The genetic Allee effect: a unified framework for the genetics and demography of small populations Gloria M. Luque, Chloé Vayssade, Benoit Facon, Thomas Guillemaud, Franck Courchamp, Xavier Fauvergue

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Gloria M. Luque, Chloé Vayssade, Benoit Facon, Thomas Guillemaud, Franck Courchamp, et al.. The genetic Allee effect: a unified framework for the genetics and demography of small populations. Ecosphere, Ecological Society of America, 2016, 7 (7), pp.e01413. ￿10.1002/ecs2.1413￿. ￿hal-01594603￿

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The genetic Allee effect: a unified framework for the genetics and demography of small populations Gloria M. Luque,1 Chloé Vayssade,2 Benoît Facon,3 Thomas Guillemaud,2 Franck Courchamp,1,4 and Xavier Fauvergue2,†

1Ecologie Systématique Evolution, Univ. Paris-Sud, CNRS, AgroParisTech, Université Paris-Saclay, 91400, Orsay, France 2ISA, UMR INRA CNRS, Universite Nicé Côte d’Azur, 06903 Sophia-Antipolis, France 3CBGP, UMR INRA, CIRAD, IRD, SupAgro, 34988, Montferrier sur Lez, France 4Department of and Evolutionary , Center for Tropical Research, Institute of the Environment and ­Sustainability, ­University of California Los Angeles, Los Angeles, California 90095 USA

Citation: Luque, G. M., C. Vayssade, B. Facon, T. Guillemaud, F. Courchamp, and X. Fauvergue. 2016. The genetic Allee effect: a unified framework for the genetics and demography of small populations. Ecosphere 7(7):e01413. 10.1002/ ecs2.1413

Abstract. The Allee effect is a theoretical model predicting low growth rates and the possible extinction of small populations. Historically, studies of the Allee effect have focused on demography. As a result, underlying processes other than the direct effect of on components arenot generally taken into account. There has been heated debate about the potential of genetic processes to drive small populations to extinction, but recent studies have shown that such processes clearly impact small populations over short time scales, and some may generate Allee effects. However, as opposed to the ecological Allee effect, which is underpinned by cooperative interactions between individuals, genetically driven Allee effects require a change in genetic structure to link the decline in with a de- crease in fitness components. We therefore define the genetic Allee effect as a two-step­ process whereby a decrease in population size leads to a change in population genetic structure and, in turn, to a decrease in individual fitness. We describe potential underlying mechanisms and review the evidence for this original type of component Allee effect, using published examples from both plants and animals. The possibility of considering demogenetic feedback in light of genetic Allee effects clarifies the analysis and interpretation of demographic and genetic processes, and the interplay between them, in small populations.

Key words: Allee effect; drift load; eco-evolutionary feedback; extinction vortex; depression; migration load; small populations.

Received 3 May 2016; accepted 11 May 2016. Corresponding Editor: D. P. C. Peters. Copyright: © 2016 Luque et al. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. † E-mail: [email protected]

Introduction et al. 2004, Taylor and Hastings 2005, Johnson et al. 2006). This concept, first introduced by the The Allee effect can be defined as a decrease in American ecologist Warder Clyde Allee in the fitness caused by a decrease in population size 1930s, has been the focus of growing interest from (Stephens et al. 1999). The Allee effect jeopardizes population ecologists over the last two decades. the persistence of small populations, whether In 1999, Stephens et al. formalized the defini- declining or bottlenecked (threatened species; tion of Allee effects, making a crucial distinction Angulo et al. 2007, Bonsall et al. 2014, Kuparinen between component and demographic Allee et al. 2014; introduced/; Davis effects. A component Allee effect is a decrease

