1 authors: noelia pérez-pereiraa band aurora garcía-dorado...2021/07/15 · 1 authors: noelia...

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Authors: Noelia Pérez-Pereiraa, Armando Caballeroa and Aurora García-Doradob 1

Article title: Reviewing the consequences of genetic purging on the success of rescue 2

programs 3

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a Centro de Investigación Mariña, Universidade de Vigo, Facultade de Bioloxía, 36310 Vigo, 6 Spain. 7 8 b Departamento de Genética, Fisiología y Microbiología, Universidad Complutense, Facultad 9

de Biología, 28040 Madrid, Spain. 10

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Corresponding author: Aurora García-Dorado. Departamento de Genética, Fisiología y 13

Microbiología, Universidad Complutense, Facultad de Biología, 28040 Madrid, Spain. 14

Email address: [email protected] 15

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ORCID CODES: 17

Noelia Pérez-Pereira: 0000-0002-4731-3712 18

Armando Caballero: 0000-0001-7391-6974 19

Aurora García-Dorado: 0000-0003-1253-2787 20

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(which was not certified by peer review) is the author/funder.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

mailto:[email protected]

http://orcid.org/0000-0001-7391-6974

http://orcid.org/0000-0003-1253-2787

https://doi.org/10.1101/2021.07.15.452459

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DECLARATIONS: 31

Funding: This work was funded by Agencia Estatal de Investigacion (AEI) (PGC2018-32

095810-B-I00 and PID2020-114426GB-C21), Xunta de Galicia (GRC, ED431C 2020-05) 33

and Centro singular de investigación de Galicia accreditation 2019-2022, and the European 34

Union (European Regional Development Fund - ERDF), Fondos Feder “Unha maneira de 35

facer Europa”. N.P.-P. is funded by a predoctoral (FPU) grant from Ministerio de Educación, 36

Cultura y Deporte (Spain). 37

Conflicts of interest/Competing interests: Not applicable 38

Ethics approval: Not applicable 39

Consent to participate: Not applicable 40

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

Availability of data and material: Not applicable 42

Code availability: Codes will be available at GitHub address 43

https://github.com/noeliaperezp/Genetic_Rescue 44

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Abstract 49

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Genetic rescue is increasingly considered a promising and underused conservation strategy to 51

reduce inbreeding depression and restore genetic diversity in endangered populations, but the 52

empirical evidence supporting its application is limited to a few generations. Here we discuss 53

on the light of theory the role of inbreeding depression arising from partially recessive 54

deleterious mutations and of genetic purging as main determinants of the medium to long-55

term success of rescue programs. This role depends on two main predictions: (1) The 56

inbreeding load hidden in populations with a long stable demography increases with the 57

effective population size; and (2) After a population shrinks, purging tends to remove its 58

(partially) recessive deleterious alleles, a process that is slower but more efficient for large 59

populations than for small ones. We also carry out computer simulations to investigate the 60

impact of genetic purging on the medium to long term success of genetic rescue programs. 61

For some scenarios, it is found that hybrid vigor followed by purging will lead to sustained 62

successful rescue. However, there may be specific situations where the recipient population is 63

so small that it cannot purge the inbreeding load introduced by migrants, which would lead to 64

increased fitness inbreeding depression and extinction risk in the medium to long term. In 65

such cases, the risk is expected to be higher if migrants came from a large non-purged 66

population with high inbreeding load, particularly after the accumulation of the stochastic 67

effects ascribed to repeated occasional migration events. Therefore, under the specific 68

deleterious recessive mutation model considered, we conclude that additional caution should 69

be taken in rescue programs. Unless the endangered population harbors some distinctive 70

genetic singularity whose conservation is a main concern, restoration by continuous stable 71

gene flow should be considered, whenever feasible, as it reduces the extinction risk compared 72

to repeated occasional migration and can also allow recolonization events. 73

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Keywords: Migration; gene flow; reconnection; inbreeding depression; population 78

extinction. 79

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Genetic rescue is the reduction of the extinction probability of endangered populations 83

through the introduction of migrant individuals. Genetic rescue programs have been 84

successful in multiple occasions (Vilà et al. 2003; Fredrickson et al. 2007; Johnson et al. 85

2010; Åkesson et al. 2016; Weeks et al. 2017; Hasselgren et al. 2018; Ralls et al. 2020), and 86

are considered a promising strategy in Conservation Biology (Waller 2015; Tallmon 2017). 87

However, most information on their consequences refer to a few generations (usually one or 88

two, rarely six, Whiteley et al. 2015). Furthermore, concern has been raised by the extinction 89

of the Isle Royale wolves population, where the genetic contribution of a single migrant wolf 90

from the large mainland population quickly spread in the resident population thanks to the 91

breeding vigor of its offspring, possibly causing an increase in inbreeding and an associated 92

fitness decline that triggered population extirpation (Hedrick et al. 2014, 2017, 2019). 93

Therefore, despite the multiple studies supporting the practice of genetic rescue (Frankham 94

2015; Kolodny et al. 2019), its consequences in the medium to long term remain uncertain 95

(Hedrick and Fredrickson 2010; Hedrick and García-Dorado 2016; Bell et al. 2019; Kyriazis 96

et al. 2020; Ralls et al. 2020). Here we review the main theoretical aspects behind the impact 97

of inbreeding depression and purging on the long-term success of rescue programs and carry 98

out computer simulations to evaluate the predicted outcome of these programs under some 99

specific scenarios. 100

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Some background on purging and on its role during genetic rescue 102

From the genetic point of view, the main determinant of early future extinction of small 103

endangered populations is the inbreeding depression of fitness (O’Grady et al. 2006; 104

Allendorf et al. 2013; Frankham et al. 2014). This is due to the expression, as inbreeding 105

accumulates, of the initial inbreeding load B, often interpreted in terms of lethal equivalents 106

(Morton et al., 1956). Here we deal with the inbreeding load B ascribed to the recessive 107

deleterious component of many rare detrimental alleles that remains hidden in the 108

heterozygous condition in a non-inbred population (see, e.g., Caballero 2020, Chap. 8), and 109

we do not consider the possible inbreeding load ascribed to overdominance. According to 110

theory, in stable populations the inbreeding load is expected to be larger for populations with 111

larger effective size N (see Eq. 13 in García-Dorado 2007), the increase being much more 112

dramatic for more recessive deleterious alleles (García-Dorado 2003; Hedrick and García-113

Dorado 2016). Thus, a historically large population can be genetically healthy in the sense of 114


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showing a high average fitness but, still, its individuals are expected to be heterozygous for 115

many rare (partially) recessive deleterious alleles. 116

Due to the reduction of N in an endangered population, both drift (the dispersion of gene 117

frequencies due to random sampling of alleles) and inbreeding (the increase in homozygosis in 118

the offspring of related individuals) increase through generations. Inbreeding increases the 119

expression of recessive deleterious effects in homozygosis, which produces inbreeding 120

depression but also triggers an increase of selection against the deleterious alleles known as 121

genetic purging. The process is described by the Inbreeding-Purging model (IP model in 122

García-Dorado 2012), according to which the fitness expected by generation t (Wt) after a 123

reduction of N is predicted as in the classical Morton’s et al. (1956) model, but replacing 124

Wright’s inbreeding coefficient F with a purged inbreeding coefficient g that is weighed by the 125

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

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

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Wt = W0 exp(–Bgt) , (1) 129

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

-inbred population, and where gt can be predicted as a function of the effective population size 132

N and of the recessive component of the deleterious effects, i.e., the purging coefficient d 133

which, for a given homozygous effect s and dominance coefficient h, amounts d = s(1 – 2h)/2. 134

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

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

Bt = B gt (1 – Ft) / Ft , (2) 137

which accounts for the joint reduction of the inbreeding load ascribed to drift and purging, that 138

is faster than under drift alone. 139

The efficiency of purging can be defined as the proportional reduction of the original 140

deleterious allele frequencies that it is expected to cause, i.e., the expected (q0 - qt )/q0. 141

