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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Supporting information Appendix S1 Factors expected to affect the magnitude of genetic rescues for fitness The magnitude of genetic rescue due to outcrossing within species is expected to equal the extent of inbreeding depression if inbreeding is totally eliminated and there is no outbreeding depression. Empirical findings from several studies supports this prediction (see main text). The magnitude of inbreeding depression (ID) depends upon the increase in inbreeding coefficient (∆F), and the genetic load in the population, as indicated by the following equation (after Falconer & Mackay 1996): # loci ID = ∑2piqidi∆F (eqn S1) i = 1, where 2piqi is the heterozygosity for each polymorphic locus and di its dominance deviation (deviation of the heterozygote mean from the mean of the homozygotes) and the summation is over all polymorphic loci with genotypes differing in their impacts on the quantitative traits (reproductive fitness in the current context). The 2piqi term is reduced by a history of small population sizes or for selfing species. For habitually inbreeding species, this term will be very small, such that there will be at best a weak relationship between inbreeding depression and F while for mixed mating species the relationship is likely to be highly variable. Thus, tests for impacts of ∆F are best restricted to outbreeding species (as I did). As expected from this equation (with the effects of loci combining additively on average), inbreeding depression is usually approximately linearly related to the inbreeding coefficient (see Falconer & Mackay 1996; Lynch & Walsh 1998). An alternative formulation is provided by Morton et al. (1956) for the ratio of survival in inbred (SI) and outbred (So) populations where the effects of loci are expected to combine multiplicatively: SI/SO = eA – BF (eqn S2) where B is the number of haploid lethal equivalents (a measure of the genetic load in the population) and eA is the survival of the non-inbred population. In this case, the natural logarithm of survival is expected to decline linearly with F, as is usually found empirically (Ralls et al. 1988). Thus, by extension the magnitude of genetic rescue effects should be positively correlated with the difference in inbreeding coefficient (ΔF) between the inbred and outcrossed populations. The amount of benefit (heterosis) on fitness from crossing two populations is predicted to depend on the genetic distinctiveness (y - difference in allele frequencies between the target and rescuing populations summed across loci affecting fitness), as illustrated by the following equation for F1 heterosis for traits determined by zygotic genotypes (Falconer & Mackay 1996) (the F2 heterosis is half that in the F1): # loci F1 heterosis = ∑diyi2 (eqn S3) i = 1, The extent of inbreeding depression is expected to differ with ploidy level (diploid ≥ polyploid > haplodiploid > haploid: Frankham et al. 2010, 2014), but there 1 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 were too few data to make meaningful comparisons of genetic rescue effects among ploidy levels in my analyses. The predictions about genetic rescue being tested are: 1. The outcrossing of inbred populations to isolated populations of the same sexually reproducing species (with the same karyotype, adapted to the same environment and isolated for ≤ 500 years) will be beneficial, especially in naturally outbreeding species (Frankham et al. 2011). 2. Genetic rescue effects will be positively correlated with ΔF for naturally outbreeding species (see above). Relationships are expected with both the maternal and the zygotic ΔF, as discussed in Appendix S2 below. 3. The magnitude of genetic rescue effects will be larger in wild or stressful environments than in benign/captive ones (Dudash 1990; Fox & Reed 2011; Enders & Nunney 2012). 4. The benefits of outcrossing will be greater in naturally outbreeding species than inbreeding (selfing or mixed mating) ones (Byers & Waller 1999). 5. Outbred immigrants will yield larger average benefits than inbred ones (Pickup et al. 2013). This assumes that the populations being crossed have been isolated for sufficient generations to have differences in their contents of deleterious alleles. No rescue is expected if the crossed populations are recent derivatives from the same source, such as source-sink populations. 