v www.esajournals.org 1 July 2016 v Volume 7(7) v Article e01413 Synthesis & Integration Luque et al. in the value of any component of individual fit- modeling ; e.g., Glémin ness caused by a decrease in population size. 2003) and dynamicists usually view genetic pro- A demographic Allee effect is the consequent cesses as affecting populations only in the long decrease in the per capita growth rate of the pop- term. This would make them likely to think that ulation caused by a decrease in population size small populations do not generally stay small for and resulting from one or several component long enough (because they grow or disappear Allee effects. Allee effects have been discovered due to demographic processes) to suffer from in a wide range of taxa, with various mechanisms genetic Allee effects. There may have been too underpinned by a shortage of cooperative inter- little dialog between the two disciplines as yet actions at low ­density (Courchamp et al. 1999, (Kokko and Lopez-­Sepulcre 2007, Metcalf and 2008). Pavard 2007, Pelletier et al. 2009) for the genetic Population dynamicists working on the Allee Allee effect to have emerged as a robust unifying effect may have overlooked the fact that genetic paradigm. processes can also impact populations at an The aim of this work was to propose the genetic ecological time scale of only a few generations Allee effect as a heuristic framework for studying (Glémin 2003, Spielman et al. 2004). This is par- the interplay between genetics and demography ticularly relevant when genetic processes are in small populations. We first propose a formal combined with demographic processes, such definition for the genetic Allee effect and describe as demographic and environmental stochas- the processes potentially underlying this effect. ticity (Tanaka 2000, Hanski and Saccheri 2006). We review the evidence for genetic Allee effects, Some of these genetic mechanisms can gener- including population genetic studies, which, ate component Allee effects (Courchamp et al. although not referring to the Allee effect, pro- 1999) because they yield a positive relationship vide numerous examples of genetic Allee effects. between population size and fitness (Fischer Based on these examples, we then propose meth- et al. 2000, Willi et al. 2005, Berec et al. 2007). ods for detecting genetic Allee effects and distin- These mechanisms are inbreeding depression guishing them from ecological Allee effects. In (Frankham 1995, Spielman et al. 2004), loss of the last section of the study, we discuss the spec- genetic variation (Gomulkiewicz and Holt 1995, ificity, limits, and demographic consequences of Amos and Balmford 2001), and the accumula- genetic Allee effects. tion of deleterious (Lande 1994, Lynch et al. 1995b). Definition Contrasting with the pervasive evidence that genetic mechanisms affect the dynamics of small One fundamental principle of evolutionary populations, even in the short term, fewer than biology is that a population is a collection of dif- ten publications have made specific reference to ferent genotypes vehicled by a number of differ- a genetic Allee effect. There are two possible rea- ent individuals. Changes in genotype frequencies sons for the lack of studies considering genetic correspond to changes in the number, frequency, Allee effects. First, although mentioned in a hand- and association of different alleles within and ful of studies, the genetic Allee effect has never between loci. These genotype frequencies are been formally defined, so the concept may still referred to hereafter as the (within-­population) be too vague to stimulate new studies. Second, genetic structure. Changes in genetic structure the genetic mechanisms occurring in small pop- yield changes in the fitness components that ulations are the classic territory of population these genotypes influence (Soulé 1980). This rela- genetics, whereas the Allee effect is a concept tionship underlies the genetic Allee effect because derived principally from . population size is one of the determinants of These two communities view populations differ- genetic structure (Nielsen and Slatkin 2013). ently and usually work on different entities (e.g., Here (following the evolutionary paradigm individual numbers vs. genotype frequencies), described by Waples and Gaggiotti 2006), the concepts and time scales. Most studies in popu- term “population” refers to a “a group of indi- lation genetics assume populations of constant viduals of the same species living in close enough size, unaffected by individual fitness (even when proximity that any member of the group can

