1 Authors: Noelia Pérez-Pereiraa band Aurora García-Dorado...2021/07/15 · 1 Authors: Noelia...
Transcript of 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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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
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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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21
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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23
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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24
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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25
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
(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
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
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Waller DM (2021). Addressing Darwin's dilemma: Can pseudo-overdominance explain 1056
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Weeks AR, Heinze D, Perrin L, Stoklosa J, Hoffmann AA, van Rooyen A, Kelly T, Mansergh 1062
I (2017) Genetic rescue increases fitness and aids rapid recovery of an endangered 1063
marsupial population. Nat Comm 8:1071. https://doi.org/10.1038/s41467-017-01182-3 1064
Weiser EL, Grueber CE, Kennedy ES, Jamieson IG (2016) Unexpected positive and negative 1065
effects of continuing inbreeding in one of the world's most inbred wild animals. Evolution 1066
70:154–166. https://doi.org/10.1111/evo.12840 1067
Whiteley AR, Fitzpatrick SW, Funk WC, Tallmon DA (2015) Genetic rescue to the rescue. 1068
Trends Ecol Evol 30:42–49. https://doi.org/10.1016/j.tree.2014.10.009 1069
Wilder AP, Navarro AY, King SN, Miller WB, Thomas SM, Steiner CC, Ryder OA, Shier 1070
DM (2020) Fitness costs associated with ancestry to isolated populations of an endangered 1071
species. Conserv Genet 21:589–601. https://doi.org/10.1007/s10592-020-01272-8 1072
Xue Y, Prado-Martinez J, Sudmant PH, Narasimhan V, Ayub Q, Szpak M, et al (2015) 1073
Mountain gorilla genomes reveal the impact of long-term population decline and 1074
inbreeding (Supl. 1). Science 348:242–245. doi: 10.1126/science.aaa3952 1075
Zajitschek SRK, Zajitschek F, Brooks RC (2009) Demographic costs of inbreeding revealed 1076
by sex-specific genetic rescue effects. BMC Evol Biol 9:289. doi: 10.1126/science.aaa3952 1077
(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
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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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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
Figure S2. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1174
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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1179
1180
Figure S3. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1181
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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1186
1187
Figure S4. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1188
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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1194
1195
1196
Figure S5. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1197
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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1204
1205
Figure S6. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1206
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
Figure S7. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1215
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
Figure S8. Evolution of fitness (w), genetic diversity (H) and inbreeding load (B) of 1224
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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Hedrick PW, García-Dorado A (2016) Understanding inbreeding depression, purging, and 1257
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Gland and Cambridge. 1261
López-Cortegano E, Bersabé D, Wang J, García-Dorado A (2018) Detection of genetic 1262
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Morton NE, Crow JF, Muller HJ (1956) An estimate of the mutational damage in man from 1268
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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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(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