Therefore, since the asymptotic value of g, 142

�� =1−2𝑑

1+2𝑑(2𝑁−1) (3) 143

predicts the asymptotic value of qt /q0 to a good approximation for Nd 1, we predict the 144

efficiency of purging as (1 − ��). This expression accounts for the opposing effects of purging 145

and genetic drift after long-term inbreeding, when all the deleterious alleles responsible for 146

the initial B are expected to be fixed or lost. It shows that the efficiency of purging increases 147


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with increasing Nd being, for any given d value, higher in large populations (i.e., under slower 148

inbreeding) than in small ones. As d approaches 0, �� approaches 1, and the role of purging 149

preventing deleterious fixation becomes negligible compared to that of drift. As Nd increases, 150

�� goes to zero, drift becomes irrelevant and the deleterious alleles responsible for B in the 151

original non-inbred population are expected to be virtually removed by purging. Figure 1 152

illustrates that purging occurs faster under faster inbreeding (i.e., for smaller N) but it is also 153

less efficient. 154

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

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 = 158

0.1; red: s = 0.5, h = 0, d = 0.25; black: neutral (no purging) predictions. a) Average of the frequency of the 159

deleterious alleles of the ancestral population through generations relative to the corresponding initial frequency 160

(qt/q0, inferred as gt/Ft). In the absence of selection this average relative frequency would remain equal to 1. 161

However, it is substantially reduced due to purging. The reduction occurs faster for smaller N. After some time, 162

an equilibrium is reached where the average relative frequency represents the fraction of ancestral deleterious 163

allele that become fixed because they have not been purged. This asymptotic average frequency is larger for 164

smaller populations, indicating less efficient purging. Purging is quicker and more efficient for larger d values; 165

b) Expected average fitness through generations showing initial inbreeding depression and later substantial 166

recovery due to purging, although never up to its ancestral value. A more comprehensive model including non-167

purging selection and new mutation (the Full Model) can also be found in García-Dorado (2012). 168


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In agreement with the above predictions, there is evidence that purging is able to 169

reduce an important fraction of the inbreeding depression in populations with effective sizes 170

about ten or above, while faster inbreeding (as continued full-sib mating or effective sizes 171

below 10) seems to promote purging just against lethal or severely deleterious mutations 172

(Templeton and Read 1984; Hedrick 1994; Wang et al. 1999; Ávila et al. 2010; Pekkala et al. 173

2012; Bersabé and García-Dorado 2013; López-Cortegano et al. 2016; Caballero et al. 2017). 174

Therefore, the success of genetic rescue programs to reduce the extinction risk ascribed 175

to inbreeding depression depends on the balance between two different effects of gene flow. 176

On the one hand, migrants reduce inbreeding, thus causing an increase of fitness that 177

corresponds to reversed inbreeding depression, which is known as hybrid vigor or heterosis 178

(Falconer and Mackay 1996, p. 253; Caballero 2020, p. 196) and is due to the introduction of 179

the beneficial allele at some of the sites where the individuals of the endangered populations 180

were homozygous for the deleterious allele. Obviously, the more purging occurred before 181

migration, the smaller is the inbreeding depression accumulated in the endangered population 182

and the corresponding hybrid vigor induced by the rescue program. On the other hand, 183

migrants bear their own inbreeding load due to partially recessive deleterious alleles hidden in 184

heterozygosis. This hidden inbreeding load may fuel future inbreeding depression in the 185

endangered population, which can be mitigated by purging. Therefore, the success of genetic 186

rescue programs can critically depend on the purging occurring on both the donor population 187

and the endangered recipient one. The impact of a rescue program on the extinction risk also 188

depends on many other factors besides inbreeding and purging, such as the possible advantage 189

due to migrants contributing new adaptive mutations accumulated in the donor population 190

after the isolation of the endangered one, the possible adaptive disruption if the two 191

populations are adapted to different environments, the increased resilience due to restoration 192

of adaptive potential, the introduction of demographic and environmental stochasticity or 193

other factors related to management as the risk of spread of infectious diseases, etc. (Ralls et 194

al. 2020). However, in this review we will focus on genetic purging considering theoretical 195

predictions and available evidence, including new simulation results, to understand its role as 196

a determinant of the success of genetic rescue programs in reducing both inbreeding 197

depression and extinction risk through generations. 198

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Genetic purging in the donor population 202

Drawing migrant individuals from large, genetically healthy populations has usually 203

prompted population recovery during a few generations (Whiteley et al. 2015; Ralls et al. 204

2020). Nevertheless, as explained in the previous section, migrant individuals sampled from a 205

historically large donor population are expected to be heterozygous for many rare (partially) 206

recessive deleterious alleles. Each of these alleles cause slight or no damage on the fitness of 207

migrants and of the offspring they produce when mating individuals of the recipient 208

population. However, they may contribute inbreeding load to the recipient population that can 209

cause an increase of the inbreeding depression in the future. Thus, using large donor 210

populations to rescue very small endangered ones could in theory enhance the risk of 211

extinction from future inbreeding depression. 212

Therefore, in some cases, migrants from slowly inbred efficiently purged populations 213

(i.e. where inbreeding has accumulated due to effective population sizes above several tens), 214

could be a better alternative in the medium to long term. These migrants can produce hybrid 215

vigor without a substantial increase of the inbreeding load and of the long-term extinction 216

risk, even if leading to smaller gains in genetic diversity and, therefore, in adaptive potential. 217

It has been stated that reliable evidence is required about the superiority of migrants sampled 218

from small populations (Ralls et al. 2020) but, in fact, except when considering just a few 219

generations, reliable evidence is required for the success of rescue using both small and large 220

donor populations. 221

It needs to be remembered that purging becomes less efficient for smaller populations. 222

Therefore, using migrants from a population that underwent drastic bottlenecking can 223

introduce high genetic load as well as little genetic diversity and adaptive potential, bringing 224

together the worst of both worlds. This seems to have been the case with one of the donor 225

populations used to rescue the endangered Pacific pocket mouse (Wilder et al. 2020). 226

Fortunately, analysis of genomic data can provide inferences on the demographic history 227

(Santiago et al. 2020, and references therein) that may allow the election of a donor 228

population with a record of moderate size allowing for efficient purging. 229

It has been proposed that the increase of extinction risk ascribed to the deleterious 230

alleles introduced during genetic rescue can be controlled by prioritizing a lower putative load 231

inferred from genomic analysis over a high genetic diversity (Kyriazis et al. 2020; Teixeira 232

and Huber 2021). However, relying on the ability to identify the mutations that are 233

responsible for a main fraction of the fitness load is not free of perils (Kardos and Shafer 234


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2018; Ralls et al. 2020; García-Dorado and Caballero 2021). For example, the number of 235

putatively deleterious variants per genome has not been found to be a reliable predictor of 236

inbreeding depression in island populations of foxes and wolves (Robinson et al. 2018). 237

Similarly, the Homozygous Mutation Load, defined by Keller et al. (2011) as the number of 238

homozygous loci for rare alleles carried by an individual, used as a proxy of the fitness load 239

due to homozygous (partially) recessive deleterious mutations, has only a moderate expected 240

correlation with phenotypic values of individuals in large populations (Caballero et al. 2020). 241

The recent evidences that purging can reduce different genomic proxies for the fitness genetic 242

load (Xue et al. 2015; Robinson et al. 2018; Van der Valk et al. 2019; Grossen et al. 2020) 243

suggest that genomic analyses could be helpful to infer the inbreeding load at the population 244

level, but this is more likely to be useful in identifying suitable donor populations than 245

optimal migrant individuals. However, even identifying the best donor population is not 246

straightforward based on genomic information, as between population differences in fitness 247

inbreeding load can be mainly due to a very small fraction of the annotated alleles of any 248

deleterious category. For example, considering two populations with a common origin but 249

different demographic history, one of them could have purged many more mildly deleterious 250

alleles than the other during a long evolutionary period, but the other one could have purged a 251

few more severely deleterious alleles during a recent shorter period with a relatively smaller 252

size. Thus, the population with the smallest count of putatively deleterious alleles per genome 253

is not necessarily the population with the lower fitness or the smaller fitness inbreeding load. 254