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Fig. 1. Two successive steps are necessary for a genetic Allee effect to occur. Step 1: A decrease in population size causes a change in (a parameter of) genetic structure (heterozygosity, frequency of detrimental and beneficial alleles, allelic richness). Step 2: The change in genetic structure causes a decrease in the value of a component of fitness through inbreeding depression, drift load, or migration load. When both steps occur in a population, a component genetic Allee effect occurs (left panel). potentially mate with any other member.” Unlike effect, in which individual fitness decreases as population dynamicists, we use the term “popu- a straightforward, one-­step consequence of a lation size” to mean the number of individuals decrease in population size or population density. that effectively reproduce. We prefer to use this term, rather than effective population size, Mechanisms Underlying Genetic because the latter is difficult to measure in natu- Allee Effects ral populations and has an ambiguous meaning resulting from its various definitions (the Our literature search identified 15 studies show- “inbreeding effective population size,” the “vari- ing strong evidence for one or several genetic Allee ance effective population size,” and the “eigen- effects in natural or experimental populations value effective population size”; see details in (Table 1). Some of these studies did not actually Sjödin et al. 2005). Population size, genetic struc- use the term genetic Allee effect. We also identified ture, and fitness components are the three cor- about another 40 studies, suggesting the occur- nerstones of the genetic Allee effect. rence of genetic Allee effects (see for instance the The term “genetic Allee effect” is not new (first literature cited in Leimu et al. 2006). Following a appearance in Fischer et al. 2000), but it has sel- thorough analysis of these published studies, we dom been used, and still lacks a proper definition. defined three types of genetic mechanisms gener- We define the genetic Allee effect as a two-step­ ating Allee effects, each involving a major evolu- process characterized by (1) a change in popula- tionary force: inbreeding, drift, or migration. tion genetic structure due to a decrease in pop- ulation size and (2) a consequent decrease in Inbreeding depression individual fitness. This decrease in individual fit- As population size declines, inbreeding becomes ness may subsequently lead to a further decrease more frequent (Fig. 2; Malécot 1969). An inbred in population size. These two steps act sequen- individual results from a cross between two genet- tially to generate a genetically driven component ically related individuals and is characterized by a Allee effect. The first step of the genetic Allee high inbreeding coefficient. Inbred individuals effect occurs when population size affects at least have fewer heterozygous loci than outbred indi- one of the following aspects of genetic structure: viduals, resulting in a decrease in heterozygosity heterozygosity, frequency of beneficial or detri- in declining populations (Fran­kham 1996, 1998). A mental alleles, or allelic richness (Fig. 1). During pervasive consequence of low heterozygosity is the second step, any of these changes in popula- inbreeding depression, defined as the lower fitness tion genetic structure may decrease a component of inbred than of outbred individuals. Hence, of individual fitness through inbreeding depres- inbreeding followed by inbreeding depression ful- sion, drift load, or migration load. If, and only fills the two conditions defining the genetic Allee if, both steps occur, a genetic Allee effect occurs. effect: (1) a decrease in population size causing a The genetic Allee effect therefore contrasts with change in population genetic structure (a decrease what could be referred to as an ecological Allee in heterozygosity) and (2) a decrease in one or

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Table 1. Published evidence for genetic Allee effects in natural and experimental populations. Genetic Allee effects in natural populations are classified according to their underlying mechanism.