6. The magnitude of rescue effects will be larger for composite fitness than for individual fitness components (Frankham et al. 2010) 7. There will be little difference in the magnitude of genetic rescue among major eukaryotic taxa. 8. Genetic rescue effects will be greater in F1 than in F2 and later generations for zygotically determined traits, but F2 > F1 for maternally determined traits (see Appendix S2). 2 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 Appendix S2 Inbreeding depression and genetic rescue for maternally and zygotically determined traits As some traits are determined by maternal genotypes, others by zygotic genotype and total and composite fitness by a combination of these (Wright 1977; Roach & Wulff 1987; Wolfe 1993; Montalvo 1994; Falconer & Mackay 1996), changes in both maternal and zygotic inbreeding coefficients need to be considered both during inbreeding and following crossing of populations (Falconer & Mackay 1996). In general, the maternal inbreeding coefficient lags the zygotic one by a generation. For example inbreeding depression in litter size for mice is modest until the mothers are inbred, whilst adult survival typically exhibits inbreeding depression as soon as the zygotes are inbred (Bowman & Falconer 1960). Similarly in plants, seed number and weight show little inbreeding depression when maternal plants are outbred and zygotes are inbred, but substantial inbreeding depression when maternal plants are inbred (Wolfe 1993; Montalvo 1994). In genetic rescue experiments, the reversal of inbreeding depression is likewise delayed for maternally determined compared to zygotically determined traits (Table A1) and the two inbreeding levels are not equal until the F3 generation. Consequently, genetic rescue effects for total and composite fitness are expected to be dependent on both maternal and zygotic ΔF values. In the F1, the maternal ΔF (ΔFm) is zero, as the inbreeding coefficient is that of the mothers and is not changed by crossing. Conversely the zygotic ΔF (ΔFz) is the difference between the maternal F [½ (Fa + Fb)] and the zygotic F (0) = ½ (Fa + Fb). Table A1 Maternal and zygotic inbreeding coefficients in F1, F2 and F3 crosses (involving multiple individuals in each case) between (a) different inbred populations, or (b) between inbred females and outbred males from different populations (with random mating of the parents of each generation) and ΔFm and ΔFz values for comparisons between crosses and the inbred parent population. __________________________________________________________________ Maternal F Zygotic F ΔFm ΔFz __________________________________________________________________ (a) Reciprocal crosses between different inbred parental populations with inbreeding coefficients of Fa and Fb with comparisons being made between crossed populations and the mean of the two inbred parents __________________________________________________________________ F1 ½ (Fa + Fb) 0 0 ½ (Fa + Fb) F2 0 ¼ (Fa + Fb) ½ (Fa + Fb) ¼ (Fa + Fb) F3 ¼ (Fa + Fb) ¼ (Fa + Fb) ¼ (Fa + Fb) ¼ (Fa + Fb) (b) Crosses between inbred female and outbred male parent populations with inbreeding coefficients of Fa and 0 with comparison being made between crossed populations and the inbred parent ___________________________________________________________________ F1 Fa 0 0 Fa 3 125 126 127 F2 F3 0 ¼ Fa ¼ Fa ¼ Fa 4 Fa ¾ Fa ¾ Fa ¾ Fa 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 Appendix S3 Additional details of data selection criteria Within studies of the same populations, I preferentially used data on the most inclusive fitness characters I could find or construct. Where there were data only on multiple separate fitness components, I computed composite fitness from the component data, as is commonly done in plant studies (e.g. Hereford 2009a). Species with permanent translocation heterozygosity across much of their genomes were excluded, as they exhibit little or no homozygosity or inbreeding depression (Heiser & Shaw 2006). I did not exclude any outbred/inbred comparisons purely on the basis of small sample size and low statistical power to minimize bias. However, I did exclude the F2/inbred parent comparison in the song sparrow data of Marr et al. (2002) as the inbreeding coefficient in the F2 (0.076) was higher than that in the inbred parent population (0.066). In assessing the risk of outbreeding depression, adaptive differentiation, where not directly known, was inferred from differences in biotic and/or physical environmental between the populations (e.g. temperature, day length, soils, large geographic distances, different host plants, and diets; (Turesson 1922; Antonovics 1976; Snaydon & Davies 1982; Bradshaw 1984; Hoffmann & Weeks 2007). Where information was unclear, I emailed