Thus, when the donor’s inbreeding load is a concern (see next section), it can be safer 255

preferring donor populations that have gone through a period of moderate effective size 256

allowing for purging in the past than choosing migrant individuals on the basis of their low 257

burden of putatively deleterious alleles. Adaptive potential could be further improved by 258

using different donor populations if available. For example, some of the populations of 259

Canadian lynx in eastern North America could need to be rescued in the future due to global 260

warming preventing natural migration through natural ice bridges. Then, migrants could be 261

sampled from the several peripheral populations in eastern Canada that are under continuous 262

partial isolation instead of from the large mainland Canada population (Koen et al. 2015). 263

A relevant question is in which situations the load introduced by non-purged migrants 264

can be more harmful than the inbreeding depression they remove. The answer depends on the 265

purging processes that take place in the recipient endangered population, analyzed in the next 266

section. 267

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Purging occurring in the recipient population 269

Theoretical arguments 270

Let us now think of a rescue program where the donor population has a long history of large 271

effective population size, so that it can be considered genetically healthy (i.e. it shows little 272

reduction of mean fitness from segregating and fixed deleterious alleles) but it is non purged 273

(i.e., it hides large inbreeding load). The success of the rescue program depends on the 274

balance between the inbreeding depression of the endangered population that is intended to be 275

reversed by the migrant gene flow and on the future depression that can arise from the load 276

concealed in the migrant individuals. 277

In the past, when the endangered population began to shrink, the inbreeding load B of 278

the ancestral non-endangered population fueled both inbreeding depression and purging. As 279

predicted by Equations (1) and (2), the slower was the increase of inbreeding during that 280

process (i.e., the larger was N) the slower but more efficient was purging (Eq. 3 and Figure 1). 281

This means that, the slower was the process that led the recipient population to its current 282

inbreeding level: a) the smaller is its expected inbreeding depression, so that less hybrid vigor 283

is expected after migration; b) the smaller inbreeding load it hides, so that migrant individuals 284

coming from a large population are more likely to carry more (partially) recessive deleterious 285

alleles than resident ones. In addition, if the recipient population is very small by the time of 286

migration and does not experience a quick demographic recovery, the load introduced by 287

migrant individuals will not be efficiently purged. The result is that, if the recipient population 288

has a history of slow inbreeding previous to migration but remains very small after that, 289

migration events could in some cases reduce fitness in the medium to long term. On the 290

contrary, migration events are expected to be particularly beneficial for populations with a 291

history of drastic bottlenecking that have recovered a moderate size allowing future purging. 292

293

A simulation illustration 294

To assess the relevance of the purging occurring in the endangered recipient population we 295

performed a simulation analysis that is summarized in the Boxes below and is reported with 296

more detail in the Supplementary Material. 297

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BOX 1. Purging and fitness rescue 301

First, we simulated a large non-threatened population of N = 104 individuals for 104 302 generations to approach the mutation-selection-drift equilibrium. Then, smaller threatened 303 populations were derived and different scenarios were simulated as shown in Fig. Box 1.1. In 304 a first phase, threatened populations with different sizes (N1 = 4, 10 or 50) were maintained 305 for t = N1 generations (e.g., up to generation 50 for populations with N1 = 50, etc.), so that the 306

average inbreeding coefficient was F 0.4. Then, in a second phase with population size N2, 307 each threatened population was maintained with the same constant size (N2 = N1), or with a 308

different size, and entered or not a genetic rescue program. Each two-phase scenario is 309 denoted by the corresponding population sizes (e.g., 50-10 for N1 = 50 and N2 = 10). Rescue 310 consisted of the addition of males randomly sampled from the large N = 104 population. 311 Between 500 and 2,500 replicated rounds were simulated. The number of individuals 312 introduced during each migration event was five for lines with N2 = 50 and one for lines with 313

N2 = 10 or N2 = 4. Regarding the number of migration events, we considered four strategies: i) 314

a single event; ii) two events with an interval of five generations; iii) periodic migration every 315

five generations; and iv) the “one migrant per generation” (OMPG) strategy, that is widely 316 recommended to retain connectivity in metapopulation management (Mills and Allendorf 317 1996). All the sizes considered for the threatened populations (4, 10 and 50) correspond to the 318 IUCN Red List category of Critically Endangered or Endangered according to Criterion D 319

(IUCN 2012). 320 Non-recurrent deleterious mutations occurred at rate λ = 0.2 per gamete and generation 321

in free recombining sites, with fitness 1, 1 – sh, 1 – s for the wild-type homozygote, the 322 heterozygote and the homozygote for the mutant allele, respectively. The inbreeding load B 323 was calculated as the sum of s(1 – 2h)pq for all selective sites, where q and p = 1 – q are the 324

frequencies of the mutant and wild allele, respectively (Morton et al. 1956). The homozygous 325

deleterious effect s was sampled from a gamma distribution with mean �� = 0.2 and shape 326

parameter β = 0.33, and the dominance coefficient h was obtained from a uniform distribution 327 between 0 and e(-ks), where k is such that the average h value is ℎ = 0.283, so that alleles that 328

are more deleterious are expected to be more recessive (Caballero and Keightley 1994). 329 Sampled s values larger than 1 were assigned a value s = 1 so that the mutational model 330

generates a lethal class. Fitness was multiplicative across loci. The rationale for this 331 mutational model is discussed below. In addition, neutral mutation was simulated to obtain 332

estimates of neutral genetic diversity. One half of the individuals were assigned to each sex, 333 and they were randomly chosen to breed according to their fitness and mated panmictically 334 allowing for polygamy. A more detailed description is given in the Supplementary Material. 335


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336

Figure Box 1.1. Simulation scheme. A small number of individuals (N1) is sampled from the base population to 337 found a threatened population. After t = N1 generations the population size can either be maintained (N2 = N1) or 338 changed, and the population can enter, or not, a rescue program. Note that the time progresses downwards and 339 that a waved edge is represented to indicate that the population was maintained with the same size before or after 340 the time represented in the figure. 341 342

343

Fig. Box 1.2 gives population fitness w and inbreeding load B averaged over replicates 344 in a representative set of scenarios, always computed excluding migrants. Complementary 345

results are given in the Supplementary Material. These results, analyzed in more detail in the 346 main text, illustrate how, after the hybrid vigor occurred in the generations following 347

migration events, some fitness rescue persists over generations when N1 ≤ N2 but a fitness 348

disadvantage can be generated compared to “non-rescued” populations when N1 > N2. It also 349

shows that periodic migration induces strong fitness oscillations. 350


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


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as N1-N2, N1 indicating the population size during phase 1, and N2 during phase 2 (red, green and black lines for 354 population sizes 4, 10 or 50, regardless the phase). Light dashed lines represent non-rescue lines. Dark solid lines 355 represent lines entering a rescue program starting at generation t = N1. (a) One unique migration of 5 males in 356 lines N2 = 50, and of 1 male otherwise. (b) Periodic migrations of 5 males every five generations in lines N2 = 50, 357 and of 1 individual otherwise. (c) One migrant male per generation (OMPG). 358 359

360 Figure Box 1.3 illustrates the between-population fitness variability introduced by 361

periodic migration (upper panels) or OMPG (lower panels) for populations with sizes N1 = 50, 362 N2 = 4. The panels on the left give the evolution of mean fitness for each of five randomly 363 sampled populations under a non-rescue program; the panels on the right are for populations 364

under rescue. Although in this 50-4 case periodic migration and OMPG increased long-term 365 fitness if averaged over generations (Fig. Box 1.2), both strategies introduce important fitness 366 variability between populations, which adds to the temporal oscillations in the case of 367 periodic migration. This figure illustrates that every input of migrants in a small population 368

can lead to a dangerous inbreeding depression after a few generations. 369 370

371

372

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

378 379

END OF BOX 1 380


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381

Results in Fig. Box 1.2 give results averaged over replicates that illustrate the expected 382

evolution of average fitness (w) and inbreeding load (B) over generations. They show that, 383

under no rescue program, the expected fitness of threatened populations declined in the early 384

generations and partially recovered a few generations later due to genetic purging. The 385

decline was more dramatic and the recovery was poorer or non-existent in the smaller 386

populations, as expected from less efficient purging. The inbreeding load also declined due to 387

both genetic purging and drift. For the larger populations, this decline was much faster than 388

that of the genetic diversity (H) for neutral loci, due to efficient purging (Supplementary 389

