Reviewing the Consequences of Genetic Purging on the Success of Rescue 3 Programs

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bioRxiv preprint doi: https://doi.org/10.1101/2021.07.15.452459; this version posted July 15, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

1 Authors: Noelia Pérez-Pereiraa, Armando Caballeroa and Aurora García-Doradob 2 Article title: Reviewing the consequences of genetic purging on the success of rescue 3 programs

4 5 6 a Centro de Investigación Mariña, Universidade de Vigo, Facultade de Bioloxía, 36310 Vigo, 7 Spain. 8 9 b Departamento de Genética, Fisiología y Microbiología, Universidad Complutense, Facultad 10 de Biología, 28040 Madrid, Spain. 11 12 13 Corresponding author: Aurora García-Dorado. Departamento de Genética, Fisiología y 14 Microbiología, Universidad Complutense, Facultad de Biología, 28040 Madrid, Spain. 15 Email address: [email protected] 16 17 ORCID CODES: 18 Noelia Pérez-Pereira: 0000-0002-4731-3712 19 Armando Caballero: 0000-0001-7391-6974 20 Aurora García-Dorado: 0000-0003-1253-2787 21 22 23 24 25 26 27 28 29 30

31 DECLARATIONS: 32 Funding: This work was funded by Agencia Estatal de Investigación (AEI) (PGC2018- 33 095810-B-I00 and PID2020-114426GB-C21), Xunta de Galicia (GRC, ED431C 2020-05) 34 and Centro singular de investigación de Galicia accreditation 2019-2022, and the European 35 Union (European Regional Development Fund - ERDF), Fondos Feder “Unha maneira de 36 facer Europa”. N.P.-P. is funded by a predoctoral (FPU) grant from Ministerio de Educación, 37 Cultura y Deporte (Spain).

38 Conflicts of interest/Competing interests: Not applicable

39 Ethics approval: Not applicable

40 Consent to participate: Not applicable

41 Consent for publication: All authors have approved the manuscript for publication

42 Availability of data and material: Not applicable

43 Code availability: Codes will be available at GitHub address 44 https://github.com/noeliaperezp/Genetic_Rescue

45 46 47 48

49 Abstract 50 51 Genetic rescue is increasingly considered a promising and underused conservation strategy to 52 reduce inbreeding depression and restore genetic diversity in endangered populations, but the 53 empirical evidence supporting its application is limited to a few generations. Here we discuss 54 on the light of theory the role of inbreeding depression arising from partially recessive 55 deleterious mutations and of genetic purging as main determinants of the medium to long- 56 term success of rescue programs. This role depends on two main predictions: (1) The 57 inbreeding load hidden in populations with a long stable demography increases with the 58 effective population size; and (2) After a population shrinks, purging tends to remove its 59 (partially) recessive deleterious alleles, a process that is slower but more efficient for large 60 populations than for small ones. We also carry out computer simulations to investigate the 61 impact of genetic purging on the medium to long term success of genetic rescue programs. 62 For some scenarios, it is found that hybrid vigor followed by purging will lead to sustained 63 successful rescue. However, there may be specific situations where the recipient population is 64 so small that it cannot purge the inbreeding load introduced by migrants, which would lead to 65 increased fitness inbreeding depression and extinction risk in the medium to long term. In 66 such cases, the risk is expected to be higher if migrants came from a large non-purged 67 population with high inbreeding load, particularly after the accumulation of the stochastic 68 effects ascribed to repeated occasional migration events. Therefore, under the specific 69 deleterious recessive mutation model considered, we conclude that additional caution should 70 be taken in rescue programs. Unless the endangered population harbors some distinctive 71 genetic singularity whose conservation is a main concern, restoration by continuous stable 72 gene flow should be considered, whenever feasible, as it reduces the extinction risk compared 73 to repeated occasional migration and can also allow recolonization events.

74 75 76 77

78 Keywords: Migration; gene flow; reconnection; inbreeding depression; population 79 extinction. 80

82 3

83 Genetic rescue is the reduction of the extinction probability of endangered populations 84 through the introduction of migrant individuals. Genetic rescue programs have been 85 successful in multiple occasions (Vilà et al. 2003; Fredrickson et al. 2007; Johnson et al. 86 2010; Åkesson et al. 2016; Weeks et al. 2017; Hasselgren et al. 2018; Ralls et al. 2020), and 87 are considered a promising strategy in Conservation Biology (Waller 2015; Tallmon 2017). 88 However, most information on their consequences refer to a few generations (usually one or 89 two, rarely six, Whiteley et al. 2015). Furthermore, concern has been raised by the extinction 90 of the Isle Royale wolves population, where the genetic contribution of a single migrant wolf 91 from the large mainland population quickly spread in the resident population thanks to the 92 breeding vigor of its offspring, possibly causing an increase in inbreeding and an associated 93 fitness decline that triggered population extirpation (Hedrick et al. 2014, 2017, 2019). 94 Therefore, despite the multiple studies supporting the practice of genetic rescue (Frankham 95 2015; Kolodny et al. 2019), its consequences in the medium to long term remain uncertain 96 (Hedrick and Fredrickson 2010; Hedrick and García-Dorado 2016; Bell et al. 2019; Kyriazis 97 et al. 2020; Ralls et al. 2020). Here we review the main theoretical aspects behind the impact 98 of inbreeding depression and purging on the long-term success of rescue programs and carry 99 out computer simulations to evaluate the predicted outcome of these programs under some 100 specific scenarios.

101 102 Some background on purging and on its role during genetic rescue 103 From the genetic point of view, the main determinant of early future extinction of small 104 endangered populations is the inbreeding depression of fitness (O’Grady et al. 2006; 105 Allendorf et al. 2013; Frankham et al. 2014). This is due to the expression, as inbreeding 106 accumulates, of the initial inbreeding load B, often interpreted in terms of lethal equivalents 107 (Morton et al., 1956). Here we deal with the inbreeding load B ascribed to the recessive 108 deleterious component of many rare detrimental alleles that remains hidden in the 109 heterozygous condition in a non-inbred population (see, e.g., Caballero 2020, Chap. 8), and 110 we do not consider the possible inbreeding load ascribed to overdominance. According to 111 theory, in stable populations the inbreeding load is expected to be larger for populations with 112 larger effective size N (see Eq. 13 in García-Dorado 2007), the increase being much more 113 dramatic for more recessive deleterious alleles (García-Dorado 2003; Hedrick and García- 114 Dorado 2016). Thus, a historically large population can be genetically healthy in the sense of

115 showing a high average fitness but, still, its individuals are expected to be heterozygous for 116 many rare (partially) recessive deleterious alleles. 117 Due to the reduction of N in an endangered population, both drift (the dispersion of gene 118 frequencies due to random sampling of alleles) and inbreeding (the increase in homozygosis in 119 the offspring of related individuals) increase through generations. Inbreeding increases the 120 expression of recessive deleterious effects in homozygosis, which produces inbreeding 121 depression but also triggers an increase of selection against the deleterious alleles known as 122 genetic purging. The process is described by the Inbreeding-Purging model (IP model in

123 García-Dorado 2012), according to which the fitness expected by generation t (Wt) after a 124 reduction of N is predicted as in the classical Morton’s et al. (1956) model, but replacing 125 Wright’s inbreeding coefficient F with a purged inbreeding coefficient g that is weighed by the

126 ratio qt /q0, where q0 is the frequency of the deleterious allele in the original non-inbred

127 population and qt is the corresponding value expected from purging by generation t: 128

129 Wt = W0 exp(–Bgt) , (1) 130

131 where W0 and B are, respectively, the expected fitness and the inbreeding load in the initial non

132 -inbred population, and where gt can be predicted as a function of the effective population size 133 N and of the recessive component of the deleterious effects, i.e., the purging coefficient d 134 which, for a given homozygous effect s and dominance coefficient h, amounts d = s(1 – 2h)/2.

