On the Consequences of Ignoring Purging on Genetic Recommendations for Minimum Viable Population Rules

NEWS AND COMMENTARY

Purging and MVP rules On the consequences of ignoring purging on genetic recommendations for minimum viable population rules

A García-Dorado

Heredity (2015) 115, 185–187; doi:10.1038/hdy.2015.28; published online 15 April 2015

nconservationpractice,preliminaryassess- 2011; Kennedy et al., 2014), concluded that in the heterozygous condition. For each Iments of extinction risk as well as emer- the inbreeding load for overall fitness in the particular deleterious allele, d depends both gency decisions are often based on scarce wild is on the average B≈6 haploid-recessive on the selection coefficient against homozy- information. Thus, a simple 50/500 rule of lethal equivalents, that is, about fourfold the gous (s) and on the degree of dominance (h) thumb has been applied for a long time as estimate obtained in a meta analysis for (d = s(1–2h)/2; note that, for any given d a guidance to determine when genetic threats captive conditions (Ralls et al., 1988) that value, the intensity of purging does not become relevant to conservation, and to settle had been widely used as a default value (Lacy, depend of the underlying s and h coeffi- the genetic threshold to the minimum size for 1993). To derive this new Ne = 100 rule, cients). It has been shown that good approx- population viability (the so-called MVP). This Frankham et al. used the classical equation imations for fitness inbreeding depression can rule, used, for example, in the elaboration of for fitness inbreeding depression be obtained using an effective purging coeffi- the International Union for the Conservation cient that applies to the overall inbreeding of Nature Red List criteria for threatened W t ¼ W 0Exp½BFt ; ð1Þ load (García-Dorado, 2012); however, it is convenient to separately consider the conse- species, states that the effective population where W and F stand, respectively, for the t t quences of purging upon the inbreeding load size (Ne) should be at least 50 to prevent the average fitness and Wright’s inbreeding coef- dramatic consequences from inbreeding ascribed to true recessive lethal alleles (B , ficient at generation t,andtheinbreeding L depression in the short term, whereas a larger with purging coefficient d ≈0.5) from those load (B) is the rate of inbreeding depression. L value (N ⩾ 500) would be needed to preserve ascribed to non-lethal alleles (B with e This expression assumes that the homozygo- NL, adaptive potential in the long term (Franklin, effective purging coefficient d ). This gives sis for (partially) recessive deleterious alleles NL 1980; Jamieson and Allendorf, 2012). As it ÂÃ increases with inbreeding at the same rate as ¼ : ð Þ is well known, these N values imply W t W 0Exp BLgLt BNLgNLt 2 e that for neutral alleles and, using B = 6, it considerably larger censuses. predicts that N = 50 would cause the In addition, the inbreeding load of the However, it has been recently proposed e expected fitness to decline to 75% of its initial reduced population ascribed to deleterious that these figures should be doubled value in just five generations and to 0.2% in alleles segregating in the original population (Frankham et al., 2014), a recommendation the long term. can also be predicted as that could have important consequences on However, as inbreeding promotes the ÀÁ resource allocation but may be based ¼ þ ðÞ = ; ð Þ expression of the recessive component of Bt BLgLt BNLgNLt 1 Ft Ft 3 on exceedingly simplifying assumptions deleterious effects, it not only causes inbreed- although the actual inbreeding load will be (Franklin et al.,2014). ing depression but also leads to an increase of larger in the long term due to new deleterious Frankham et al.’s proposal that N should e the efficiency of natural selection, known as mutation. For d = d = 0, Equations (2) and be at least 100 to prevent extinction risk from L NL genetic purging. Here I discuss the conse- (3) produce the corresponding classical inbreeding depression, was prompted by quences of purging on Frankham et al.’s neutral predictions. a bulk of recent estimates of the inbreeding recommendation using the inbreeding– To date, the only empirical estimate of the load in the wild that are much larger than purging approach (García-Dorado, 2012), intensity of purging in the fraction of B not those previously obtained in captive condi- where the evolution of fitness is approxi- due to recessive lethal alleles, obtained in the tions. Thus, a meta-analysis by O’Grady et al. mated by replacing F with a purged inbreed- lab for a partial measure of fitness in (2006) on wild mammalian and avian species, t ing coefficient (g ⩽ F ) that determines the Drosophila (Bersabé and García‐Dorado, corroborated by additional reports (Kruuk t t increase in homozygosis for the alleles that 2013), suggests 0.02od o0.08. However, it et al., 2002; Liberg et al., 2005; Walling et al., NL are being purged. This parameter can be is reasonable to assume that, as B estimates in computed as a function of Ne and of the the wild are about four times those for captive A García-Dorado is at Departamento de Genética, intensity of purging, which is measured by a and laboratory populations, dNL in the wild Facultad de Biología, Universidad Complutense, Madrid, fi o o Spain purging coef cient (d) that represents the should behave similarly (0.08 dNL 0.32). To E-mail: [email protected] magnitude of the deleterious effects concealed be conservative, I will illustrate the possible News and Commentary 186