authors in an attempt to clarify details. Assessments of the above characteristics were made on the balance of probabilities to include as many studies as possible. Where information on one characteristic in the outbreeding depression screen was not available (often the case for chromosomes) the risk assessments were based on the remaining information (potentially increasing the risk of outbreeding depression). In minimizing pseudoreplication, I chose traditional measures of mean populations fitness (composite fitness, or survival or fecundity), rather than demographic measures such as population growth rate or increase in populations size (recommended by Whiteley et al. 2015), as fitness differences may not be detectable under conditions of density regulation when populations are at carrying capacity (Frankham et al. 2010 p. 292), as observed, for example by Adams et al. (2011). However, genetic rescue in traditional measures of population fitness are expected when populations are recovering from low population sizes (Frankham et al. 2010 p. 292). Since there were often uncertainties in information for screening against a high risk of outbreeding depression, especially in inbreeding levels, isolation of populations and likelihood of adaptive differentiation of populations, data were categorised as higher versus lower certainty of assessments, based on strength of evidence relating to risk of outbreeding depression and the statistical power of the data, and the two categories compared. As the two had similar characteristics and did not differ significantly in the fitness benefits of outcrossing, analyses reported here were completed on the combined data. Information on variables expected to affect the magnitude of genetic rescue effects were recorded, namely items 2-7 in Appendix S1, with the addition of number of inbred and outcrossed populations (for computing the weighting factor used in tests for publication bias). Inbreeding coefficients 5 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 The inbreeding coefficients (F) in the inbred and crossed populations were based on the probability that two alleles at a locus in an individual are identical by descent (Malécot 1969; Falconer & Mackay 1996). F values were zygotic inbreeding coefficients, except were indicated otherwise. When inbreeding coefficients were not reported (often), indirect estimates were obtained where possible from allozyme or microsatellite heterozygosity data using the equation (Frankham et al. 2010): F = 1 – (HI/HO) (eqn S4) where HI is the heterozygosity of the inbred populations and Ho that of the non-inbred comparator population. Only estimates from outbreeding species were used in analyses. The inbreeding coefficients for admixed populations (after two or more generations) formed from populations with inbreeding coefficients of Fi with proportions pi of alleles from each population were computed using the following equation (Margan et al 1998): Fpooled = ∑pi2Fi (eqn S5) This assumes that there is no selective difference between immigrant and resident alleles, as do pedigree inbreeding coefficients. 6 198 199 Table S1. Genetic rescue (GR) data set 1 for fitness (uploaded as a separate Supporting Information Excel file). 7 200 201 202 203 204 205 206 Table S2 Genetic rescue data set for evolutionary potential (GREvP) for fitness traits Generations Finbredb 1.179 3.55 0.405 0.203 1.34073 Holleley et al. (2011) 1.064 12 0.165 0.03 1.16168 Invertebrate Holleley et al. (2011) 1.036 26 0.165 0.115 1.05988 mysid shrimp Invertebrate Market et al. (2010) 1.270 3 0.313 0.156 1.22727 Americamysis bahia mysid shrimp Invertebrate Market et al. (2010) 1.861 3 0.313 0.052 1.37879 Americamysis bahia mysid shrimp Invertebrate Market et al. (2010) 1.847 3 0.313 0.039 1.39773 Species Common name Major taxa Reference Drosophila melanogaster fruit fly Invertebrate Margan et al. (1998) Drosophila melanogaster fruit fly Invertebrate Drosophila melanogaster fruit fly Americamysis bahia GREvP/Gena aGenetic Fcrossc GDX/GDId Comments Comparison of Ne = 50 vs 2x50 treatments Comparison of N = 50 migration rates of 0.04 vs 0.0025 Comparison of N = 50 migration rates of 0.01 vs 0.0025 Comparison of 1X vs 2X treatments Comparison of 1x vs 6X treatments Comparison of 1x vs 8X treatments rescue ratio per generation. coefficient of inbred parent population(s). cInbreeding coefficient of zygotes in crossed population. dRatio of genetic diversity in outcrossed population to that in the inbred parent population, estimated from (1 - F cross)/(1 – Finbred). bInbreeding 8 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 