135 Thus, B is the sum of 2d(1 – q0)q0 over all the sites with segregating deleterious alleles.

136 Similarly, the corresponding inbreeding load at generation t (Bt) can be predicted as

137 Bt = B gt (1 – Ft) / Ft , (2) 138 which accounts for the joint reduction of the inbreeding load ascribed to drift and purging, that 139 is faster than under drift alone. 140 The efficiency of purging can be defined as the proportional reduction of the original

141 deleterious allele frequencies that it is expected to cause, i.e., the expected (q0 - qt )/q0. 142 Therefore, since the asymptotic value of g, 1−2푑 143 𝑔̂ = (3) 1+2푑(2푁−1)

144 predicts the asymptotic value of qt /q0 to a good approximation for Nd  1, we predict the 145 efficiency of purging as (1 − 𝑔̂). This expression accounts for the opposing effects of purging 146 and genetic drift after long-term inbreeding, when all the deleterious alleles responsible for 147 the initial B are expected to be fixed or lost. It shows that the efficiency of purging increases

148 with increasing Nd being, for any given d value, higher in large populations (i.e., under slower 149 inbreeding) than in small ones. As d approaches 0, 𝑔̂ approaches 1, and the role of purging 150 preventing deleterious fixation becomes negligible compared to that of drift. As Nd increases, 151 𝑔̂ goes to zero, drift becomes irrelevant and the deleterious alleles responsible for B in the 152 original non-inbred population are expected to be virtually removed by purging. Figure 1 153 illustrates that purging occurs faster under faster inbreeding (i.e., for smaller N) but it is also 154 less efficient.

155 156 157 Figure 1. Consequences of purging over 200 generations after the effective population size of an ancestral large

158 population with W0 = 1 and B = 2 drops to N = 10 (thin lines) or N = 100 (thick lines); blue: s = 0.2, h = 0, d = 159 0.1; red: s = 0.5, h = 0, d = 0.25; black: neutral (no purging) predictions. a) Average of the frequency of the 160 deleterious alleles of the ancestral population through generations relative to the corresponding initial frequency

161 (qt/q0, inferred as gt/Ft). In the absence of selection this average relative frequency would remain equal to 1. 162 However, it is substantially reduced due to purging. The reduction occurs faster for smaller N. After some time, 163 an equilibrium is reached where the average relative frequency represents the fraction of ancestral deleterious 164 allele that become fixed because they have not been purged. This asymptotic average frequency is larger for 165 smaller populations, indicating less efficient purging. Purging is quicker and more efficient for larger d values; 166 b) Expected average fitness through generations showing initial inbreeding depression and later substantial 167 recovery due to purging, although never up to its ancestral value. A more comprehensive model including non- 168 purging selection and new mutation (the Full Model) can also be found in García-Dorado (2012).

169 In agreement with the above predictions, there is evidence that purging is able to 170 reduce an important fraction of the inbreeding depression in populations with effective sizes 171 about ten or above, while faster inbreeding (as continued full-sib mating or effective sizes 172 below 10) seems to promote purging just against lethal or severely deleterious mutations 173 (Templeton and Read 1984; Hedrick 1994; Wang et al. 1999; Ávila et al. 2010; Pekkala et al. 174 2012; Bersabé and García-Dorado 2013; López-Cortegano et al. 2016; Caballero et al. 2017). 175 Therefore, the success of genetic rescue programs to reduce the extinction risk ascribed 176 to inbreeding depression depends on the balance between two different effects of gene flow. 177 On the one hand, migrants reduce inbreeding, thus causing an increase of fitness that 178 corresponds to reversed inbreeding depression, which is known as hybrid vigor or heterosis 179 (Falconer and Mackay 1996, p. 253; Caballero 2020, p. 196) and is due to the introduction of 180 the beneficial allele at some of the sites where the individuals of the endangered populations 181 were homozygous for the deleterious allele. Obviously, the more purging occurred before 182 migration, the smaller is the inbreeding depression accumulated in the endangered population 183 and the corresponding hybrid vigor induced by the rescue program. On the other hand, 184 migrants bear their own inbreeding load due to partially recessive deleterious alleles hidden in 185 heterozygosis. This hidden inbreeding load may fuel future inbreeding depression in the 186 endangered population, which can be mitigated by purging. Therefore, the success of genetic 187 rescue programs can critically depend on the purging occurring on both the donor population 188 and the endangered recipient one. The impact of a rescue program on the extinction risk also 189 depends on many other factors besides inbreeding and purging, such as the possible advantage 190 due to migrants contributing new adaptive mutations accumulated in the donor population 191 after the isolation of the endangered one, the possible adaptive disruption if the two 192 populations are adapted to different environments, the increased resilience due to restoration 193 of adaptive potential, the introduction of demographic and environmental stochasticity or 194 other factors related to management as the risk of spread of infectious diseases, etc. (Ralls et 195 al. 2020). However, in this review we will focus on genetic purging considering theoretical 196 predictions and available evidence, including new simulation results, to understand its role as 197 a determinant of the success of genetic rescue programs in reducing both inbreeding 198 depression and extinction risk through generations. 199

200

201

202 Genetic purging in the donor population

203 Drawing migrant individuals from large, genetically healthy populations has usually 204 prompted population recovery during a few generations (Whiteley et al. 2015; Ralls et al. 205 2020). Nevertheless, as explained in the previous section, migrant individuals sampled from a 206 historically large donor population are expected to be heterozygous for many rare (partially) 207 recessive deleterious alleles. Each of these alleles cause slight or no damage on the fitness of 208 migrants and of the offspring they produce when mating individuals of the recipient 209 population. However, they may contribute inbreeding load to the recipient population that can 210 cause an increase of the inbreeding depression in the future. Thus, using large donor 211 populations to rescue very small endangered ones could in theory enhance the risk of 212 extinction from future inbreeding depression. 213 Therefore, in some cases, migrants from slowly inbred efficiently purged populations 214 (i.e. where inbreeding has accumulated due to effective population sizes above several tens), 215 could be a better alternative in the medium to long term. These migrants can produce hybrid 216 vigor without a substantial increase of the inbreeding load and of the long-term extinction 217 risk, even if leading to smaller gains in genetic diversity and, therefore, in adaptive potential. 218 It has been stated that reliable evidence is required about the superiority of migrants sampled 219 from small populations (Ralls et al. 2020) but, in fact, except when considering just a few 220 generations, reliable evidence is required for the success of rescue using both small and large 221 donor populations. 222 It needs to be remembered that purging becomes less efficient for smaller populations. 223 Therefore, using migrants from a population that underwent drastic bottlenecking can 224 introduce high genetic load as well as little genetic diversity and adaptive potential, bringing 225 together the worst of both worlds. This seems to have been the case with one of the donor 226 populations used to rescue the endangered Pacific pocket mouse (Wilder et al. 2020). 227 Fortunately, analysis of genomic data can provide inferences on the demographic history 228 (Santiago et al. 2020, and references therein) that may allow the election of a donor 229 population with a record of moderate size allowing for efficient purging. 230 It has been proposed that the increase of extinction risk ascribed to the deleterious 231 alleles introduced during genetic rescue can be controlled by prioritizing a lower putative load 232 inferred from genomic analysis over a high genetic diversity (Kyriazis et al. 2020; Teixeira 233 and Huber 2021). However, relying on the ability to identify the mutations that are 234 responsible for a main fraction of the fitness load is not free of perils (Kardos and Shafer