Material Figs. S1-S4). Finally, a new mutation-selection-drift balance was attained where B 390

depended just on N2, while fitness depended on the size of the population through the whole 391

period considered and continued to decline in the smaller populations due to the continuous 392

fixation of deleterious mutations. 393

The introduction of migrants into the threatened populations always resulted in the 394

increase of expected fitness (hybrid vigor) in the next generation, at the cost of an increase of 395

the inbreeding load. Under occasional migration (one or two migration event), B declined 396

after this initial increase, approaching the same equilibrium values as those of populations 397

under no rescue program. In contrast, under periodic migration and OMPG, B oscillated 398

around a plateau for values larger than those achieved under no rescue program. 399

The hybrid vigor after occasional migration was followed by new inbreeding depression 400

to the point that, for N1 > N2, where purging is more efficient before than after genetic flow, 401

the expected fitness soon dropped to values persistently smaller than those of non-rescued 402

lines. 403

Periodic migration every five generations produced a persistent rescue effect on 404

expected fitness in all the same scenarios as occasional migration, as well as in all the cases 405

with N2 = 4 including those with N1 > N2. However, it led to a strongly oscillatory behavior of 406

the expected fitness (Fig. Box 2.1 and S3). 407

OMPG also improved expected fitness in all cases with the exception of 50-50 and 50-408

10, where it induced a slight disadvantage that still persisted by generation 100 (Fig. Box 2.1 409

and S4). The average advantages were stable through generations and were larger than under 410

periodic migration. 411

These results are in general agreement with the qualitative predictions presented above 412

(see Theoretical arguments). But, still, the main purpose in conservation genetics is not 413


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maximizing the expected average fitness but preventing population extinction (Bell et al. 414

2019). Fig. Box 1.3 shows the evolution of average fitness for five randomly sampled non 415

rescued lines and for five lines under periodic migration or OMPG for the 50-4 scenario. It 416

illustrates that rescue events introduce temporal instability for the fitness of each line and 417

increase the between-lines fitness variance which, particularly under periodic migration, often 418

leads to null or very small fitness values that would imply population extinction. Therefore, a 419

positive effect of rescue on expected fitness does not imply a reduction in extinction risk. 420

421

BOX 2. Consequences on population extinction. 422

Here we show extinction results corresponding to the scenarios described in Box 1. In these 423

simulations, a population was considered extinct when the average fitness (w) of males and/or 424 females was less than 0.05 and/or when there were only breeding males or only breeding 425 females (counted after migration when appropriate). Figure Box 2.1 shows the percentage of 426 initial populations that survived through generations. Genetic parameters averaged over 427 surviving lines are given in Figs. S5-S8. 428


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429 Figure Box 2.1. Percentage of surviving populations through generations. Different rows of panels give results 430 under a different migration scenario: one unique migration event; two migrations with an interval of five 431 generations; periodic migrations every five generations; “one migrant per generation” strategy. Different 432 columns are for different N1-N2 demographic scenarios, coded as in Fig. Box. 1.2 panels. Light dashed lines give 433 the percentage of surviving populations under no rescue program while solid lines give results under the rescue 434 program. Number of migrants per event as explained in Box 1. 435

436

Under occasional migration, the rescue program increases the extinction risk in the 437

cases where it induces a reduction of fitness compared to the non-rescue scenario (basically, 438 when N1 > N2). Periodic migration and OMPG increase the extinction risk of small 439 populations (N = 4 or 10) in the medium or long term even in cases where they cause an 440

increase of fitness averaged over generations. The reason for this increased extinction risk is 441 the genetic stochasticity introduced by migration events, as illustrated in Figure Box 1.3. 442 443

END OF BOX 2 444


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Figure Box 2.1 gives simulation results illustrating the effect of rescue programs on 445

population survival. In these simulations, occasional migration after a history of severe census 446

decline produced a small but relevant reduction of the accumulated extinction risk when 447

coupled with an increase of the population size (scenarios 4-10 and 4-50). However, for very 448

small populations where purging had been more efficient previously (scenarios 10-4 and 50-449

4), occasional migration caused more extinction risk than no migration. 450

Except for the largest population sizes (N2 = 50) where no further extinction occurred, 451

periodic migration or OMPG increased extinction risk in the medium to long term, the 452

reduction being more dramatic under periodic migration. Both strategies caused an increased 453

extinction risk even in scenarios where they cause higher expected fitness. The reason is the 454

stochastic nature of the introduced load, a phenomenon already noted in other simulation 455

analyses (Robert et al. 2003). Under periodic migration this stochasticity adds to the periodic 456

oscillations of fitness, due to accelerated inbreeding depression following the initial hybrid 457

vigor after migration. The OMPG strategy removes the periodic component (Box 1.3), which 458

makes more likely to reduce extinctions during some time. In both cases, each migration 459

event introduced randomly sampled deleterious alleles leading to occasional abrupt fitness 460

declines in individual populations, which can boost the risk of extinction. The fact that 461

successive migration events favor extinction in cases where a single or two events improved 462

survival, suggest that extinction occurs due to the fortuitous accumulation of successive 463

random fitness declines in the same population, each fueled by a migration event where the 464

sampled migrants harbored large load. Additional extinction results under other extinction 465

criteria are shown in Figs. S9-S10, giving similar results to those reported above. 466

467

Discussion 468

Our theoretical arguments and simulation results show that, considering a model of 469

inbreeding load and genetic purging ascribed to partial recessive deleterious mutations, there 470

are some specific situations where genetic rescue could be problematic. These situations are 471

characterized by the use of migrants from non-purged donor populations that can introduce a 472

substantial inbreeding load and genetic stochasticity into persistently small populations. The 473

results suggest that additional caution needs to be introduced in the current genetic rescue 474

paradigm (Ralls et al. 2018, 2020). 475

476

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


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In practical situations, the relevance of purging on the outcome of a rescue program depends 478

on many circumstances that have not been addressed here, such as demographic and 479

environmental stochasticity (particularly that affecting carrying capacity), adaptation to local 480

conditions or the sex composition of migrants. Some of the factors not considered here can 481

favor successful rescue. One main factor of hardly quantifiable consequences is the increased 482

adaptive potential, which is favored by using large non-purged donor populations. Another 483

possibly relevant factor is the introduction of favorable mutations occurred since the 484

divergence between the donor and the recipient population, which are more likely to have 485

accumulated in a large than in a small donor population (Ralls et al. 2020). This process of 486

accumulation of new adaptive mutations is typically slow, so that it should not be relevant if 487

the divergence is recent. On the contrary, if the divergence is more remote, the recipient 488

population needs to have had large size during the majority of the divergence period in order 489

to survive, so that it could have also accumulated different advantageous mutations, possibly 490

implying some evolutionary divergence and risk of outbreeding depression (Edmands 2007). 491

This is a subject that requires further investigation but, so far, there is little information 492

available on the rate and nature of advantageous mutation for eukaryotes. 493

We have considered a model of inbreeding load B ascribed to the recessive deleterious 494

component of many rare detrimental alleles that remain hidden in the heterozygous condition 495

in a non-inbred population. This is the most parsimonious explanation of inbreeding 496

depression for which estimates of mutation rates and distribution of effects have been widely 497

found empirically, and has repeatedly been consistent with the analysis of laboratory 498

evolutionary experiments (see, e.g., Caballero 2020, Chap. 8). We have not considered 499

overdominance, which may also contribute to inbreeding depression, but whose relative 500

contribution is speculative and, according to most evidence, probably minor (Charlesworth 501

and Charlesworth 1999; Charlesworth and Willis 2009; Hedrick 2012; Thurman and Barrett 502