consequences of purging in the wild consider- populations, leading to reduced asymptotic has not been detected in several experiments, ing dNL = 0.05 or dNL = 0.15. fitness values. In fact, simulation results have but it has been observed in other instances, Figure 1 (upper panels) gives the evolution shown that purging becomes inefficient for mainly under slow inbreeding (Crnokrak and fi of the tness average of a previously large Neo1/d, due to genetic drift. As the appro- Barrett, 2002; Leberg and Firmin, 2008). population after a reduction in size to priate Ne in this respect is the drift-effective However, purging can pass undetected in Ne = 25, Ne = 50 and Ne = 100, as predicted population size, some inbreeding due to non- experimentation, even for populations where by the classical neutral model or by the panmictic mating in moderate to large popu- it should be relevant in the medium term. inbreeding–purging theory. As in O’Grady lations could produce situations particularly The main reason is that, as shown by the et al. (2006), I assume that the inbreeding favorable for genetic purging, in agreement inbreeding–purging predictions, either load (B = 6) consists of a fraction BL = 2.5 with theoretical and experimental results experimental inbreeding increases too fast to ascribed to recessive lethal alleles (purging (Glémin, 2003; Ávila et al., 2010). allow efficient purging or inbreeding is slow coefficient dL = 0.5) and another fraction Figure 1 (lower panels) also gives an enough but the number of generations ana- BNL = 3.5 due to non-lethal alleles undergoing approximation for the evolution of the lyzed is too small (Hedrick, 1994; Frankham purging (dNL = 0.05 or dNL = 0.15) or not inbreeding load ascribed to deleterious alleles et al., 2001; Kennedy et al., 2014). Further- (dNL = 0). Figure 1 shows that: (i) the con- segregating in the original population, which more, experimental detection is often sequences of purging on fitness decline only drops much faster in the presence of purging obscured by many factors, such as concurrent become apparent after some inbreeding has than under drift alone (dL = dNL = 0). It adaptation, genetic management or uncer- fi accumulated, usually leading to a later tness clearly shows that the reduction of B caused tainty regarding B or Ne values, and few rebound; (ii) the larger the effective popula- bypurgingduringthefirst generations can experiments have addressed the evaluation tion size, the more generations are needed for be mainly ascribed to lethal alleles, whereas of purging in the wild. Thus, the experimental purging consequences to become relevant, that caused by less intense purge is delayed. support for the claim that purging is modest but this occurs at lower inbreeding levels Frankham et al. (2014) argued that classical is, at least, controversial. and, therefore, after smaller fitness declines; neutral predictions for the reduction of mean O’Grady et al. (2006) performed viability (iii) the efficiency of purging in reducing fitness are appropriate because purging has analyses assuming B = 6 for a range of mam- fitness depression is lower for the smaller been shown to be modest. In fact, purging mal and avian species, concluding that the