Appendix S4 Effect size for evolutionary potential and variables expected to affect it Effect size The response ratio was used as the effect size for evolutionary potential, but was expressed on a per generation basis, as different studies had different durations in generations (t). Selection responses (selected – control) per generation in the outcrossed/inbred populations was converted to a per generation basis by raising the response ratio to the power of 1/t. Response ratios for Margan et al. (1998) data were obtained by subtracting the NaCl concentrations at extinction for the fully inbred control populations from that of the populations of interest. For the remaining studies where population sizes under selection were reported after different numbers of generations (t, and t – x), the ratio of Nt/Nt-x for the crossed populations was divided by the corresponding ratio for inbred parent populations, and the resulting ratio raised to the power of 1/x. Variables affecting genetic rescue for evolutionary potential The extent of evolutionary genetic adaptation (GA) in the short term is predicted by the breeders’ equation GA = h2S, where h2 is the heritability and S the selection differential (Falconer & Mackay 1996). This provides a basis for determining the variables expected to predict genetic rescue for evolutionary potential (GREvP), as follows: GREvP = hX2 Sx hI2 SI (eqn S6) where the subscripts I and X stand for the inbred parent and the crossed population in F2 and later generations. The effect of crossing on heritability is predicted to be closely related to the increase in genetic diversity, as follows: hX2 = VAX/VPX = VAX (VPI) = ∑2pixqixaix2(VPI) hI2 VAI/VPI VAI (VPX) ∑2piIqiIaiI2 (VPX) (eqn S7) where VA is the additive genetic variation, VP the phenotypic variation, 2pq is the heterozygosity for alleles affecting fitness, and a is half the difference in mean between the two homozygotes at the locus. Thus, genetic rescue for fitness will depend on the increase in heterozygosity in the crossed population after Hardy-Weinberg equilibrium has been established, compared to that in the inbred parent population. While VA for fitness traits often increases initially before decreasing with inbreeding in the environment to which the population is adapted (Willi et al. 2006), this is unlikely in the context of adaptation to new environments, as then genetic variation for fitness is primarily additive, rather than non-additive (Frankham et al. 1999; England et al. 2003; Frankham et al. 2011). The benefits of gene flow on evolutionary potential should depend upon the proportionate increase in genetic diversity for fitness, if there is no outbreeding depression. In the current context this proportion should typically be similar to that for neutral markers (Briscoe et al. 1992; Frankham et al. 9 257 258 259 260 261 1999; England et al. 2003; Gilligan et al. 2005). It there is heterozygosity data, then GREvP should be related to the ratio of heterozygositycross/heterozygosityparent (GDX/GDI) while if there are only inbreeding coefficient, the ratio can be estimated as (1- FX)/(1 - FP). The latter expression has been used to determine the ratios in this paper. 10 262 263 Table S3 Characteristics of the nine studies that reported deleterious effects of outcrossing. Species Mating system GR Caenorhabditis elegans Selfing 0.90 Inbreeding difference ΔF ≥ 0.75 Environment Fitness measure Statistical power Gen Details Benign Total Good F1 Two F1 crosses of populations were mildly deleterious, compared to the inbred parent strains collected from <10cm and 15m apart. Convincing evidence for mild outbreeding depression A panmictic population formed from four isolated Ne = 100 populations (at an advanced generation) was mildly deleterious compared to the mean of the parent populations, when assessed in benign conditions, but strongly beneficial under stressful conditions (GR = 2.14). Other related crosses of replicates of different Ne treatments were also beneficial. Five lines subject to a single generation of full-sib mating had a slightly higher average fitness than their 10 F1’s. Two other related treatments from the same base population with higher F’s showed beneficial Drosophila melanogaster Outbreeding 0.91 0.18 Benign Composite Low >F2 Drosophila melanogaster Outbreeding (but inbred base population) 0.98 0.25 (0.0375)a Benign Egg-adult survival Low F1 11 References Dolgin et al. (2007) Woodworth et al. (2002) Tantawy (1957); Falconer (1954) Drosophila melanogaster Outbreeding (but inbred base population) 1.00 0.51 (0.0765)a Benign