2016). In a reanalysis of some available estimates of genetic variance components for 503

viability in Drosophila melanogaster, Charlesworth (2015) concluded that balancing selection 504

should partly explain the excess of variance observed in some populations for viability with 505

respect to mutation-selection balance (MSB) predictions. This conclusion, that could imply 506

unrealistic low average viability (high segregating load) in large Drosophila populations (i.e., 507

high segregating load), is based on many crucial assumptions, including the supposition that h 508

is fully determined by s, or that the additive variance ascribed to recessive deleterious alleles 509

at large populations corresponds to the MSB expectation and can be predicted in terms of the 510

average h value. However, the residual variability of h conditional on s can account for large 511


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amounts of inbreeding load and of variance, and recessive deleterious alleles can contribute 512

substantially more additive variance in finite populations than expected at the MSB. No doubt 513

that balancing selection due to antagonistic pleiotropy between fitness components can 514

produce some excess in additive variance for viability (Fernández et al. 2005). However, an 515

excess can also be expected in Drosophila due to pseudo-overdominance generated by linked 516

deleterious mutations (see Waller 2021, for a recent study on the subject), because of the 517

reduced length of the genome and its multiple inversions, as well as to genotype-environment 518

interactions, as suggested by Mukai (1988) and Santos (1997). Contrary to the result of 519

Charlesworth (2015), Sharp and Agrawal (2018) found no excess of variance for viability in 520

laboratory Drosophila populations when compared to expected values computed using the 521

decline of average viability in mutation accumulation lines. Although there was an excess of 522

variance with respect to MSB predictions for fecundity and male mating success, it should be 523

interpreted with caution due to i) natural selection possibly biasing the estimate of mutational 524

mean decline in the mutation accumulation lines; b) possible differences between the 525

magnitude of effects expressed during traits' assay protocol and during population 526

maintenance, as noted by the authors. In what follows, we concentrate on the consequences 527

on rescue of the inbreeding load ascribed to deleterious alleles, and we left the consequences 528

of overdominant loci to be explored in the future in cases where it might prove to be relevant. 529

In our simulations, migrant individuals were always males, but results would have been 530

the same if migrants had been all females, because the distribution of the number of matings 531

per individual, as well as that of the number of offspring contributed to the next generation, 532

was the same for both sexes. However, in practical cases, using just female migrants can 533

allow a better control of the amount and variability of inbreeding load introduced, while using 534

males with a mating advantage can boost the short-term demographic rescue (Zajitschek et al. 535

2009) but also the spread of the immigrant’s inbreeding load, as in the case of the wolf’s 536

population of Isle Royale (Hedrick et al. 2014, 2017 and 2019). 537

A consequence of all migrants having the same sex is that they always mate individuals 538

of the endangered population. Therefore, a maximum hybrid vigor is expected in the first 539

generation, but half of it would be expected to be lost in the absence of selection after one 540

generation of panmixia. In the real world, the existence of maternal genetic effects on fitness 541

may add a delayed component for hybrid vigor and inbreeding depression, obscuring the 542

temporal fitness profile (Caballero 2020, p. 197). Therefore, the importance of the sex of 543

migrants and of genetic maternal components on the dynamics of hybrid vigor and inbreeding 544

load under repeated migration deserve being investigated. 545


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Our finding of increased extinction risk for small populations under some scenarios of 546

rescue programs seems to be in contradiction with the quite general view that, after excluding 547

cases where outbreeding depression was to be expected, introduction of migrants always 548

causes successful genetic rescue, usually assayed in terms of improved fitness or population 549

sizes (Waller 2015; Frankham 2015, 2016; Ralls et al. 2020). However, evaluating genetic 550

rescue effects is not simple (Robinson et al. 2020), and this view is grounded on rescue 551

programs that had been tracked for just a few generations after immigration events (usually 1-552

3 generations, 5-6 on a few occasions) or on hybridization of populations (Chan et al. 2018), 553

which is not the common situation in genetic rescue programs (Whiteley et al. 2015). 554

Our results are in disagreement in some respects with the simulation results obtained by 555

Kyriazis et al. (2020), who found a substantial extinction rate for endangered populations with 556

Ne = 50 (or 25) which was always reduced under rescue programs. There are two main 557

differences between the simulations by Kyriazis et al. (2020) and those presented here that 558

could explain these disagreements. One is that they chose to simulate more realistic scenarios 559

from an ecological point of view, in order to assess the joint consequences of genetic and 560

nongenetic factors. We chose to illustrate the relevance of purging in simplified ecological 561

conditions, an approach that allows a clearer understanding of the main genetic processes but 562

lefts unexplored the relevance of their interaction with ecological factors. This could explain 563

the larger extinction risks observed by Kyriazis et al. (2020). However, the different findings 564

regarding the success of genetic rescue to prevent extinction is more likely to be due to the 565

different mutational models used. Kyriazis et al. (2020), following a recent accepted trend, 566

take the mutational model from estimates based on the evolutionary analysis of genomic data 567

on site frequency spectra (Kim et al. 2017), which are very sensitive to the distribution of 568

mild deleterious effects (s < 0.02 in homozygosis) but quite insensitive to the differences in 569

deleterious effects above this threshold, which are conceptually pooled into a single “strongly 570

deleterious” effect class. The problem is that, under these mutational models, the rate of 571

mutations with s > 0.1 is tiny (Fig. 2A). However, there is evidence that a large fraction of the 572

inbreeding depression that compromises the survival of endangered populations is due to 573

large deleterious effects spread in the interval (0.1, 1], including lethals (Caballero and 574

Keightley 1998; Bijlsma et al. 1999; García-Dorado et al. 2007; Fox et al. 2008; Charlesworth 575

and Willis 2009; Hedrick et al. 2016; Domínguez-García et al. 2019). In addition, despite 576

using a distribution of deleterious effects inferred assuming additivity, non-additive gene 577

action is simulated. This is achieved by using a model equivalent to assigning h = 0.25 to any 578

deleterious mutation with s < 0.02 and assigning h = 0 for s 0.02. This model is not 579


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consistent with inferences from classical experiments according to which deleterious 580

mutations with s 0.02 are on the average only partially recessive (García-Dorado and 581

Caballero 2000; Halligan and Keightley 2009; Ralls et al. 2020), as illustrated in Figure 2B. 582

Under this mutational model, the inbreeding load concealed in each individual is ascribed to 583

very many recessive deleterious alleles, each with a very small effect. Therefore, the 584

coefficient of variation of the inbreeding load introduced by migrant individuals is very small, 585

and the corresponding extinction risk ascribed to the genetic stochasticity is negligible. 586

587

Figure 2. Mutational models. (a): Probability density function (PDF) of the homozygous deleterious mutational 588 effects multiplied by the deleterious mutation rate. Red line: Model inferred from evolutionary genomic analysis 589 by Kim et al. (2017) (best fit model for the 1000 genomes data: mutation rate per gamete and generation 0.314, 590 homozygous effect s gamma distributed with shape parameter 0.186 and mean 0.0161, predicted equilibrium 591 inbreeding load B = 3.07 for effective size 104). Black line: Model used in our simulations (mutation rate per 592 gamete and generation 0.2, s gamma distributed with shape parameter 0.33 and mean 0.2, predicted equilibrium 593 inbreeding load B = 6.3 for effective size 104); the lethal class generated in this model by assigning s = 1 to s 594 values above 1 is represented in the [0.99-1] interval. (b): The black thick line gives the average inbreeding 595 coefficient as a function of s assumed in our simulations, where h is uniformly distributed between 0 and the thin 596 black line (extracted from García-Dorado and Caballero 2000 and García-Dorado 2003). The red line gives the h 597 values used by Kyriazis et al. (2020) simulations, which are constant for each value of s. 598 599

600

In our simulations, we used a deleterious mutation rate and a joint distribution of s and h 601

chosen to jointly account for: (a) the large rate of deleterious mutations unveiled by the 602

evolutionary analysis of genomic data, with prevailing mild deleterious effect s < 0.01 that are 603

likely to be roughly additive (Keightley and Eyre-Walker 2007; Boyko et al. 2008; Kim et al. 604

2017); (b) the results from classical mutation accumulation and fitness assay experiments, 605

which are unlikely to detect small deleterious effects (say, s < 10–3) but imply a relevant rate 606

of deleterious mutations with effects s > 0.1 that are severe from a conservation point of view 607