Evidence Evidence Parameter of genetic Evidence for Allee Taxon for Step 1 structure for Step 2 Fitness component effect Reference (A) Inbreeding depression Plant Cochealaria Yes Number of polymorphic Untested Fruit set Yes Fischer et al. bavarica loci and observed He (2003) for 8 allozymes Plant Ranunculus Yes Mean kinship Yes Clonal performance;‡ No Willi et al. reptans coefficient† seed production (2005) Insect Melitaea Yes Observed He at 7 Yes Larval survival; adult Untested Saccheri et al. cinxia enzymes and 1 longevity; egg (1998) microsatellite hatching rate (B) Drift load Plant Ranunculus Yes Allelic diversity at 7 Yes Seed production No Willi et al. reptans allozymes (2005) Plant Hypericum Yes Effective population size Untested Cumulative fitness§ Yes Oakley and cumulicola estimated from 10 Winn (2012) microsatellites Mollusk Physa Yes Gene diversity at 10 Untested Reproductive life span Yes Escobar et al. acuta microsatellites (2008) Insect Melitaea Yes Observed and expected Untested Mating rate; egg clutch Yes Mattila et al. cinxia He and allelic richness size; hatching rate; (2012) at 9 microsatellites larval survival; larval weight; larval group size at diapause; lifetime larval production Amphibian Rana Yes Difference Fst-­Qst for Yes Body size; larval survival Untested Johansson temporaria larval body size; allelic et al. (2007) richness at 7 microsatellites Plant Cochealaria Yes Number of alleles per Untested Compatibility of crosses Yes Fischer et al. bavarica locus, number of (2003) polymorphic loci and observed He for isoenzymes Plant Ranunculus Yes Allelic diversity at 7 Yes Compatibility of crosses No Willi et al. reptans allozymes (2005) Plant Brassica Yes Number and frequencies Untested Proportion of flowers Yes Glémin et al. insularis of self-­incompatibility pollinated with (2008) alleles compatible pollen; fruit set Plant Rutidosis Yes Number and frequencies Untested Seed set Yes Young and leptorrhyn- of self-­incompatibility Pickup choides alleles (2010) Plant Primula Yes Morph frequencies Untested Number of fruits per Yes Brys et al. vulgaris flower (2007) (C) Migration load Plant Eucalyptus Yes Hybridization rate Yes Germination rate; No Field et al. aggregata survivorship (2008) (D) Experimental populations (genetic structure manipulated independently of population size) Plant Clarkia – Number of founding – Germination rate; survival Yes Newman and pulchella families rate from flower to fruit Pilson (1997) Plant Raphanus – Relatedness of founders – Fruit set; number of seeds Yes Elam et al. sativus per fruit (2007) Plant Lolium – Number and relatedness – Seed set; proportion of Yes Firestone and multiflorum of founders florets producing seeds Jasieniuk (2013) Insect Bemisia – Relatedness of founders – Number of offspring Yes Hufbauer et al. tabaci (2013) Insect Tribolium – Relatedness of founders – Number of offspring Yes Szücs et al. castaneum (2014)

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Notes: Evidence for Step 1 indicates whether a relationship between population size and genetic structure was tested and found in the expected direction. Evidence for Step 2 indicates whether a relationship between genetic structure and a compo- nent of fitness was tested and found in the expected direction. Strong evidence for a genetic Allee effect implies evidence for both Steps 1 and 2. Evidence for Allee effect indicates whether a positive relationship between population size and a fitness component was observed; this corroborates but does not prove that a genetic Allee effect is occurring. Experimental popula- tions are populations in which genetic structure was manipulated independently of population size. For the four examples concerning experimental populations, the mechanism causing the genetic Allee effect was not identified. He: heterozygosity. † Smaller populations have a lower allelic diversity at allozyme loci, and populations with lower allelic diversity have a higher kinship coefficient, but the relationship between population size and kinship coefficient was not tested. ‡ Proportion of ovules producing seedlings × number of rooted rosettes. § Proportion fruit set × seed number per fruit × proportion germinating × proportion surviving and reproducing × fecundity. several components of fitness caused by this number and frequencies of alleles result princi- change (Fig. 2; Frankham 1998, Reed and Frankham pally from drift rather than selection (Kimura 2003, Spielman et al. 2004). The mechanisms caus- 1983, Whitlock 2000). ing inbreeding depression (increased expression of The change in the selection/drift balance at deleterious recessive alleles, overdominance, and modifies the frequency of epistasis; Li et al. 2008, Charlesworth and Willis beneficial alleles, allelic richness, and the hetero- 2009) underlie the second step of a genetic Allee zygosity of populations, driving the first step of effect. For instance, the buttercup Ranunculus rep- the genetic Allee effect (Fig. 2). The exact nature tans suffers from a genetic Allee effect due to of the change in genetic structure depends on the inbreeding depression (Table 1A; Willi et al. 2005): type of selection at work. When drift overwhelms small populations have a higher mean inbreeding negative selection, mildly deleterious alleles coefficient (Step 1), and populations with higher increase in frequency (Lanfear et al. 2014). Mildly inbreeding coefficients have lower levels of seed deleterious alleles sometimes become fixed and production (Step 2). constitute the drift load (Whitlock 2000, Glémin 2003). The corollary is that some beneficial alleles, Drift load despite being under positive selection, decrease Here, we define drift as a change in allele fre- in frequency or even disappear (Lanfear et al. quencies due to the random sampling of alleles 2014). The value of fitness components decreases from one generation to the next (Wright 1969) if these components are influenced by loci that fix and drift load as the decrease in the mean fitness detrimental alleles and lose beneficial ones (Step of a population due to drift (Charlesworth et al. 2). Variations in larval body size in the European 1993, Whitlock 2000). is a conse- common frog Rana temporaria provide an inter- quence of finite population size, and, like other esting example, with drift stronger than selection random processes, such as demographic stochas- in small populations and weaker than selection in ticity, the manifestations of genetic drift are more large populations (Step 1). Consequently, small evident in small populations (Fig. 2; Gabriel et al. populations have a higher drift load on larval 1991, Gabriel and Bürger 1994, Lynch et al. 1995a, body size and display lower values for this fit- Oostermeijer et al. 2003, Frankham 2005, Grueber ness component (Table 1B; Johansson et al. 2007). et al. 2013). The balance between drift and selec- Balancing selection also results in drift load. tion determines allelic and genotypic frequen- Balancing selection maintains several alleles at a cies. Selection is a deterministic process whereby locus under selection. Balancing selection can be the frequency of an allele (or a genotype) changes due to overdominance and negative frequency-­ across generations according to its effect on fit- dependent selection. In small populations, in ness: Beneficial alleles increase in frequency, which drift overwhelms balancing selection, rare whereas deleterious alleles decrease in fre- alleles can be lost (Zayed and Packer 2005, Levin quency. Unlike drift, the intensity of which et al. 2009, Eimes et al. 2011) and allele frequen- increases with decreasing population size, selec- cies move away from the optimum value (Step 1), tion does not vary in intensity as a function of decreasing the values of the fitness components population size (Fig. 2), that is, we do not con- they influence (Step 2). For instance, plant self-­ sider density-­dependent selection here. Hence, incompatibility loci undergo balancing selec- in small populations, drift intensity often over- tion, triggering a genetic Allee effect. This has whelms selection, so that any changes in the been shown in the rare plant Brassica insularis,