Egg-adult survival Low F1 Lymnaea stagnalis Mixed mating 0.86 0.0625 Benign Composite Low F1 12 effects of crossing. The base population was highly inbred (F > 0.85) before this experiment commenced, as it originated from a single inseminated wild females and was maintained with a small population size (~ 20 pairs/generation) for ~ 6 years (~ 150 generations). Thus, the ΔF with respect to similar inbreeding from an outbred base population is effectively only ~ 0.04). Five lines inbred by double first-cousin mating had a slightly lower fitness than their 10 F1’s under benign conditions. Another related treatment with higher F showed beneficial effects of outcrossing. The base population was already highly inbred (F > 0.85) before this experiment commenced (see above). The effective ΔF is only ~ 0.08. Six F1 crosses of four Ne = 8 bottlenecked populations were mildly deleterious compared to their parent lines, but crosses of a related treatment with Ne = 5 were beneficial compared to Tantawy (1957); Falconer (1954) Coutellec & Caquet (2011) Musca domestica Outbreeding 0.95 < 0.20 Benign Egg-adult survival Low >F2 Diodia teres Mixed mating 0.94 ≥ 0.76 (FIS) Benign Pollination success Low F1 Echinacea angustifolia Selfincompatible 0.89 NAb Field Composite Low F1 Viola stagnina Mixed mating 0.91 NA Benign Seeds/capsule Very low F1 13 their parent populations. A comparison of isolated inbred populations versus the same sized populations with low migration (0.025) every generation exhibited a slightly lower fitness in the migration treatment at generation 5, but a strongly beneficial effect at generation 24, as were both assessments for a treatment with a high immigration rate. Pollination success in F1 crosses was variable, but mildly deleterious on average, compared to parent populations (variable), but composite fitness in F2 crosses in the field were beneficial compared to inbred parents. Inbred parents had slightly higher average fitness than their F1 but the comparison was strongly affected by one major outlier in within population cross with about double the achene count of the next highest. Many plants were alive but had not yet flowered (much of the life-cycle was not included). Cross of two populations had slightly lower fitness Backus et al. (1995); Bryant et al. (1999) Hereford (2009b) Wagenius et al. (2010) Eckstein & Otte (2005) than the F1, but this was a very small study (9 plants), with no information presented on the habitats of the populations. 264 265 266 aThe numbers in brackets are the equivalent inbreeding coefficients from similar inbreeding in an outbred base population. not available bInformation 14 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 Appendix S5 Additional consideration of results Mating system effect on genetic rescue When mating system was tested at a finer scale, the fitness benefit was 78% in self-incompatible species, 59% in other outbreeders, 16% in mixed mating and 39% in selfers (Kruskall-Wallis H = 10.76, df = 3, P = 0.013). While the latter two are in reverse order compared to expectations, the numbers of data points were only 6 for selfing species. Difference between F1 and F2 genetic rescue effects An alternative explanation for F2 > F1 genetic rescue effects is that the inbreeding levels and ΔF values might be higher for studies reporting F2 than F1 data. This can be excluded, as differences are in the opposite direction to this. Mean F values in inbred parental populations were 0.615 and 0.440 for studies with F1 and F2 data, respectively, while corresponding ΔFz values were 0.567 and 0.261. ΔFzygotic and ΔFmaternal effects Conclusion about the predictive power of ΔFz depended on whether regression models fitted an intercept or not, while ∆Fm was significantly supported irrespective of whether the single factor regressions were fitted with an intercept, or through the origin. For both simple regressions and both AICc model selection analyses the intercept terms were significant, so I preferentially reported analyses with intercepts fitted, despite tests of inbreeding effects being more powerful when regressed through the origin (e.g. Montgomery et al. 2010). In simple linear regressions using data set 2 with an intercept fitted, ∆Fm was a significant predictor of ln GR for outbreeding species (Fig. 1: b = 0.563 + 0.298, P = 0.032, n = 69), whilst ΔFz was not (b = - 0.109 + 0.177, P = 0.770, n = 68). There is much lower power associated with ∆Fm, compared to ∆Fz, as it is only F2 and later generation data (26 of 69) that have non-zero values of ∆Fm, while all ∆Fz are > 0. Single fitness component