235 2018; Ralls et al. 2020; García-Dorado and Caballero 2021). For example, the number of 236 putatively deleterious variants per genome has not been found to be a reliable predictor of 237 inbreeding depression in island populations of foxes and wolves (Robinson et al. 2018). 238 Similarly, the Homozygous Mutation Load, defined by Keller et al. (2011) as the number of 239 homozygous loci for rare alleles carried by an individual, used as a proxy of the fitness load 240 due to homozygous (partially) recessive deleterious mutations, has only a moderate expected 241 correlation with phenotypic values of individuals in large populations (Caballero et al. 2020). 242 The recent evidences that purging can reduce different genomic proxies for the fitness genetic 243 load (Xue et al. 2015; Robinson et al. 2018; Van der Valk et al. 2019; Grossen et al. 2020) 244 suggest that genomic analyses could be helpful to infer the inbreeding load at the population 245 level, but this is more likely to be useful in identifying suitable donor populations than 246 optimal migrant individuals. However, even identifying the best donor population is not 247 straightforward based on genomic information, as between population differences in fitness 248 inbreeding load can be mainly due to a very small fraction of the annotated alleles of any 249 deleterious category. For example, considering two populations with a common origin but 250 different demographic history, one of them could have purged many more mildly deleterious 251 alleles than the other during a long evolutionary period, but the other one could have purged a 252 few more severely deleterious alleles during a recent shorter period with a relatively smaller 253 size. Thus, the population with the smallest count of putatively deleterious alleles per genome 254 is not necessarily the population with the lower fitness or the smaller fitness inbreeding load. 255 Thus, when the donor’s inbreeding load is a concern (see next section), it can be safer 256 preferring donor populations that have gone through a period of moderate effective size 257 allowing for purging in the past than choosing migrant individuals on the basis of their low 258 burden of putatively deleterious alleles. Adaptive potential could be further improved by 259 using different donor populations if available. For example, some of the populations of 260 Canadian lynx in eastern North America could need to be rescued in the future due to global 261 warming preventing natural migration through natural ice bridges. Then, migrants could be 262 sampled from the several peripheral populations in eastern Canada that are under continuous 263 partial isolation instead of from the large mainland Canada population (Koen et al. 2015). 264 A relevant question is in which situations the load introduced by non-purged migrants 265 can be more harmful than the inbreeding depression they remove. The answer depends on the 266 purging processes that take place in the recipient endangered population, analyzed in the next 267 section. 268

269 Purging occurring in the recipient population

270 Theoretical arguments

271 Let us now think of a rescue program where the donor population has a long history of large 272 effective population size, so that it can be considered genetically healthy (i.e. it shows little 273 reduction of mean fitness from segregating and fixed deleterious alleles) but it is non purged 274 (i.e., it hides large inbreeding load). The success of the rescue program depends on the 275 balance between the inbreeding depression of the endangered population that is intended to be 276 reversed by the migrant gene flow and on the future depression that can arise from the load 277 concealed in the migrant individuals. 278 In the past, when the endangered population began to shrink, the inbreeding load B of 279 the ancestral non-endangered population fueled both inbreeding depression and purging. As 280 predicted by Equations (1) and (2), the slower was the increase of inbreeding during that 281 process (i.e., the larger was N) the slower but more efficient was purging (Eq. 3 and Figure 1). 282 This means that, the slower was the process that led the recipient population to its current 283 inbreeding level: a) the smaller is its expected inbreeding depression, so that less hybrid vigor 284 is expected after migration; b) the smaller inbreeding load it hides, so that migrant individuals 285 coming from a large population are more likely to carry more (partially) recessive deleterious 286 alleles than resident ones. In addition, if the recipient population is very small by the time of 287 migration and does not experience a quick demographic recovery, the load introduced by 288 migrant individuals will not be efficiently purged. The result is that, if the recipient population 289 has a history of slow inbreeding previous to migration but remains very small after that, 290 migration events could in some cases reduce fitness in the medium to long term. On the 291 contrary, migration events are expected to be particularly beneficial for populations with a 292 history of drastic bottlenecking that have recovered a moderate size allowing future purging. 293 294 A simulation illustration

295 To assess the relevance of the purging occurring in the endangered recipient population we 296 performed a simulation analysis that is summarized in the Boxes below and is reported with 297 more detail in the Supplementary Material. 298

299 300

301 BOX 1. Purging and fitness rescue 302 First, we simulated a large non-threatened population of N = 104 individuals for 104 303 generations to approach the mutation-selection-drift equilibrium. Then, smaller threatened 304 populations were derived and different scenarios were simulated as shown in Fig. Box 1.1. In 305 a first phase, threatened populations with different sizes (N1 = 4, 10 or 50) were maintained 306 for t = N1 generations (e.g., up to generation 50 for populations with N1 = 50, etc.), so that the 307 average inbreeding coefficient was F  0.4. Then, in a second phase with population size N2, 308 each threatened population was maintained with the same constant size (N2 = N1), or with a 309 different size, and entered or not a genetic rescue program. Each two-phase scenario is 310 denoted by the corresponding population sizes (e.g., 50-10 for N1 = 50 and N2 = 10). Rescue 311 consisted of the addition of males randomly sampled from the large N = 104 population. 312 Between 500 and 2,500 replicated rounds were simulated. The number of individuals 313 introduced during each migration event was five for lines with N2 = 50 and one for lines with 314 N2 = 10 or N2 = 4. Regarding the number of migration events, we considered four strategies: i) 315 a single event; ii) two events with an interval of five generations; iii) periodic migration every 316 five generations; and iv) the “one migrant per generation” (OMPG) strategy, that is widely 317 recommended to retain connectivity in metapopulation management (Mills and Allendorf 318 1996). All the sizes considered for the threatened populations (4, 10 and 50) correspond to the 319 IUCN Red List category of Critically Endangered or Endangered according to Criterion D 320 (IUCN 2012). 321 Non-recurrent deleterious mutations occurred at rate λ = 0.2 per gamete and generation 322 in free recombining sites, with fitness 1, 1 – sh, 1 – s for the wild-type homozygote, the 323 heterozygote and the homozygote for the mutant allele, respectively. The inbreeding load B 324 was calculated as the sum of s(1 – 2h)pq for all selective sites, where q and p = 1 – q are the 325 frequencies of the mutant and wild allele, respectively (Morton et al. 1956). The homozygous 326 deleterious effect s was sampled from a gamma distribution with mean 푠̅ = 0.2 and shape 327 parameter β = 0.33, and the dominance coefficient h was obtained from a uniform distribution 328 between 0 and e(-ks), where k is such that the average h value is ℎ̅ = 0.283, so that alleles that 329 are more deleterious are expected to be more recessive (Caballero and Keightley 1994). 330 Sampled s values larger than 1 were assigned a value s = 1 so that the mutational model 331 generates a lethal class. Fitness was multiplicative across loci. The rationale for this 332 mutational model is discussed below. In addition, neutral mutation was simulated to obtain 333 estimates of neutral genetic diversity. One half of the individuals were assigned to each sex, 334 and they were randomly chosen to breed according to their fitness and mated panmictically 335 allowing for polygamy. A more detailed description is given in the Supplementary Material.

336

337 Figure Box 1.1. Simulation scheme. A small number of individuals (N1) is sampled from the base population to 338 found a threatened population. After t = N1 generations the population size can either be maintained (N2 = N1) or 339 changed, and the population can enter, or not, a rescue program. Note that the time progresses downwards and 340 that a waved edge is represented to indicate that the population was maintained with the same size before or after 341 the time represented in the figure. 342 343 344 Fig. Box 1.2 gives population fitness w and inbreeding load B averaged over replicates 345 in a representative set of scenarios, always computed excluding migrants. Complementary 346 results are given in the Supplementary Material. These results, analyzed in more detail in the 347 main text, illustrate how, after the hybrid vigor occurred in the generations following 348 migration events, some fitness rescue persists over generations when N1 ≤ N2 but a fitness 349 disadvantage can be generated compared to “non-rescued” populations when N1 > N2. It also 350 shows that periodic migration induces strong fitness oscillations.

351 352 Figure Box 1.2. Evolution of average fitness (w; upper panels) and inbreeding load (B, lower panels) for 353 endangered populations under different demographic and migration scenarios. Demographic scenarios are coded

354 as N1-N2, N1 indicating the population size during phase 1, and N2 during phase 2 (red, green and black lines for 355 population sizes 4, 10 or 50, regardless the phase). Light dashed lines represent non-rescue lines. Dark solid lines 356 represent lines entering a rescue program starting at generation t = N1. (a) One unique migration of 5 males in 357 lines N2 = 50, and of 1 male otherwise. (b) Periodic migrations of 5 males every five generations in lines N2 = 50, 358 and of 1 individual otherwise. (c) One migrant male per generation (OMPG). 359 360 361 Figure Box 1.3 illustrates the between-population fitness variability introduced by 362 periodic migration (upper panels) or OMPG (lower panels) for populations with sizes N1 = 50, 363 N2 = 4. The panels on the left give the evolution of mean fitness for each of five randomly 364 sampled populations under a non-rescue program; the panels on the right are for populations 365 under rescue. Although in this 50-4 case periodic migration and OMPG increased long-term 366 fitness if averaged over generations (Fig. Box 1.2), both strategies introduce important fitness 367 variability between populations, which adds to the temporal oscillations in the case of 368 periodic migration. This figure illustrates that every input of migrants in a small population 369 can lead to a dangerous inbreeding depression after a few generations. 370 371