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Fig. 2. Scenarios underlying a genetic Allee effect. During Step 1, a decrease in population size causes an increase in inbreeding, a change in the drift/selection balance in favor of drift, and/or a higher proportion of immigrants in the population (assuming that both selection and migration are density independent). Various population genetic structure variables are affected: heterozygosity, allelic richness, and the frequencies of detrimental and beneficial alleles. During Step 2, these changes in genetic variation cause a decrease in the value of fitness components through inbreeding depression, drift load, or migration load. in which smaller populations have fewer alleles decreasing population size, and germination at the self-­incompatibility locus and, thus, lower rates and seedling survival are lower in popula- rates of fruit set (Glémin et al. 2008). tions with a higher proportion of hybrids (Field et al. 2008). Migration load Migration load is defined as the decrease in the Combined mechanisms mean fitness of a population due to the immigra- As already reported for ecological component tion of maladapted alleles and outbreeding Allee effects (Berec et al. 2007), several genetic depression (e.g. Bolnick and Nosil 2007). With Allee effects may occur simultaneously in the effective dispersal, immigrants from a source same population. A good example is provided population can bring new alleles into a sink pop- by the concomitant influences inbreeding depres- ulation. Assuming a constant number of dispers- sion, drift load, and loss of incompatibility self-­ ers, the proportion of new alleles in the gene pool alleles on small populations of the buttercup is higher in small sink populations than in large Ranunculus reptans (Willi et al. 2005). Genetic ones (Fig. 2), so the change in genetic structure Allee effects can also act in conjunction with eco- depends on population size, fulfilling the condi- logical Allee effects, as shown in experimental tions for the first step of the genetic Allee effect populations of the self-incompatible­ plants (Fig. 1). A migration load can occur as a result of Raphanus sativus and Lolium multiflorum (Elam local maladaptation and/or outbreeding depres- et al. 2007, Firestone and Jasieniuk 2013). sion (Ronce and Kirkpatrick 2001, Lenormand 2002) due to underdominance or deleterious epi- How Can a Genetic Allee Effect be static interactions (Edmands 2002). The overrep- Detected? resentation of new alleles in small populations results in a higher migration load in small popu- The detection of a genetic Allee effect requires lations, satisfying the conditions for the second investigations of each of the two successive steps: step of the genetic Allee effect (Fig. 2). We were (1) a decrease in population size causing a change able to identify a single published example of a in the within-­population genetic structure and genetic Allee effect due to migration load (2) a decrease in a fitness component caused by (Table 1C). Populations of Eucalyptus aggregata this change. For demonstration of the causal rela- can hybridize with closely related species of tionship underlying Step 2, two confounding eucalypts; the hybridization rate increases with effects must be avoided: environmental effects