versus composite fitness effect The prediction that genetic rescue effects would be greater for composite fitness than its components was not supported in either single variables tests (Table 1) or AICc model selection with multiple variables (Table 2). This is, at least partially, an artefact due to a low proportion of self-incompatible species having composite fitness data, but predominantly showing large genetic rescue effects. Best fitting AICc model The best fitting model as defined by Akaike model selection in Table 2 was: ln GR = 0.4468 + 0.587 Environment 15 317 318 319 320 321 322 323 324 325 326 327 328 329 where environments are coded 0 benign and 1 stressful. Effect of outbred versus inbred immigrants on genetic rescue Gene flow from both outbred and inbred donors were beneficial (GR of 2.136 and 1.519, respectively), but the benefits were 40.6% greater with outbred than inbred immigrants. The test for effects of outbred versus inbred immigrants was supported by the non-parametric single variable test, but not by either of the AICc model selections. These tests had low statistical power as differences are only expected in F2 and later generations and there were very few such data points for outbred immigrants beyond the F1. 16 330 331 332 333 334 Fig. S1 Histograms of natural logarithm of genetic rescue ratio (ln GR) for composite fitness in outbreeding species in benign versus stressful environments. Medians for ln GR and de-transformed GR values are also presented. Benign Median = 0.412 GR = 1.509 40 Percent 30 20 10 0 0 1 2 3 4 5 ln GR 335 40 Stressful Median 0.954 GR 2.625 Percent 30 20 10 0 0 1 2 3 ln GR 336 337 338 17 4 5 339 340 341 342 Table S4 Variables affecting the magnitude of genetic rescue for composite fitness based on model selection statistics using the Akaike AICc procedure on dataset 5 (n = 29). The best fitting model is bolded. Model C, environment, σ2 C, ΔFm, environment, σ2 C, ΔFm, environment, immigrant source, σ2 C, ΔFm, ΔFz, environment, immigrant source, σ2 C, σ2 Ki AICc 3 - 48.090 Δi 0 wi 0.6580 4 -46.092 1.998 0.2423 5 - 43.884 4.206 0.0803 6 - 40.674 7.416 0.0161 2 - 37.439 10.661 0.0032 Ki = number of parameters estimated, AICc = Akaike’s information criteria adjusted for small sample size, Δi = deviation of the model from the best fitting model, and wi = Akaike weights (approximate probability that the model is the best information theoretic one), C is the constant (intercept), ΔFm and ΔFz are the difference in maternal and zygotic inbreeding coefficient between crossed and inbred populations. . 343 344 345 18 346 347 348 349 350 Fig. S2 Funnel plot for all genetic rescue data for fitness (ln GR) from data set 1 against logarithm of the sample size weighting factor (log w) with line of best fit inserted (the slope is non-significant). 351 352 19 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 Table S5 Mean genetic rescue ratios (GR: F1/inbred parents) for outcrosses of inbred parental populations for fitness traits in several domestic plant and animal species Species Plants Maize Sorghum Cotton Wheat Barley Tomato Animals Poultry Swine GR Trait Mating system Reference 2.90 2.00 1.48 1.29 1.32 1.45 grain yield grain yield grain yield grain yield grain yield fruit yield outcrossing mainly selfing selfer selfer selfer selfer Sinha & Khanna (1975) Sinha & Khanna (1975) Sinha & Khanna (1975) Sinha & Khanna (1975) Sinha & Khanna (1975) Williams & Gilbert (1960) 1.22 eggs to 500 days litter weight at 154 days outbreeding Shoffner et al. (1966) outbreeding Dickerson et al. (1946) 1.79 20 373 374 375 376 377 378 379 380 381 382 383 Appendix S6 Additional Discussion On the basis that genetic rescue is the reversal of inbreeding depression (see Introduction), the proportion of studies reporting beneficial effects of outcrossing should equal the proportion of studies reporting inbreeding depression (given similar sized studies and environmental regimes). This prediction was supported, as 92.9% of studies herein exhibited beneficial effects following outcrossing of inbred populations, compared to inbreeding depression for fitness traits in 93.2% of captive mammal populations (Ralls and Ballou 1983) and 91.2% for a broad array of animal and plant taxa in wild environments (Crnokrak & Roff 1999). 