372 373 Figure Box 1.3. Genetic stochasticity for average fitness (w) on sets of five random populations from those 374 described in Fig. Box 1.2 for a scenario with population size N1 = 50 during phase 1 and N2 = 4 during phase 2 375 (rescue starting at generation 50). Left panels: populations under no rescue program. Right panels: populations 376 under a rescue program starting at generation 50 (upper panels for periodic migration every 5 generations, lower 377 panels for OMPG). 378 379 380 END OF BOX 1

381

382 Results in Fig. Box 1.2 give results averaged over replicates that illustrate the expected 383 evolution of average fitness (w) and inbreeding load (B) over generations. They show that, 384 under no rescue program, the expected fitness of threatened populations declined in the early 385 generations and partially recovered a few generations later due to genetic purging. The 386 decline was more dramatic and the recovery was poorer or non-existent in the smaller 387 populations, as expected from less efficient purging. The inbreeding load also declined due to 388 both genetic purging and drift. For the larger populations, this decline was much faster than 389 that of the genetic diversity (H) for neutral loci, due to efficient purging (Supplementary 390 Material Figs. S1-S4). Finally, a new mutation-selection-drift balance was attained where B

391 depended just on N2, while fitness depended on the size of the population through the whole 392 period considered and continued to decline in the smaller populations due to the continuous 393 fixation of deleterious mutations. 394 The introduction of migrants into the threatened populations always resulted in the 395 increase of expected fitness (hybrid vigor) in the next generation, at the cost of an increase of 396 the inbreeding load. Under occasional migration (one or two migration event), B declined 397 after this initial increase, approaching the same equilibrium values as those of populations 398 under no rescue program. In contrast, under periodic migration and OMPG, B oscillated 399 around a plateau for values larger than those achieved under no rescue program. 400 The hybrid vigor after occasional migration was followed by new inbreeding depression

401 to the point that, for N1 > N2, where purging is more efficient before than after genetic flow, 402 the expected fitness soon dropped to values persistently smaller than those of non-rescued 403 lines. 404 Periodic migration every five generations produced a persistent rescue effect on 405 expected fitness in all the same scenarios as occasional migration, as well as in all the cases

406 with N2 = 4 including those with N1 > N2. However, it led to a strongly oscillatory behavior of 407 the expected fitness (Fig. Box 2.1 and S3). 408 OMPG also improved expected fitness in all cases with the exception of 50-50 and 50- 409 10, where it induced a slight disadvantage that still persisted by generation 100 (Fig. Box 2.1 410 and S4). The average advantages were stable through generations and were larger than under 411 periodic migration. 412 These results are in general agreement with the qualitative predictions presented above 413 (see Theoretical arguments). But, still, the main purpose in conservation genetics is not

414 maximizing the expected average fitness but preventing population extinction (Bell et al. 415 2019). Fig. Box 1.3 shows the evolution of average fitness for five randomly sampled non 416 rescued lines and for five lines under periodic migration or OMPG for the 50-4 scenario. It 417 illustrates that rescue events introduce temporal instability for the fitness of each line and 418 increase the between-lines fitness variance which, particularly under periodic migration, often 419 leads to null or very small fitness values that would imply population extinction. Therefore, a 420 positive effect of rescue on expected fitness does not imply a reduction in extinction risk. 421 422 BOX 2. Consequences on population extinction. 423 Here we show extinction results corresponding to the scenarios described in Box 1. In these 424 simulations, a population was considered extinct when the average fitness (w) of males and/or 425 females was less than 0.05 and/or when there were only breeding males or only breeding 426 females (counted after migration when appropriate). Figure Box 2.1 shows the percentage of 427 initial populations that survived through generations. Genetic parameters averaged over 428 surviving lines are given in Figs. S5-S8.

429 430 Figure Box 2.1. Percentage of surviving populations through generations. Different rows of panels give results 431 under a different migration scenario: one unique migration event; two migrations with an interval of five 432 generations; periodic migrations every five generations; “one migrant per generation” strategy. Different 433 columns are for different N1-N2 demographic scenarios, coded as in Fig. Box. 1.2 panels. Light dashed lines give 434 the percentage of surviving populations under no rescue program while solid lines give results under the rescue 435 program. Number of migrants per event as explained in Box 1. 436 437 Under occasional migration, the rescue program increases the extinction risk in the 438 cases where it induces a reduction of fitness compared to the non-rescue scenario (basically, 439 when N1 > N2). Periodic migration and OMPG increase the extinction risk of small 440 populations (N = 4 or 10) in the medium or long term even in cases where they cause an 441 increase of fitness averaged over generations. The reason for this increased extinction risk is 442 the genetic stochasticity introduced by migration events, as illustrated in Figure Box 1.3. 443 444 END OF BOX 2

445 Figure Box 2.1 gives simulation results illustrating the effect of rescue programs on 446 population survival. In these simulations, occasional migration after a history of severe census 447 decline produced a small but relevant reduction of the accumulated extinction risk when 448 coupled with an increase of the population size (scenarios 4-10 and 4-50). However, for very 449 small populations where purging had been more efficient previously (scenarios 10-4 and 50- 450 4), occasional migration caused more extinction risk than no migration.

451 Except for the largest population sizes (N2 = 50) where no further extinction occurred, 452 periodic migration or OMPG increased extinction risk in the medium to long term, the 453 reduction being more dramatic under periodic migration. Both strategies caused an increased 454 extinction risk even in scenarios where they cause higher expected fitness. The reason is the 455 stochastic nature of the introduced load, a phenomenon already noted in other simulation 456 analyses (Robert et al. 2003). Under periodic migration this stochasticity adds to the periodic 457 oscillations of fitness, due to accelerated inbreeding depression following the initial hybrid 458 vigor after migration. The OMPG strategy removes the periodic component (Box 1.3), which 459 makes more likely to reduce extinctions during some time. In both cases, each migration 460 event introduced randomly sampled deleterious alleles leading to occasional abrupt fitness 461 declines in individual populations, which can boost the risk of extinction. The fact that 462 successive migration events favor extinction in cases where a single or two events improved 463 survival, suggest that extinction occurs due to the fortuitous accumulation of successive 464 random fitness declines in the same population, each fueled by a migration event where the 465 sampled migrants harbored large load. Additional extinction results under other extinction 466 criteria are shown in Figs. S9-S10, giving similar results to those reported above. 467

468 Discussion

469 Our theoretical arguments and simulation results show that, considering a model of 470 inbreeding load and genetic purging ascribed to partial recessive deleterious mutations, there 471 are some specific situations where genetic rescue could be problematic. These situations are 472 characterized by the use of migrants from non-purged donor populations that can introduce a 473 substantial inbreeding load and genetic stochasticity into persistently small populations. The 474 results suggest that additional caution needs to be introduced in the current genetic rescue 475 paradigm (Ralls et al. 2018, 2020).

476 477 Implications for conservation practice and some caveats of the simulation findings