Figure 1 Average fitness predicted for B = 6 using the inbreeding–purging approach (W, upper panels) together with the corresponding inbreeding load ascribed to deleterious alleles in the original population (B, lower panels), computed from Equations 2 and 3. Black Dotted lines: classical prediction (dL = 0; dNL = 0); magenta solid lines: purging acts only against recessive lethals (BL = 2.5, with dL = 0.5; BNL = 3.5, with dNL = 0), as assumed by O’Grady et al. (2006); blue dashed lines: purging acts against recessive lethals (BL = 2.5, with dL = 0.5) and against the remaining inbreeding load (BNL = 3.5, with dNL = 0.05); green dotted-dashed lines: purging acts against recessive lethals (BL = 2.5, with dL = 0.5) and against the remaining inbreeding load (BNL = 3.5, with dNL = 0.15). In all cases, the horizontal line represents the asymptotic fitness value. Plates, from left to right, are for Ne = 25, 50 and 100. A full color version of this figure is available at the Heredity journal online.

Heredity News and Commentary 187 extinction rate increased dramatically in the potential is large enough so that the popula- Boakes E, Wang J, Amos W (2006). An investigation of medium term due to inbreeding depression. tion can afford an important reduction of inbreeding depression and purging in captive pedigreed populations. Heredity 98:172–182. However, the VORTEX (Miller and Lacy, fitness for a few generations, before purging Crnokrak P, Barrett SC (2002). Perspective: purging the 1999) software used by O’Grady et al. only becomes capable of reversing the decline. If it genetic load: a review of the experimental evidence. Evolution 56:2347–2358. considers purging upon the fraction of is, the long-term survival will depend on the Facon B, Hufbauer RA, Tayeh A, Loiseau A, Lombaert E, inbreeding depression ascribed to truly lethal recovery of large numbers before adaptive Vitalis R et al. (2011). Inbreeding depression is purged in the invasive Insect Harmonia axyridis. Curr Biol 21: alleles (BL = 2.5, extrapolated from Droso- potential is substantially eroded, rather than 424–427. phila), but neglects purging upon the remain- on inbreeding depression. Furthermore, after Frankham R, Bradshaw CJ, Brook BW (2014). Genetics in ing inbreeding load (B = 3.5).Figure1 conservation management: revised recommendations NL size recovery, purging upon previously shows that, when B is large, considering for the 50/500 rules, Red List criteria and population accumulated inbreeding becomes more effi- viability analyses. Biol Conserv 170:56–63. purging only against recessive lethal alleles, as cient, which can accelerate fitness rebound Frankham R, Gilligan DM, Morris D, Briscoe DA (2001). in O’Grady et al. (2006), accounts just for a Inbreeding and extinction: effects of purging. Conserv – small fraction of the medium-term conse- (see Figure 2 in García-Dorado, 2012). In Genet 2:279 284. addition, as purged populations are expected Franklin IR (1980). Evolutionary change in small popula- quences of overall purging, and for a negligible tions. Conservation Biology: An Evolutionary-Ecological fraction of the long-term ones (solid lines). to conceal smaller inbreeding load, they Perspective. Sinauer Associates: Sunderland, Massa- ’ should be more resilient against future chusetts, 135–149. Thus, O Grady et al. could have underrated the Franklin IR, Allendorf FW, Jamieson IG (2014). The role of purging to a very relevant extent. episodes of drastic size reduction. Taking all 50/500 rule is still valid—reply to Frankham et al. Biol As the consequences of purging will often things together, there is no reason to spare Cons 176:284–285. García-Dorado A (2012). Understanding and predicting the be negligible during the first generations, conservation efforts just because Ne is going fitness decline of shrunk populations: inbreeding, Frankham et al.’s warning regarding the to be small (even Ne≈25) in the near future. purging, mutation, and standard selection. Genetics – In other words, the recommendation by 190:14611476. immediate consequences of inbreeding Glémin S (2003). How are deleterious mutations purged? depression should be taken into account. Frankham et al. (2014) to increase Ne from 50 Drift versus nonrandom mating. Evolution 57: However, populations with