21 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 Appendix S7 Beneficial effects of outcrossing on evolutionary potential for traits peripherally related to fitness Benefits of crossing on evolutionary potential for traits peripherally related to fitness have also been reported for sternopleural bristle number in Drosophila (Robertson 1969; Swindell & Bouzat 2006), body weight in mice (Falconer & King 1953; Roberts 1967 [only in a line selected for high, not in a line selected for low weight]; Eisen 1975) and nesting-building behavior in mice (Bult & Lynch 2000). In the Robertson (1969) study (the largest one), response to selection in crossed lines exceeded that of the mean of the parent lines in 27/30 cases. The crosses that failed to exceed the parents in response or only gave limited response typically involved conditions where there was little differentiation between crossed populations and little effective augmentation of genetic diversity, as expected. 22 399 400 401 402 403 404 Appendix S8 Additional discussion of genetic rescue guidelines 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 (i) Jonathan D. Ballou and Robert C. Lacy (pers. comm.) are currently working on means for managing gene flow in fragmented populations. My guidelines for genetic rescue are less stringent, than those of Edmands (2007) and Hedrick and Fredrickson (2010), due to: the urgency to act promptly, as conservation biology is a crisis discipline (Soulé 1985) where inaction is often a recipe for further decline and extinction of threatened populations for genetic and nongenetic reasons, (ii) the ubiquity of inbreeding depression in adequately studied naturally outbreeding diploid species, due to either recent matings between relatives, and/or longer term genetic drift effects due to increase in frequency and fixation of deleterious alleles plus fixation of alleles at loci exhibiting heterozygote advantage (the latter issues are also referred to as increased genetic load) (Lacy 1997; Frankham et al. 2014), (iii) the low power of most experiments on threatened populations to detect inbreeding or outbreeding depression, even if it truly exists (e.g. Lacy 1997; Kalinowski & Hedrick 1999), while meta-analyses will usually give a more reliable overview of likely effects. For example, Ralls & Ballou (1983) reported that 41/44 mammal populations had high juvenile mortality for inbred than outbred progeny, but only 34% of the comparisons were significantly different. Further, 90% of the valid data sets in the Crnokrak & Roff (1999) meta-analysis indicated that inbreeding reduced means, but only 53% were significant. (iv) the low power of experiments on genetic rescue of threatened, populations in captivity, the long-time involved and possible difficulties in getting permission to do experiments on them. First, an experiment in captivity would likely involve only a single replicate with low sample sizes and would likely yield a lower benefit or disadvantage than in wild conditions. Second, this approach is not feasible for species that have not been successfully bred in captivity (e.g. northern hairy-nosed wombats). Third, to be convincing the experiment would need to go to at least the F3 generation (Appendix S2) and to encompass the full life cycle for that generation, leading to substantial delays during which the wild population may well be extirpated. This would not be feasible in large long-lived species such as elephants, or long-lived trees where > 100 years would be required, (v) the development of effective means to predict the risk of outbreeding depression (Frankham et al. 2011), and (vi) evidence of consistent and highly beneficial effects of outcrossing on fitness and evolutionary potential documented herein. Edmands (2007) recommended that genetic rescue only proceed when there is clear evidence of inbreeding depression and where evaluations have already been done of crosses over two generations (wherever possible). I disagree with these recommendations for all five of the reasons above. Edmands (2007) also recommended that the population(s) chosen for outcrossing be as similar genetically and adaptively as possible. I agree with 23 448 449 450 451 452 453 454 455 456 457 458 459 460 the need for adaptive similarity (Frankham et al. 2011), but query the requirement for genetic similarity, as theory predicts that the benefits of outcrossing increase with differences in allele frequencies between target and donor populations (Appendix S1). My guidelines are closer to those of Hedrick & Fredrickson (2010) but also less stringent than theirs. For example, I have stronger views about the urgency of action to avoid population extinction, and do not require experimental data from captive populations prior to proceeding, as outcrossing of inbred populations is consistently beneficial in such species as shown herein. 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