478 In practical situations, the relevance of purging on the outcome of a rescue program depends 479 on many circumstances that have not been addressed here, such as demographic and 480 environmental stochasticity (particularly that affecting carrying capacity), adaptation to local 481 conditions or the sex composition of migrants. Some of the factors not considered here can 482 favor successful rescue. One main factor of hardly quantifiable consequences is the increased 483 adaptive potential, which is favored by using large non-purged donor populations. Another 484 possibly relevant factor is the introduction of favorable mutations occurred since the 485 divergence between the donor and the recipient population, which are more likely to have 486 accumulated in a large than in a small donor population (Ralls et al. 2020). This process of 487 accumulation of new adaptive mutations is typically slow, so that it should not be relevant if 488 the divergence is recent. On the contrary, if the divergence is more remote, the recipient 489 population needs to have had large size during the majority of the divergence period in order 490 to survive, so that it could have also accumulated different advantageous mutations, possibly 491 implying some evolutionary divergence and risk of outbreeding depression (Edmands 2007). 492 This is a subject that requires further investigation but, so far, there is little information 493 available on the rate and nature of advantageous mutation for eukaryotes. 494 We have considered a model of inbreeding load B ascribed to the recessive deleterious 495 component of many rare detrimental alleles that remain hidden in the heterozygous condition 496 in a non-inbred population. This is the most parsimonious explanation of inbreeding 497 depression for which estimates of mutation rates and distribution of effects have been widely 498 found empirically, and has repeatedly been consistent with the analysis of laboratory 499 evolutionary experiments (see, e.g., Caballero 2020, Chap. 8). We have not considered 500 overdominance, which may also contribute to inbreeding depression, but whose relative 501 contribution is speculative and, according to most evidence, probably minor (Charlesworth 502 and Charlesworth 1999; Charlesworth and Willis 2009; Hedrick 2012; Thurman and Barrett 503 2016). In a reanalysis of some available estimates of genetic variance components for 504 viability in Drosophila melanogaster, Charlesworth (2015) concluded that balancing selection 505 should partly explain the excess of variance observed in some populations for viability with 506 respect to mutation-selection balance (MSB) predictions. This conclusion, that could imply 507 unrealistic low average viability (high segregating load) in large Drosophila populations (i.e., 508 high segregating load), is based on many crucial assumptions, including the supposition that h 509 is fully determined by s, or that the additive variance ascribed to recessive deleterious alleles 510 at large populations corresponds to the MSB expectation and can be predicted in terms of the 511 average h value. However, the residual variability of h conditional on s can account for large

512 amounts of inbreeding load and of variance, and recessive deleterious alleles can contribute 513 substantially more additive variance in finite populations than expected at the MSB. No doubt 514 that balancing selection due to antagonistic pleiotropy between fitness components can 515 produce some excess in additive variance for viability (Fernández et al. 2005). However, an 516 excess can also be expected in Drosophila due to pseudo-overdominance generated by linked 517 deleterious mutations (see Waller 2021, for a recent study on the subject), because of the 518 reduced length of the genome and its multiple inversions, as well as to genotype-environment 519 interactions, as suggested by Mukai (1988) and Santos (1997). Contrary to the result of 520 Charlesworth (2015), Sharp and Agrawal (2018) found no excess of variance for viability in 521 laboratory Drosophila populations when compared to expected values computed using the 522 decline of average viability in mutation accumulation lines. Although there was an excess of 523 variance with respect to MSB predictions for fecundity and male mating success, it should be 524 interpreted with caution due to i) natural selection possibly biasing the estimate of mutational 525 mean decline in the mutation accumulation lines; b) possible differences between the 526 magnitude of effects expressed during traits' assay protocol and during population 527 maintenance, as noted by the authors. In what follows, we concentrate on the consequences 528 on rescue of the inbreeding load ascribed to deleterious alleles, and we left the consequences 529 of overdominant loci to be explored in the future in cases where it might prove to be relevant. 530 In our simulations, migrant individuals were always males, but results would have been 531 the same if migrants had been all females, because the distribution of the number of matings 532 per individual, as well as that of the number of offspring contributed to the next generation, 533 was the same for both sexes. However, in practical cases, using just female migrants can 534 allow a better control of the amount and variability of inbreeding load introduced, while using 535 males with a mating advantage can boost the short-term demographic rescue (Zajitschek et al. 536 2009) but also the spread of the immigrant’s inbreeding load, as in the case of the wolf’s 537 population of Isle Royale (Hedrick et al. 2014, 2017 and 2019). 538 A consequence of all migrants having the same sex is that they always mate individuals 539 of the endangered population. Therefore, a maximum hybrid vigor is expected in the first 540 generation, but half of it would be expected to be lost in the absence of selection after one 541 generation of panmixia. In the real world, the existence of maternal genetic effects on fitness 542 may add a delayed component for hybrid vigor and inbreeding depression, obscuring the 543 temporal fitness profile (Caballero 2020, p. 197). Therefore, the importance of the sex of 544 migrants and of genetic maternal components on the dynamics of hybrid vigor and inbreeding 545 load under repeated migration deserve being investigated.

546 Our finding of increased extinction risk for small populations under some scenarios of 547 rescue programs seems to be in contradiction with the quite general view that, after excluding 548 cases where outbreeding depression was to be expected, introduction of migrants always 549 causes successful genetic rescue, usually assayed in terms of improved fitness or population 550 sizes (Waller 2015; Frankham 2015, 2016; Ralls et al. 2020). However, evaluating genetic 551 rescue effects is not simple (Robinson et al. 2020), and this view is grounded on rescue 552 programs that had been tracked for just a few generations after immigration events (usually 1- 553 3 generations, 5-6 on a few occasions) or on hybridization of populations (Chan et al. 2018), 554 which is not the common situation in genetic rescue programs (Whiteley et al. 2015). 555 Our results are in disagreement in some respects with the simulation results obtained by 556 Kyriazis et al. (2020), who found a substantial extinction rate for endangered populations with

557 Ne = 50 (or 25) which was always reduced under rescue programs. There are two main 558 differences between the simulations by Kyriazis et al. (2020) and those presented here that 559 could explain these disagreements. One is that they chose to simulate more realistic scenarios 560 from an ecological point of view, in order to assess the joint consequences of genetic and 561 nongenetic factors. We chose to illustrate the relevance of purging in simplified ecological 562 conditions, an approach that allows a clearer understanding of the main genetic processes but 563 lefts unexplored the relevance of their interaction with ecological factors. This could explain 564 the larger extinction risks observed by Kyriazis et al. (2020). However, the different findings 565 regarding the success of genetic rescue to prevent extinction is more likely to be due to the 566 different mutational models used. Kyriazis et al. (2020), following a recent accepted trend, 567 take the mutational model from estimates based on the evolutionary analysis of genomic data 568 on site frequency spectra (Kim et al. 2017), which are very sensitive to the distribution of 569 mild deleterious effects (s < 0.02 in homozygosis) but quite insensitive to the differences in 570 deleterious effects above this threshold, which are conceptually pooled into a single “strongly 571 deleterious” effect class. The problem is that, under these mutational models, the rate of 572 mutations with s > 0.1 is tiny (Fig. 2A). However, there is evidence that a large fraction of the 573 inbreeding depression that compromises the survival of endangered populations is due to 574 large deleterious effects spread in the interval (0.1, 1], including lethals (Caballero and 575 Keightley 1998; Bijlsma et al. 1999; García-Dorado et al. 2007; Fox et al. 2008; Charlesworth 576 and Willis 2009; Hedrick et al. 2016; Domínguez-García et al. 2019). In addition, despite 577 using a distribution of deleterious effects inferred assuming additivity, non-additive gene 578 action is simulated. This is achieved by using a model equivalent to assigning h = 0.25 to any 579 deleterious mutation with s < 0.02 and assigning h = 0 for s  0.02. This model is not

580 consistent with inferences from classical experiments according to which deleterious 581 mutations with s  0.02 are on the average only partially recessive (García-Dorado and 582 Caballero 2000; Halligan and Keightley 2009; Ralls et al. 2020), as illustrated in Figure 2B. 583 Under this mutational model, the inbreeding load concealed in each individual is ascribed to 584 very many recessive deleterious alleles, each with a very small effect. Therefore, the 585 coefficient of variation of the inbreeding load introduced by migrant individuals is very small, 586 and the corresponding extinction risk ascribed to the genetic stochasticity is negligible.