a history of size to 100 is based on the assumption that 2678–2687. Hedrick PW (1994). Purging inbreeding depression and the decline or occasional bottlenecking can purging upon non-lethal deleterious alleles probability of extinction: full-sib mating. Heredity 73: conceal smaller inbreeding load than the is irrelevant but, considering empirical evi- 363–372. ancestral non-endangered populations, due Jamieson IG, Allendorf FW (2012). How does the 50/500 dences on the light of theoretical predictions, rule apply to MVPs? Trends Ecol Evol 27:578–584. to previous purging (Boakes et al.,2006; this assumption is not supported. As shown Kennedy ES, Grueber CE, Duncan RP, Jamieson IG Pujol et al., 2009; Facon et al.,2011).Cer- (2014). Severe inbreeding depression and no evidence here, we need to account for purging upon — tainly, the more drastic the bottlenecks, the of purging in an extremely inbred wild species the the inbreeding load caused by both lethal and chatham island black robin. Evolution 68:987–995. larger should be the d value of the alleles that non-lethal deleterious alleles in order to Kruuk LE, Sheldon BC, Merilä J (2002). Severe inbreeding were efficiently purged, so that previous depression in collared flycatchers (Ficedula albicollis). determine the minimum effective size Proc R Soc Lond Ser B: Biol Sci 269:1581–1589. purging can lead to a smaller contribution required to preserve populations that, even Lacy RC (1993). VORTEX: a computer simulation model of lethal alleles to overall B, and to smaller for population viability analysis. Wildl Res 20: purging coefficients for non-lethal ones. been actually endangered, can eventually 45–65. recover from inbreeding depression. On the Leberg PL, Firmin BD (2008). Role of inbreeding depres- Nevertheless, this reduction of purging inten- sion and purging in captive breeding and restoration sity should be ascribed to the load that has basis of present evidence, this effective size programmes. Mol Ecol 17:334–343. will often be closer to 50 than to 100. Liberg O, Andrén H, Pedersen H-C, Sand H, Sejberg D, already been purged, so that future inbreed- Wabakken P et al. (2005). Severe inbreeding depres- ing depression should be smaller than what sion in a wild wolf Canis lupus population. Biol Lett 1: would have been expected starting from the CONFLICT OF INTEREST 17–20. Theauthordeclaresnoconflict of interest. Miller PM, Lacy RC (1999). VORTEX: A Stochastic Simula- ancestral population. In any case, when pre- tion of the Extinction Process. Version 8, User’sManual. dicting the short-term impact of inbreeding Conservation Breeding Specialist Group (SSC/IUCN): fi ACKNOWLEDGEMENTS Apple Valley, MN. on tness, it should be taken into account ’ I am grateful to Carlos López-Fanjul, to Benoit O Grady JJ, Brook BW, Reed DH, Ballou JD, Tonkyn DW, that many endangered populations may have Frankham R (2006). Realistic levels of inbreeding inbreeding loads substantially smaller than Facon and to an anonymous reviewer for their depression strongly affect extinction risk in wild popula- – the B = 6 value proposed by Frankham et al. helpful comments on this manuscript. tions. Biol Conserv 133:4251. Pujol B, Zhou S-R, Vilas JS, Pannell JR (2009). (2014). Reduced inbreeding depression after species range For the medium-long term, however, expansion. Proc Natl Acad Sci 106: 15379– properly accounting for purging will produce 15383. ‐ much more optimistic prospects, as popula- Ávila V, Amador C, García Dorado A (2010). The purge of Ralls K, Ballou JD, Templeton A (1988). Estimates of genetic load through restricted panmixia in a Drosophila lethal equivalents and the cost of inbreeding in mam- tions surviving the initial stages are likely to experiment. J Evol Biol 23:1937–1946. mals. Conserv Biol 2:185–193. recover from most inbreeding depression. Bersabé D, García‐Dorado A (2013). On the genetic parameter determining the efficiency of purging: an Walling CA, Nussey DH, Morris A, Clutton-Brock TH, Kruuk Thus, for many endangered populations, the estimate for Drosophila egg‐to‐pupae viability. JEvol LE, Pemberton JM (2011). Inbreeding depression in red critical issue is whether its reproductive Biol 26:375–385. deer calves. BMC Evol Biol 11:318.

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