(García-Dorado 1997; Caballero et al. 2002; Halligan and Keightley 2009; Thurman and 608

Barrett 2016) and whose average degree of dominance is inversely related to their deleterious 609


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effect (García-Dorado and Caballero 2000; García-Dorado 2003); (c) the large inbreeding 610

load concealed in large wild populations: under our deleterious mutation model, the expected 611

haploid inbreeding load B for an equilibrium population with effective size N = 104, computed 612

by integrating the equation for the equilibrium inbreeding load (García-Dorado 2007) into the 613

joint distribution for s and h was B = 6.23 (1.885 for lethal alleles), which is on the order of 614

that found in several wild populations of mammals and birds (O’Grady et al. 2006; Hedrick 615

and García-Dorado 2016); (d) The relatively large efficiency of genetic purging obtained from 616

appropriate data under moderate bottlenecking (Bersabé and García-Dorado 2013; López-617

Cortegano et al. 2016). Fig. 2A illustrates that, under this model, the small rate of mutation 618

with deleterious alleles that are severe in the conservation context (say, s > 0.1), is much 619

larger than that assumed under the mutational model inferred from genomic evolutionary 620

analysis. In our model, the dominance coefficient (Fig. 2B) is not completely determined by 621

the homozygous deleterious effect although, according to empirical evidence, its expected 622

value progressively decays with increasing s, so that most semilethal mutations are virtually 623

recessive. Our knowledge on the joint distribution of mutational deleterious effects and 624

dominance coefficients, including the spectra of severely deleterious effects above 0.1, is 625

quite limited for species of conservation concern, so more information is needed in this 626

respect. In any case, our results illustrate that it is necessary to be cautious, since the 627

inbreeding load introduced by migrants from large non-purged populations can have an 628

important sampling variance and the potential to compromise population survival depending 629

on the demographic past and future of the endangered population. 630

631 632

Considering the difference between reconnection and occasional or recurrent rescue 633

Our simulation results illustrate that continuous stable reconnection is safer than occasional or 634

recurrent migration events. Furthermore, an important feature of reconnection in the wild is 635

that population extirpation can in principle be reverted by recolonization, so that extinction 636

should be referred to the metapopulation (Brown and Kodric-Brown 1977; Eriksson et al. 637

2014). Therefore, in this context, our simulation results for the evolution of fitness average 638

under OMPG are more relevant than those for population survival which did not account for 639

recolonization. Those fitness results suggest that continuous connection should improve the 640

persistence of small populations. In practice, after restoring connectivity between the 641

endangered population and a larger population or a metapopulation, the endangered 642


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population can enter an extirpation-recolonization dynamic that depends on many 643

demographic and ecological factors (Franken and Hik 2004), as well as on the genetic 644

stochasticity arising from the migration pattern. Then, an equilibrium is expected in the long 645

term where the genetic identity of each population is scarcely affected by historical 646

extirpation-recolonization events. In such situation, a stable but limited connectivity (e.g., 647

OMPG) can allow enough inbreeding from partial fragmentation to promote some purging, 648

while preventing both the further progress of inbreeding depression and the metapopultion 649

extinction. 650

Therefore, it is convenient to establish a conceptual distinction between genetic rescue 651

programs based on occasional or even periodic migration, and programs aiming the 652

continuous stable connection between the endangered population and a large healthy one (or a 653

metapopulation). The former could be considered “sensu stricto rescue” programs, in the 654

sense that they are intended to avoid the extinction of an isolated population whose stable 655

reconnection is not feasible or whose differentiated genetic identity is worth to be preserved, 656

although they involve some risk of swamping such identity. The second ones, say 657

“reconnection rescue” programs, here represented by what might be considered its minimum 658

migration rate (OMPG), may rather be aimed to preserve the endangered population as one of 659

the valuable pieces integrating a metapopulation and the whole ecosystem, but one that does 660

not show distinctive genetic features or adaptations to be preserved. This reconnection could 661

be achieved either by actively moving individuals on a regular basis or by reconnecting 662

landscapes, which has the advantage of setting an autonomous non-assisted mechanism. 663

Besides allowing recolonization after extirpation, reconnecting landscapes will allow 664

bidirectional flow, shifting the conservation aim from avoiding extinction of the endangered 665

subpopulation to improving its long-term expected contribution to the metapopulation 666

survival. 667

668

The relevance of purging to rescue success under different conservation scenarios 669

The preceding sections show that, before introducing migrants from a large population into a 670

critically endangered one, we should analyze the prospects that the increased reproductive 671

potential expected from hybrid vigor immediately after migration and the habitat availability 672

will allow the population to recover at least a moderate effective size in the near future, as in 673

the case of Scandinavian wolves (Vilà et al. 2003). Furthermore, it is also convenient to 674

gather information on the demographic history of the donor and the recipient population so 675


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that we can infer whether they underwent efficient purging in the past, as well as on the 676

possibility that a stable reconnection can be achieved. To illustrate how our results can be 677

considered to assist decisions regarding the introduction of migrants from a large non-purged 678

population into an endangered one, below we present three different representative simplified 679

scenarios. 680

i) In the first scenario, we consider the introduction of migrants to restore adaptive 681

potential in an endangered population that has persisted for a long time with a moderate 682

effective size (50 or above). In this case, the main purpose is not to reduce inbreeding 683

depression or to ameliorate the load accumulated from continuous deleterious mutation, as 684

both should be small due to past efficient purging (as well as to non-purging selection). 685

Furthermore, if the population size does not decline further, purging is also expected to 686

remove the load contributed by migrants, so that the genetic rescue program is not expected to 687

be crucial by reducing inbreeding depression. In this situation, the main purpose of the rescue 688

program is to restore adaptive potential and to prevent long term risk due to fixation of new 689

deleterious mutation. Note, however, that inducing gene flow in populations that have 690

survived for a very long time with moderate size and whose reproductive potential is large 691

enough to allow population persistency may imply an unjustified risk, as has been appreciated 692

in the case of Island foxes (Robinson et al. 2018). In particular, it could increase their 693

inbreeding depression in case of future inbreeding. Special consideration deserves the case of 694

endangered populations that have evolved differential adaptation or distinctive features, 695

which could be swamped due to introgression or could lead to outbreeding depression 696

(Hedrick and Fredrickson 2010; Frankham et al. 2011; Harris et al. 2019). However, there is 697

some evidence that natural selection favoring locally adaptive alleles can efficiently prevent 698

introgression of mis-adapted alleles during genetic rescue (Fitzpatrick et al. 2020). 699

ii) In the second scenario, the rescue program is intended to restore both fitness and 700

genetic diversity in a population that gets over a critical period of very small effective size (Ne 701

< 10) but has now recovered to some degree or is expected to do so quickly. During the past 702

bottleneck, this population underwent high inbreeding, low purging and, therefore, an 703

important reduction of fitness and of adaptive potential. The rescue program is expected to 704

produce an immediate hybrid vigor and to provide wild alternatives to the deleterious alleles 705

that might have been previously fixed in the endangered population. If the effective 706

population size is moderately large at present (50 or above under our mutational model), or is 707

expected to be so soon after receiving migrants, natural selection is expected to favor these 708

introduced wild variants and to, slowly but efficiently, purge introduced recessive deleterious 709


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26

ones. And, of course, immigration will help to restore genetic diversity. Therefore, a rescue 710

program integrated with measures that prompt early demographic restoration is expected to be 711

helpful both in the short and the long term (Hufbauer et al. 2015). If the population recovery 712

is less prosperous, one or two migratory events may be helpful to reduce the extinction risk 713

before purging restores the population fitness, but periodic migration, advised in order to 714

prevent the progressive loss of genetic diversity (Miller et al. 2020), could increase the 715

extinction risk in the long term due to random accumulation of migration events introducing 716

large amounts of inbreeding load. Then, a compromise should be achieved by favoring donor 717

populations that are expected to be purged but that still contribute to enrich the genetic 718

diversity of the recipient one. 719

iii) Finally, the third scenario corresponds to rather extreme situations within the 720

unfortunately paradigmatic case of an isolated population whose size has progressively 721

declined over time, often beginning with a period where the decline was cryptic. With such 722

demographic history, the ancestral inbreeding load should have been purged to a considerable 723

extent. At present, the habitat has been reduced or degraded to a point that the effective size is 724

dramatically small and is unlikely to grow in the near future. In such a situation, each 725

migration event with individuals sampled from a large non-purged population produces some 726

increase in mean fitness, but can be followed by accelerated inbreeding depression, increased 727

stochasticity for fitness average, and increased extinction risk. The reason is that, due to the 728

purging occurred while the size of the endangered population was moderate, the inbreeding 729

load introduced by migrant individuals can be larger than the overall deleterious load of 730

resident ones. Furthermore, the introduced load is boosted by the fitness advantage of the 731

migrants and their vigorous crossed offspring (Saccheri and Brakefield 2002; Bijlsma et al. 732