587 588 Figure 2. Mutational models. (a): Probability density function (PDF) of the homozygous deleterious mutational 589 effects multiplied by the deleterious mutation rate. Red line: Model inferred from evolutionary genomic analysis 590 by Kim et al. (2017) (best fit model for the 1000 genomes data: mutation rate per gamete and generation 0.314, 591 homozygous effect s gamma distributed with shape parameter 0.186 and mean 0.0161, predicted equilibrium 592 inbreeding load B = 3.07 for effective size 104). Black line: Model used in our simulations (mutation rate per 593 gamete and generation 0.2, s gamma distributed with shape parameter 0.33 and mean 0.2, predicted equilibrium 594 inbreeding load B = 6.3 for effective size 104); the lethal class generated in this model by assigning s = 1 to s 595 values above 1 is represented in the [0.99-1] interval. (b): The black thick line gives the average inbreeding 596 coefficient as a function of s assumed in our simulations, where h is uniformly distributed between 0 and the thin 597 black line (extracted from García-Dorado and Caballero 2000 and García-Dorado 2003). The red line gives the h 598 values used by Kyriazis et al. (2020) simulations, which are constant for each value of s. 599 600 601 In our simulations, we used a deleterious mutation rate and a joint distribution of s and h 602 chosen to jointly account for: (a) the large rate of deleterious mutations unveiled by the 603 evolutionary analysis of genomic data, with prevailing mild deleterious effect s < 0.01 that are 604 likely to be roughly additive (Keightley and Eyre-Walker 2007; Boyko et al. 2008; Kim et al. 605 2017); (b) the results from classical mutation accumulation and fitness assay experiments, 606 which are unlikely to detect small deleterious effects (say, s < 10–3) but imply a relevant rate 607 of deleterious mutations with effects s > 0.1 that are severe from a conservation point of view 608 (García-Dorado 1997; Caballero et al. 2002; Halligan and Keightley 2009; Thurman and 609 Barrett 2016) and whose average degree of dominance is inversely related to their deleterious

610 effect (García-Dorado and Caballero 2000; García-Dorado 2003); (c) the large inbreeding 611 load concealed in large wild populations: under our deleterious mutation model, the expected 612 haploid inbreeding load B for an equilibrium population with effective size N = 104, computed 613 by integrating the equation for the equilibrium inbreeding load (García-Dorado 2007) into the 614 joint distribution for s and h was B = 6.23 (1.885 for lethal alleles), which is on the order of 615 that found in several wild populations of mammals and birds (O’Grady et al. 2006; Hedrick 616 and García-Dorado 2016); (d) The relatively large efficiency of genetic purging obtained from 617 appropriate data under moderate bottlenecking (Bersabé and García-Dorado 2013; López- 618 Cortegano et al. 2016). Fig. 2A illustrates that, under this model, the small rate of mutation 619 with deleterious alleles that are severe in the conservation context (say, s > 0.1), is much 620 larger than that assumed under the mutational model inferred from genomic evolutionary 621 analysis. In our model, the dominance coefficient (Fig. 2B) is not completely determined by 622 the homozygous deleterious effect although, according to empirical evidence, its expected 623 value progressively decays with increasing s, so that most semilethal mutations are virtually 624 recessive. Our knowledge on the joint distribution of mutational deleterious effects and 625 dominance coefficients, including the spectra of severely deleterious effects above 0.1, is 626 quite limited for species of conservation concern, so more information is needed in this 627 respect. In any case, our results illustrate that it is necessary to be cautious, since the 628 inbreeding load introduced by migrants from large non-purged populations can have an 629 important sampling variance and the potential to compromise population survival depending 630 on the demographic past and future of the endangered population. 631 632

633 Considering the difference between reconnection and occasional or recurrent rescue

634 Our simulation results illustrate that continuous stable reconnection is safer than occasional or 635 recurrent migration events. Furthermore, an important feature of reconnection in the wild is 636 that population extirpation can in principle be reverted by recolonization, so that extinction 637 should be referred to the metapopulation (Brown and Kodric-Brown 1977; Eriksson et al. 638 2014). Therefore, in this context, our simulation results for the evolution of fitness average 639 under OMPG are more relevant than those for population survival which did not account for 640 recolonization. Those fitness results suggest that continuous connection should improve the 641 persistence of small populations. In practice, after restoring connectivity between the 642 endangered population and a larger population or a metapopulation, the endangered

643 population can enter an extirpation-recolonization dynamic that depends on many 644 demographic and ecological factors (Franken and Hik 2004), as well as on the genetic 645 stochasticity arising from the migration pattern. Then, an equilibrium is expected in the long 646 term where the genetic identity of each population is scarcely affected by historical 647 extirpation-recolonization events. In such situation, a stable but limited connectivity (e.g., 648 OMPG) can allow enough inbreeding from partial fragmentation to promote some purging, 649 while preventing both the further progress of inbreeding depression and the metapopultion 650 extinction. 651 Therefore, it is convenient to establish a conceptual distinction between genetic rescue 652 programs based on occasional or even periodic migration, and programs aiming the 653 continuous stable connection between the endangered population and a large healthy one (or a 654 metapopulation). The former could be considered “sensu stricto rescue” programs, in the 655 sense that they are intended to avoid the extinction of an isolated population whose stable 656 reconnection is not feasible or whose differentiated genetic identity is worth to be preserved, 657 although they involve some risk of swamping such identity. The second ones, say 658 “reconnection rescue” programs, here represented by what might be considered its minimum 659 migration rate (OMPG), may rather be aimed to preserve the endangered population as one of 660 the valuable pieces integrating a metapopulation and the whole ecosystem, but one that does 661 not show distinctive genetic features or adaptations to be preserved. This reconnection could 662 be achieved either by actively moving individuals on a regular basis or by reconnecting 663 landscapes, which has the advantage of setting an autonomous non-assisted mechanism. 664 Besides allowing recolonization after extirpation, reconnecting landscapes will allow 665 bidirectional flow, shifting the conservation aim from avoiding extinction of the endangered 666 subpopulation to improving its long-term expected contribution to the metapopulation 667 survival. 668 669 The relevance of purging to rescue success under different conservation scenarios

670 The preceding sections show that, before introducing migrants from a large population into a 671 critically endangered one, we should analyze the prospects that the increased reproductive 672 potential expected from hybrid vigor immediately after migration and the habitat availability 673 will allow the population to recover at least a moderate effective size in the near future, as in 674 the case of Scandinavian wolves (Vilà et al. 2003). Furthermore, it is also convenient to 675 gather information on the demographic history of the donor and the recipient population so

676 that we can infer whether they underwent efficient purging in the past, as well as on the 677 possibility that a stable reconnection can be achieved. To illustrate how our results can be 678 considered to assist decisions regarding the introduction of migrants from a large non-purged 679 population into an endangered one, below we present three different representative simplified 680 scenarios. 681 i) In the first scenario, we consider the introduction of migrants to restore adaptive 682 potential in an endangered population that has persisted for a long time with a moderate 683 effective size (50 or above). In this case, the main purpose is not to reduce inbreeding 684 depression or to ameliorate the load accumulated from continuous deleterious mutation, as 685 both should be small due to past efficient purging (as well as to non-purging selection). 686 Furthermore, if the population size does not decline further, purging is also expected to 687 remove the load contributed by migrants, so that the genetic rescue program is not expected to 688 be crucial by reducing inbreeding depression. In this situation, the main purpose of the rescue 689 program is to restore adaptive potential and to prevent long term risk due to fixation of new 690 deleterious mutation. Note, however, that inducing gene flow in populations that have 691 survived for a very long time with moderate size and whose reproductive potential is large 692 enough to allow population persistency may imply an unjustified risk, as has been appreciated 693 in the case of Island foxes (Robinson et al. 2018). In particular, it could increase their 694 inbreeding depression in case of future inbreeding. Special consideration deserves the case of 695 endangered populations that have evolved differential adaptation or distinctive features, 696 which could be swamped due to introgression or could lead to outbreeding depression 697 (Hedrick and Fredrickson 2010; Frankham et al. 2011; Harris et al. 2019). However, there is 698 some evidence that natural selection favoring locally adaptive alleles can efficiently prevent 699 introgression of mis-adapted alleles during genetic rescue (Fitzpatrick et al. 2020). 700 ii) In the second scenario, the rescue program is intended to restore both fitness and

701 genetic diversity in a population that gets over a critical period of very small effective size (Ne 702 < 10) but has now recovered to some degree or is expected to do so quickly. During the past 703 bottleneck, this population underwent high inbreeding, low purging and, therefore, an 704 important reduction of fitness and of adaptive potential. The rescue program is expected to 705 produce an immediate hybrid vigor and to provide wild alternatives to the deleterious alleles 706 that might have been previously fixed in the endangered population. If the effective 707 population size is moderately large at present (50 or above under our mutational model), or is 708 expected to be so soon after receiving migrants, natural selection is expected to favor these 709 introduced wild variants and to, slowly but efficiently, purge introduced recessive deleterious

