000 35000 22443 0.01 0.6 160000 35000 52166 0.01 0.7 160000 35000 74903 0.01 0.8 160000 35000 93593 0.01 0.9 160000 35000 110448 0.01 0.5 170000 35000 32067 0.01 0.6 170000 35000 61871 0.01 0.7 170000 35000 84670 0.01 0.8 170000 35000 103411 0.01 0.9 170000 35000 120312 0.01 0.5 180000 35000 41691 0.01 0.6 180000 35000 71577 0.01 0.7 180000 35000 94438 0.01 0.8 180000 35000 113230 0.01 0.9 180000 35000 130177 0.01 0.4 190000 35000 9182 0.01 0.5 190000 35000 51315 0.01 0.6 190000 35000 81282 0.01 0.7 190000 35000 104205 0.01 0.8 190000 35000 123049 0.01 0.9 190000 35000 140042 0.01 0.4 200000 35000 18692 0.01 0.5 200000 35000 60940 0.01 0.6 200000 35000 90988 0.01 0.7 200000 35000 113973 0.01 0.8 200000 35000 132867 0.01 0.9 200000 35000 149906 0.01 0.4 210000 35000 28201 0.01 0.5 210000 35000 70564 0.01 0.6 210000 35000 100693 0.01 0.7 210000 35000 123740 0.01 0.8 210000 35000 142686 0.01 0.9 210000 35000 159771 0.01 0.4 220000 35000 37711 0.01 0.5 220000 35000 80188 0.01 0.6 220000 35000 110398 0.01 0.7 220000 35000 133508 0.01 0.8 220000 35000 152504 0.01 0.9 220000 35000 169636 0.01 0.4 230000 35000 47221 0.01 0.5 230000 35000 89812 0.01 0.6 230000 35000 120104 0.01 0.7 230000 35000 143275 0.01 0.8 230000 35000 162323 0.01 0.9 230000 35000 179500 0.01 0.4 240000 35000 56731 0.01 0.5 240000 35000 99436 0.01 0.6 240000 35000 129809 0.01 0.7 240000 35000 153043 0.01 0.8 240000 35000 172141 0.01 0.9 240000 35000 189365 0.01 0.3 250000 35000 275 0.01 0.4 250000 35000 66241 0.01 0.5 250000 35000 109060 0.01 0.6 250000 35000 139514 0.01 0.7 250000 35000 162810 0.01 0.8 250000 35000 181960 0.01 0.9 250000 35000 199229 0.01 0.3 260000 35000 9609 0.01 0.4 260000 35000 75751 0.01 0.5 260000 35000 118685 0.01 0.6 260000 35000 149220 0.01 0.7 260000 35000 172578 0.01 0.8 260000 35000 191778 0.01 0.9 260000 35000 209094 0.01 0.3 270000 35000 18943 0.01 0.4 270000 35000 85261 0.01 0.5 270000 35000 128309 0.01 0.6 270000 35000 158925 0.01 0.7 270000 35000 182345 0.01 0.8 270000 35000 201597 0.01 0.9 270000 35000 218959 0.01 0.3 280000 35000 28277 0.01 0.4 280000 35000 94771 0.01 0.5 280000 35000 137933 0.01 0.6 280000 35000 168631 0.01 0.7 280000 35000 192113 0.01 0.8 280000 35000 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