2010), and it is inefficiently purged due to the small effective size. In these cases, periodically 733

repeated rescue cycles allow the fortuitous concatenation of migration events introducing too 734

high inbreeding load, worsening the survival prospects. Note that we are considering that, 735

although the initial increase of fitness is expected to improve the intrinsic growth rate, the 736

population size will continue to be small due to the limiting environmental factors and 737

carrying capacity. 738

This scenario (iii) is vividly illustrated by the extinction of the Isle Royale wolves 739

population, occurred after a sudden fitness increase caused by a single migrant from the 740

continental population (Hedrick et al. 2019; Robinson et al. 2019). This scenario may seem of 741

limited practical interest, as it refers to a very small effective population size. However, in 742

wild populations, the effective size is usually much smaller than the actual number of 743


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27

breeding adults (Frankham 1995; Vucetich et al. 1997; Palstra and Ruzzante 2008). 744

Furthermore, the effective size of many endangered populations has progressively declined 745

down to values on the order of tens, as in the cases the Chatham Island black robin Petroica 746

traversi (Ardern and Lambert 1997; Weiser et al. 2016) or the Fennoscandian arctic fox 747

Vulpes lagopus (Angerbjörn et al. 2013; Norén et al. 2016), and many others. In some of these 748

cases, population growth is limited by non-genetic factors, as habitat or prey limitations 749

(Adams et al. 2011; Hedrick et al. 2014). Population growth can also be limited by inbreeding 750

depression that could later be reverted to some extent due to genetic purging. Thus, this 751

scenario, although extreme, can cover some practical conservation cases. Nevertheless, the 752

specific risks in each situation are unknown due to the uncertainties surrounding the rate and 753

effect distribution of deleterious mutation or the demographic history of populations, as well 754

as to the many other genetic and non-genetic factors discussed above. 755

It is true that there is a pressure for taking action regarding critically endangered 756

populations (Ralls et al. 2018), as their medium-term persistence is critically compromised if 757

only due to demographic stochasticity. However, these results show that rescue interventions 758

in persistently small populations may increase their long term extinction risk in some cases, 759

calling for additional caution. In such cases, the rescue program should be coupled with 760

reinforced habitat interventions in order to restore an effective population sizes large enough 761

to allow efficient purging. Note that if, due to past purging under slow inbreeding, the 762

endangered population shows no evidence of inbreeding depression, the rescue program is 763

mainly intended to restore adaptive potential and might be postponed until a larger size is 764

attained. Alternatively, one or several donor populations with a history of slow inbreeding, 765

and therefore more purged, could be preferred, although the decision should weight the risk 766

arisen from the introduced load with others derived from causes not included in these 767

simulations, as the loss of adaptive potential. In any case, as far as the population singularity 768

is not a main concern, the restoration of continuous connectivity should be preferred to 769

recurrent migration events from time to time, due to fortuitous accumulation of random 770

episodes introducing high load. 771

772

Future advances and conclusions 773

The impact on conservation practice of the theoretical considerations and the simulation 774

results discussed here depend on many factors that determine the genetic architecture of the 775

inbreeding load, as the distribution of mutational effects and dominance patterns for 776

deleterious mutations or the complexity of demographic histories, and all of them are 777


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28

worthwhile to be explored. Simulation approaches and experiments with model organisms can 778

be very useful, both to advance in our understanding of this genetic features and to test the 779

predictions generated in this analysis. It would also be helpful to understand how the genomic 780

load assayed in terms of the burden of alleles annotated for different deleterious categories 781

can inform on the fitness load and, in particular, on the inbreeding load measured in terms of 782

concealed deleterious effects. Furthermore, there is a need for long term empirical observation 783

of case studies, based on careful evaluation of the inbreeding load and the demographic and 784

genetic flow history in both the donor and the recipient population, the evolution of fitness in 785

the latter and the occurrence of extinction. These studies could benefit on the combined assay 786

of fitness traits and genomic information. 787

The prospects of a rescue program depend on the demographic history of the 788

endangered and donor populations but, in agreement with the small population paradigm, 789

future population growth is essential to guarantee successful rescue and improve population 790

survival. Our results illustrate that understanding all the consequences of conservation 791

interventions is an arduous enterprise riddled with difficulties, and that the only safe strategy 792

for in situ conservation and the one that should be prioritized and taken as a paradigm, is the 793

recovery of large effective population size through the restoration of the habitat and of a 794

healthy and continuous connectivity. 795

796

Acknowledgements 797

We are grateful to the editor and to three anonymous reviewers by their helpful comments. 798

799

References 800

Adams JR, Vucetich LM, Hedrick PW, Peterson RO, Vucetich JA (2011) Genomic sweep 801

and potential genetic rescue during limiting environmental conditions in an isolated wolf 802

population. Proc R Soc B 278:3336–3344. https://doi.org/10.1098/rspb.2011.0261 803

Åkesson M, Liberg O, Sand H, Wabakken P, Bensch S, Flagstad Ø (2016) Genetic rescue in a 804

severely inbred wolf population. Mol Ecol 25:4745–4756. 805

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SUPPLEMENTARY MATERIAL 1078

1079

1080

Methodology of simulations 1081

We use computer simulations to explore the consequences of purging on genetic rescue 1082

programs considering different scenarios, always under mutation, natural selection and drift in 1083

a discrete generations model. First, we simulated a non-threatened population of N = 104 1084

dioecious diploid individuals with random mating for 10,000 generations in order to obtain a 1085

base population at the mutation-selection-drift equilibrium. Then, a smaller threatened 1086

population was derived and maintained until it was considerably inbred. The rescue program 1087

consisted in the introduction of a certain number of individuals from the large base population 1088

into the threatened one. Effective population size was assumed to equal the number of 1089

breeding adults (Ne N). 1090

1091

1092

1093

Simulation model and mutational parameters 1094

Non-recurrent deleterious mutations occurred at rate λ = 0.2 per haploid genome and 1095

generation, with fitness effects being simulated through fecundity differences. For each locus, 1096

the fitness was 1, 1 – sh, 1 – s for the wild-type homozygote, the heterozygote and the 1097

homozygote for the mutant allele, respectively. The homozygous deleterious effect s was 1098

sampled from a gamma distribution with mean �� = 0.2 and shape parameter β = 0.33, and the 1099

dominance coefficient h was obtained from a uniform distribution between 0 and e(-ks), where 1100

k is a constant used to obtain the desired average value and ℎ = 0.283 (López-Cortegano et al. 1101

2018). Thus, more deleterious alleles are expected to be more recessive (Caballero and 1102

Keightley 1994). Sampled s values larger than one were assigned a value s = 1 so that the 1103

mutational model generates a lethal class. The fitness of each individual was obtained as the 1104

product of genotypic fitnesses across loci. In order to produce each offspring, parental 1105

individuals were randomly chosen according to their fitness allowing for polygamous mating 1106

and free recombination. The haploid inbreeding load B for the base population (Morton et al. 1107

1956), calculated as the sum of s(1 – 2h)pq for all selective loci, where q and p = 1 – q are the 1108

frequencies of the mutant and wild allele, respectively, was B = 6.23 (1.885 for lethal alleles), 1109

which is on the order of that found in several wild populations of mammals and birds 1110

(O’Grady et al. 2006; Hedrick and García-Dorado 2016). The number of segregating genomic 1111