710 ones. And, of course, immigration will help to restore genetic diversity. Therefore, a rescue 711 program integrated with measures that prompt early demographic restoration is expected to be 712 helpful both in the short and the long term (Hufbauer et al. 2015). If the population recovery 713 is less prosperous, one or two migratory events may be helpful to reduce the extinction risk 714 before purging restores the population fitness, but periodic migration, advised in order to 715 prevent the progressive loss of genetic diversity (Miller et al. 2020), could increase the 716 extinction risk in the long term due to random accumulation of migration events introducing 717 large amounts of inbreeding load. Then, a compromise should be achieved by favoring donor 718 populations that are expected to be purged but that still contribute to enrich the genetic 719 diversity of the recipient one. 720 iii) Finally, the third scenario corresponds to rather extreme situations within the 721 unfortunately paradigmatic case of an isolated population whose size has progressively 722 declined over time, often beginning with a period where the decline was cryptic. With such 723 demographic history, the ancestral inbreeding load should have been purged to a considerable 724 extent. At present, the habitat has been reduced or degraded to a point that the effective size is 725 dramatically small and is unlikely to grow in the near future. In such a situation, each 726 migration event with individuals sampled from a large non-purged population produces some 727 increase in mean fitness, but can be followed by accelerated inbreeding depression, increased 728 stochasticity for fitness average, and increased extinction risk. The reason is that, due to the 729 purging occurred while the size of the endangered population was moderate, the inbreeding 730 load introduced by migrant individuals can be larger than the overall deleterious load of 731 resident ones. Furthermore, the introduced load is boosted by the fitness advantage of the 732 migrants and their vigorous crossed offspring (Saccheri and Brakefield 2002; Bijlsma et al. 733 2010), and it is inefficiently purged due to the small effective size. In these cases, periodically 734 repeated rescue cycles allow the fortuitous concatenation of migration events introducing too 735 high inbreeding load, worsening the survival prospects. Note that we are considering that, 736 although the initial increase of fitness is expected to improve the intrinsic growth rate, the 737 population size will continue to be small due to the limiting environmental factors and 738 carrying capacity. 739 This scenario (iii) is vividly illustrated by the extinction of the Isle Royale wolves 740 population, occurred after a sudden fitness increase caused by a single migrant from the 741 continental population (Hedrick et al. 2019; Robinson et al. 2019). This scenario may seem of 742 limited practical interest, as it refers to a very small effective population size. However, in 743 wild populations, the effective size is usually much smaller than the actual number of

744 breeding adults (Frankham 1995; Vucetich et al. 1997; Palstra and Ruzzante 2008). 745 Furthermore, the effective size of many endangered populations has progressively declined 746 down to values on the order of tens, as in the cases the Chatham Island black robin Petroica 747 traversi (Ardern and Lambert 1997; Weiser et al. 2016) or the Fennoscandian arctic fox 748 Vulpes lagopus (Angerbjörn et al. 2013; Norén et al. 2016), and many others. In some of these 749 cases, population growth is limited by non-genetic factors, as habitat or prey limitations 750 (Adams et al. 2011; Hedrick et al. 2014). Population growth can also be limited by inbreeding 751 depression that could later be reverted to some extent due to genetic purging. Thus, this 752 scenario, although extreme, can cover some practical conservation cases. Nevertheless, the 753 specific risks in each situation are unknown due to the uncertainties surrounding the rate and 754 effect distribution of deleterious mutation or the demographic history of populations, as well 755 as to the many other genetic and non-genetic factors discussed above. 756 It is true that there is a pressure for taking action regarding critically endangered 757 populations (Ralls et al. 2018), as their medium-term persistence is critically compromised if 758 only due to demographic stochasticity. However, these results show that rescue interventions 759 in persistently small populations may increase their long term extinction risk in some cases, 760 calling for additional caution. In such cases, the rescue program should be coupled with 761 reinforced habitat interventions in order to restore an effective population sizes large enough 762 to allow efficient purging. Note that if, due to past purging under slow inbreeding, the 763 endangered population shows no evidence of inbreeding depression, the rescue program is 764 mainly intended to restore adaptive potential and might be postponed until a larger size is 765 attained. Alternatively, one or several donor populations with a history of slow inbreeding, 766 and therefore more purged, could be preferred, although the decision should weight the risk 767 arisen from the introduced load with others derived from causes not included in these 768 simulations, as the loss of adaptive potential. In any case, as far as the population singularity 769 is not a main concern, the restoration of continuous connectivity should be preferred to 770 recurrent migration events from time to time, due to fortuitous accumulation of random 771 episodes introducing high load. 772 773 Future advances and conclusions 774 The impact on conservation practice of the theoretical considerations and the simulation 775 results discussed here depend on many factors that determine the genetic architecture of the 776 inbreeding load, as the distribution of mutational effects and dominance patterns for 777 deleterious mutations or the complexity of demographic histories, and all of them are

778 worthwhile to be explored. Simulation approaches and experiments with model organisms can 779 be very useful, both to advance in our understanding of this genetic features and to test the 780 predictions generated in this analysis. It would also be helpful to understand how the genomic 781 load assayed in terms of the burden of alleles annotated for different deleterious categories 782 can inform on the fitness load and, in particular, on the inbreeding load measured in terms of 783 concealed deleterious effects. Furthermore, there is a need for long term empirical observation 784 of case studies, based on careful evaluation of the inbreeding load and the demographic and 785 genetic flow history in both the donor and the recipient population, the evolution of fitness in 786 the latter and the occurrence of extinction. These studies could benefit on the combined assay 787 of fitness traits and genomic information. 788 The prospects of a rescue program depend on the demographic history of the 789 endangered and donor populations but, in agreement with the small population paradigm, 790 future population growth is essential to guarantee successful rescue and improve population 791 survival. Our results illustrate that understanding all the consequences of conservation 792 interventions is an arduous enterprise riddled with difficulties, and that the only safe strategy 793 for in situ conservation and the one that should be prioritized and taken as a paradigm, is the 794 recovery of large effective population size through the restoration of the habitat and of a 795 healthy and continuous connectivity. 796 797 Acknowledgements 798 We are grateful to the editor and to three anonymous reviewers by their helpful comments. 799 800 References 801 Adams JR, Vucetich LM, Hedrick PW, Peterson RO, Vucetich JA (2011) Genomic sweep 802 and potential genetic rescue during limiting environmental conditions in an isolated wolf 803 population. Proc R Soc B 278:3336–3344. https://doi.org/10.1098/rspb.2011.0261 804 Åkesson M, Liberg O, Sand H, Wabakken P, Bensch S, Flagstad Ø (2016) Genetic rescue in a 805 severely inbred wolf population. Mol Ecol 25:4745–4756. 806 https://doi.org/10.1111/mec.13797 807 Allendorf FW, Luikart G, Aitken SN (2013) Conservation and the genetics of populations. 808 2nd edition. Wiley-Blackwell, West Sussex. 809 Angerbjörn A, Eide NE, Dalén L, Elmhagen B, Hellström P, Ims RA, Killengreen S, Landa 810 A, Meijer T, Mela M, Niemimaa J, Norén K, Tannerfeldt M, Yoccoz NG, Henttonen H

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1078 SUPPLEMENTARY MATERIAL 1079 1080 1081 Methodology of simulations 1082 We use computer simulations to explore the consequences of purging on genetic rescue 1083 programs considering different scenarios, always under mutation, natural selection and drift in 1084 a discrete generations model. First, we simulated a non-threatened population of N = 104 1085 dioecious diploid individuals with random mating for 10,000 generations in order to obtain a 1086 base population at the mutation-selection-drift equilibrium. Then, a smaller threatened 1087 population was derived and maintained until it was considerably inbred. The rescue program 1088 consisted in the introduction of a certain number of individuals from the large base population 1089 into the threatened one. Effective population size was assumed to equal the number of