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38

sites with deleterious mutations was about 42,000 in the base population. In addition, 2,000 1112

neutral sites, with reverse mutation allowed and the same mutation rate as sites under natural 1113

selection, were simulated to obtain estimates of neutral genetic diversity. 1114

1115

Threatened populations and rescue program 1116

Different scenarios were simulated as shown in Fig. Box 1.1 of the main text. In a first phase, 1117

threatened populations with different sizes (N1 = 4, 10 or 50) were maintained under the same 1118

conditions as the base population except in that offspring were randomly assigned to male or 1119

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

generation 50 for populations with N1 = 50, etc.) so that the expected average inbreeding 1121

coefficient was F 0.4. At this point, four alternative scenarios were simulated for each 1122

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

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

size (N2 ≠ N1), and entered or not a genetic rescue program. Regarding the population size in 1125

these two phases, these scenarios will be denoted by the corresponding numbers (e.g., 50-10 1126

stands for threatened populations with population size 50 during phase 1 and 10 during phase 1127

2). In order to enforce mating between native and migrant individuals, these were assumed to 1128

be males. Migrants did not replace the individuals of the line (i.e., the number of individuals 1129

after a migration event was the size of the line plus the number of migrants). The whole 1130

scheme was simulated in a single round, so that each set of four scenarios shared the same 1131

original threatened population. Depending on the case, between 500 and 2,500 replicated 1132

rounds were simulated. The number of individuals introduced during each migration event 1133

was five for lines with N2 = 50 and one for lines with N2 < 50. Regarding the number of 1134

migration events, we considered four strategies: i) a single event; ii) two events with an 1135

interval of five generations; iii) periodic migration every five generations; iv) the “one 1136

migrant per generation” (OMPG) strategy, that is widely recommended to retain connectivity 1137

in metapopulation management (Mills and Allendorf 1996). All the sizes considered for the 1138

threatened populations (4, 10 and 50) correspond to the IUCN Red List category of Critically 1139

Endangered or Endangered according to Criterion D (IUCN 2012). Extinction of a line 1140

occurred when the average fitness (w) of males and/or females was less than 0.05 and/or when 1141

there were only breeding males or only breeding females (counted after migration when 1142

appropriate). Alternative criteria assumed extinction when w = 0 or w < 0.1, or no extinction 1143

at all. 1144


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39

Each generation we computed average fitness (w), genetic diversity (H) for the neutral 1145

loci, and overall inbreeding load (B), always excluding migrants. 1146

1147

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

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

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

genetic rescue program. 1151

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

Results 1152

Evolution of threatened populations without genetic rescue 1153

Figures S1-S4 give the evolution of different genetic parameters averaged over replicates 1154

under different scenarios assuming no extinction (results for a subset of scenarios are given in 1155

Fig. Box 1.2). Figures S5-S8 give analogous results obtained for the set of surviving lines, 1156

which are qualitatively similar to Figs. S1-S4 except in that fitness averages are a little higher 1157

when extinction is high, and in that the sampling error of the over-replicates averages for the 1158

different parameters increases as the number of surviving lines drops. 1159

Results on the percent of surviving lines, analogous to those presented in the main text 1160

but assuming different extinction criteria are shown in figures S9 and S10. Results are similar 1161

under the different extinction criteria. 1162


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1163

Figure S1. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1164

threatened populations entering a genetic rescue program (one unique migration of 5 1165

individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and of control threatened 1166

populations (dashed lines). No extinction allowed. To avoid extinction due to all breeding 1167

individuals being homozygous for lethal alleles, we assigned s = 0.99 whenever the s value 1168

sampled from the gamma distribution was larger than 0.99 (the standard procedure in the 1169

cases with extinction allowed was assigning s = 1 when the sampled value was larger than 1). 1170

1171


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1172

1173


threatened populations entering a genetic rescue program (two migrations of 5 individuals in 1175

lines N2 = 50 with an interval of five generations, and 1 individual otherwise; solid lines) and 1176

of control threatened populations (dashed lines) without extinction (as in Figure S1). 1177

1178


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42

1179

1180


threatened populations entering a genetic rescue program (periodic migrations every five 1182

generations of 5 individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and of 1183

control threatened populations (dashed lines) without extinction (as in Figure S1). 1184

1185


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43

1186

1187


threatened populations entering a genetic rescue program (“one migrant per generation” 1189

strategy; solid lines) and of control threatened populations (dashed lines) without extinction 1190

(as in Figure S1). 1191

1192

1193


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44

1194

1195

1196


threatened populations entering a genetic rescue program (one unique migration of 5 1198

individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and of control threatened 1199

populations (dashed lines). Extinction of a line occurred when the average fitness (w) of 1200

males and/or females was less than 0.05 and/or when there were only breeding males or only 1201

breeding females. 1202

1203


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45

1204

1205


threatened populations entering a genetic rescue program (two migrations with an interval of 1207

five generations of 5 individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and 1208

of control threatened populations (dashed lines). Extinction of a line occurred when the 1209

average fitness (w) of males and/or females was less than 0.05 and/or when there were only 1210

breeding males or only breeding females. 1211

1212


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1213

1214


threatened populations entering a genetic rescue program (periodic migrations every five 1216

generations of 5 individuals in lines N2 = 50, and 1 individual otherwise; solid lines) and of 1217

control threatened populations (dashed lines). Extinction of a line occurred when the average 1218

fitness (w) of males and/or females was less than 0.05 and/or when there were only breeding 1219

males or only breeding females. 1220

1221


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1222

1223


threatened populations entering a genetic rescue program (“one migrant per generation” 1225

strategy; solid lines) and of control threatened populations (dashed lines). Extinction of a line 1226

occurred when the average fitness (w) of males and/or females was less than 0.05 and/or when 1227

there were only breeding males or only breeding females. 1228

1229

1230 1231


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1232

1233

Figure S9. Percent of surviving threatened populations under a genetic rescue program (one 1234

unique migration; two migrations with an interval of five generations; periodic migrations 1235

every five generations; “one migrant per generation” strategy; solid lines) and of surviving 1236

control threatened populations (dashed lines). Extinction due only to homozygosis for lethal 1237

alleles (i.e., extinction occurs when fitness is 0 for all the males or/and all the females in the 1238

line) or to all breeding individuals being of the same sex. 1239

1240

1241

1242


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1243

1244

Figure S10. Legend as in Figure S9, but extinction occurs when the average fitness (w) of 1245

males and/or females is less than 0.1. 1246

1247

1248

1249

1250

1251

1252

1253


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Supplemntary Material References 1254

Caballero A, Keightley PD (1994) A pleiotropic nonadditive model of variation in 1255

quantitative traits. Genetics 138:883–900. 1256

Hedrick PW, García-Dorado A (2016) Understanding inbreeding depression, purging, and 1257

genetic rescue. Trends Ecol Evol 31:940–952. https://doi.org/10.1016/j.tree.2016.09.005 1258

IUCN (International Union for the Conservation of Nature). (2012). IUCN Red List 1259

categories and criteria: version 3.1. 2nd edition. IUCN Species Survival Commission, 1260

Gland and Cambridge. 1261

López-Cortegano E, Bersabé D, Wang J, García-Dorado A (2018) Detection of genetic 1262

purging and predictive value of purging parameters estimated in pedigreed populations. 1263

Heredity 121:38–51. https://doi.org/10.1038/s41437-017-0045-y 1264

Mills LS, Allendorf FW (1996) The one-migrant-per-generation rule in conservation and 1265

management. Conserv Biol 10:1509–1518. https://doi.org/10.1046/j.1523-1266

1739.1996.10061509.x 1267

Morton NE, Crow JF, Muller HJ (1956) An estimate of the mutational damage in man from 1268

data on consanguineous marriages. Proc Natl Acad Sci USA 42:855–863. doi: 1269

10.1073/pnas.42.11.855 1270

O’Grady JJ, Brook BW, Reed DH, Ballou JD, Tonkyn DW, Frankham R (2006) Realistic 1271

levels of inbreeding depression strongly affect extinction risk in wild populations. Biol 1272

Conserv 133:42–51. https://doi.org/10.1016/j.biocon.2006.05.016 1273

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