1090 breeding adults (Ne  N). 1091 1092 1093 1094 Simulation model and mutational parameters 1095 Non-recurrent deleterious mutations occurred at rate λ = 0.2 per haploid genome and 1096 generation, with fitness effects being simulated through fecundity differences. For each locus, 1097 the fitness was 1, 1 – sh, 1 – s for the wild-type homozygote, the heterozygote and the 1098 homozygote for the mutant allele, respectively. The homozygous deleterious effect s was 1099 sampled from a gamma distribution with mean 푠̅ = 0.2 and shape parameter β = 0.33, and the 1100 dominance coefficient h was obtained from a uniform distribution between 0 and e(-ks), where 1101 k is a constant used to obtain the desired average value and ℎ̅ = 0.283 (López-Cortegano et al. 1102 2018). Thus, more deleterious alleles are expected to be more recessive (Caballero and 1103 Keightley 1994). Sampled s values larger than one were assigned a value s = 1 so that the 1104 mutational model generates a lethal class. The fitness of each individual was obtained as the 1105 product of genotypic fitnesses across loci. In order to produce each offspring, parental 1106 individuals were randomly chosen according to their fitness allowing for polygamous mating 1107 and free recombination. The haploid inbreeding load B for the base population (Morton et al. 1108 1956), calculated as the sum of s(1 – 2h)pq for all selective loci, where q and p = 1 – q are the 1109 frequencies of the mutant and wild allele, respectively, was B = 6.23 (1.885 for lethal alleles), 1110 which is on the order of that found in several wild populations of mammals and birds 1111 (O’Grady et al. 2006; Hedrick and García-Dorado 2016). The number of segregating genomic

1112 sites with deleterious mutations was about 42,000 in the base population. In addition, 2,000 1113 neutral sites, with reverse mutation allowed and the same mutation rate as sites under natural 1114 selection, were simulated to obtain estimates of neutral genetic diversity. 1115 1116 Threatened populations and rescue program 1117 Different scenarios were simulated as shown in Fig. Box 1.1 of the main text. In a first phase,

1118 threatened populations with different sizes (N1 = 4, 10 or 50) were maintained under the same 1119 conditions as the base population except in that offspring were randomly assigned to male or

1120 female sex with equal probability. A second phase started at generation t = N1 (e.g., at

1121 generation 50 for populations with N1 = 50, etc.) so that the expected average inbreeding 1122 coefficient was F  0.4. At this point, four alternative scenarios were simulated for each

1123 threatened population (second phase, with population size N2; Table S1), where the

1124 population was maintained with the same constant size (N2 = N1) or with a different constant

1125 size (N2 ≠ N1), and entered or not a genetic rescue program. Regarding the population size in 1126 these two phases, these scenarios will be denoted by the corresponding numbers (e.g., 50-10 1127 stands for threatened populations with population size 50 during phase 1 and 10 during phase 1128 2). In order to enforce mating between native and migrant individuals, these were assumed to 1129 be males. Migrants did not replace the individuals of the line (i.e., the number of individuals 1130 after a migration event was the size of the line plus the number of migrants). The whole 1131 scheme was simulated in a single round, so that each set of four scenarios shared the same 1132 original threatened population. Depending on the case, between 500 and 2,500 replicated 1133 rounds were simulated. The number of individuals introduced during each migration event

1134 was five for lines with N2 = 50 and one for lines with N2 < 50. Regarding the number of 1135 migration events, we considered four strategies: i) a single event; ii) two events with an 1136 interval of five generations; iii) periodic migration every five generations; iv) the “one 1137 migrant per generation” (OMPG) strategy, that is widely recommended to retain connectivity 1138 in metapopulation management (Mills and Allendorf 1996). All the sizes considered for the 1139 threatened populations (4, 10 and 50) correspond to the IUCN Red List category of Critically 1140 Endangered or Endangered according to Criterion D (IUCN 2012). Extinction of a line 1141 occurred when the average fitness (w) of males and/or females was less than 0.05 and/or when 1142 there were only breeding males or only breeding females (counted after migration when 1143 appropriate). Alternative criteria assumed extinction when w = 0 or w < 0.1, or no extinction 1144 at all.

1145 Each generation we computed average fitness (w), genetic diversity (H) for the neutral 1146 loci, and overall inbreeding load (B), always excluding migrants. 1147

1148 Table S1. Simulation scenarios. N1: population size of the threatened population during the

1149 first phase. N2: population size of different scenarios derived from the initial threatened

1150 population (phase 2). t: generation at which N1 is modified to N2 and some populations enter a 1151 genetic rescue program.

Case N1 N2 t 50-50 50 50 50 50-10 50 10 50 50-4 50 4 50 10-50 10 50 10 10-10 10 10 10 10-4 10 4 10 4-50 4 50 4 4-10 4 10 4 4-4 4 4 4 1152 Results 1153 Evolution of threatened populations without genetic rescue 1154 Figures S1-S4 give the evolution of different genetic parameters averaged over replicates 1155 under different scenarios assuming no extinction (results for a subset of scenarios are given in 1156 Fig. Box 1.2). Figures S5-S8 give analogous results obtained for the set of surviving lines, 1157 which are qualitatively similar to Figs. S1-S4 except in that fitness averages are a little higher 1158 when extinction is high, and in that the sampling error of the over-replicates averages for the 1159 different parameters increases as the number of surviving lines drops.

1160 Results on the percent of surviving lines, analogous to those presented in the main text 1161 but assuming different extinction criteria are shown in figures S9 and S10. Results are similar 1162 under the different extinction criteria.

1163 1164 Figure S1. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1165 threatened populations entering a genetic rescue program (one unique migration of 5

1166 individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and of control threatened 1167 populations (dashed lines). No extinction allowed. To avoid extinction due to all breeding 1168 individuals being homozygous for lethal alleles, we assigned s = 0.99 whenever the s value 1169 sampled from the gamma distribution was larger than 0.99 (the standard procedure in the 1170 cases with extinction allowed was assigning s = 1 when the sampled value was larger than 1). 1171

1172 1173 1174 Figure S2. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1175 threatened populations entering a genetic rescue program (two migrations of 5 individuals in

1176 lines N2 = 50 with an interval of five generations, and 1 individual otherwise; solid lines) and 1177 of control threatened populations (dashed lines) without extinction (as in Figure S1). 1178

1179 1180 1181 Figure S3. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1182 threatened populations entering a genetic rescue program (periodic migrations every five

1183 generations of 5 individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and of 1184 control threatened populations (dashed lines) without extinction (as in Figure S1). 1185

1186 1187 1188 Figure S4. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1189 threatened populations entering a genetic rescue program (“one migrant per generation” 1190 strategy; solid lines) and of control threatened populations (dashed lines) without extinction 1191 (as in Figure S1). 1192 1193

1194

1195 1196 1197 Figure S5. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1198 threatened populations entering a genetic rescue program (one unique migration of 5

1199 individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and of control threatened 1200 populations (dashed lines). Extinction of a line occurred when the average fitness (w) of 1201 males and/or females was less than 0.05 and/or when there were only breeding males or only 1202 breeding females. 1203

1204 1205 1206 Figure S6. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1207 threatened populations entering a genetic rescue program (two migrations with an interval of

1208 five generations of 5 individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and 1209 of control threatened populations (dashed lines). Extinction of a line occurred when the 1210 average fitness (w) of males and/or females was less than 0.05 and/or when there were only 1211 breeding males or only breeding females. 1212

1213 1214 1215 Figure S7. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1216 threatened populations entering a genetic rescue program (periodic migrations every five

1217 generations of 5 individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and of 1218 control threatened populations (dashed lines). Extinction of a line occurred when the average 1219 fitness (w) of males and/or females was less than 0.05 and/or when there were only breeding

1220 males or only breeding females. 1221

1222 1223 1224 Figure S8. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1225 threatened populations entering a genetic rescue program (“one migrant per generation” 1226 strategy; solid lines) and of control threatened populations (dashed lines). Extinction of a line 1227 occurred when the average fitness (w) of males and/or females was less than 0.05 and/or when 1228 there were only breeding males or only breeding females. 1229 1230 1231

1232 1233 1234 Figure S9. Percent of surviving threatened populations under a genetic rescue program (one 1235 unique migration; two migrations with an interval of five generations; periodic migrations 1236 every five generations; “one migrant per generation” strategy; solid lines) and of surviving 1237 control threatened populations (dashed lines). Extinction due only to homozygosis for lethal 1238 alleles (i.e., extinction occurs when fitness is 0 for all the males or/and all the females in the 1239 line) or to all breeding individuals being of the same sex. 1240 1241 1242

1243 1244 1245 Figure S10. Legend as in Figure S9, but extinction occurs when the average fitness (w) of 1246 males and/or females is less than 0.1. 1247 1248 1249 1250 1251 1252

1253

1254 Supplemntary Material References

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