v www.esajournals.org 6 July 2016 v Volume 7(7) v Article e01413 Synthesis & Integration Luque et al. and ecological Allee effects. It is possible to con- for a quantitative fitness component, then drift is trol for environmental effects using experimental probably stronger than selection for this compo- designs involving constant environments (e.g., nent. A positive relationship between the value Charlesworth 2006, Oakley and Winn 2012) or of this fitness component and the difference extracting fitness responses to environmental between Qst and Fst may indicate a relationship variability before analyzing the effect of popula- between genetic variation and fitness (Oakley tion genetic structure (e.g., Saccheri et al. 1998, and Winn 2012). In the particular case of drift Hanski and Saccheri 2006). However, controlling load involving plant self-incompatibility­ and bal- for environmental variability may nevertheless ancing selection, the role of self-incompatibility­ fail to separate genetic and ecological Allee in the relationship between genetic structure and effects, and some previously described ecological fitness can be investigated by determining the Allee effects may actually turn out to be genetic proportion of incompatible crosses for which Allee effects. For instance, mating failures in plants received pollen but produced no seeds small populations may result from a shortage of (Fischer et al. 2003, Willi et al. 2005, Glémin et al. genetically compatible mates rather than a 2008). Finally, the demonstration that immigrants decrease in the frequency of encounters with and/or hybrids have lower fitness components conspecifics (Amos et al. 2001, Moller and than residents is indicative of the presence of a Legendre 2001, Kokko and Rankin 2006). Only migration load. by experimental manipulations of population size and genetic variation with factorial designs At the Core of the Extinction Vortex can the genetic and ecological underpinnings of Allee effects be correctly disentangled. For exam- A central concept in the biology of small popula- ple, genetic variation can be manipulated by tions is the extinction vortex, defined as a positive modifying the number of founding families, feedback between environmental, demographic, while keeping census size constant (e.g., Elam and genetic factors, reinforcing one another in a et al. 2007, Hufbauer et al. 2013, Szücs et al. 2014). downward spiral until the last individual has dis- Three main mechanisms underlie the second appeared (the F-vortex;­ Gilpin and Soulé 1986). step of genetic Allee effects: inbreeding depres- Meta-analyses­ of small populations suggest that sion, drift load, and migration load. Inbreeding extinction vortices do occur in declining popula- depression occurs when individuals with higher tions (Fagan and Holmes 2006), and a body of inbreeding coefficients have lower fitness. It can models and data support the significant roles of be assessed by studying individuals from pop- genetic factors (Frankham and Ralls 1998, Tanaka ulations with known inbreeding coefficients or 2000, Spielman et al. 2004, Frankham 2005). offspring from controlled inbred and outbred Nonetheless, despite its importance for the man- crosses (e.g., Elam et al. 2007, Hufbauer et al. agement of threatened species, the extinction vor- 2013). Drift load is detected when between-­ tex suffers from the rarity of clear demonstrations. population crosses result in heterosis and if Formalizing the causal relations between this effect is stronger in populations with lower population size, genetic structure, and fitness, heterozygosity or allelic richness (Escobar et al. via the genetic Allee effect, should strengthen 2008, Oakley and Winn 2012). The respective the approach of extinction vortices (Fig. 3). The strengths of drift and selection can be estimated rationale is that thinking in terms of Allee effects by comparing Fst and Qst between pairs of popu- makes it possible to capitalize on the known dual- lations, under certain conditions: (1) comparison ity of component and demographic Allee effects, of several groups of populations, with similar thereby bridging the gap between individual fit- population sizes within groups and different ness and (Fauvergue 2013). population sizes between groups (Fst and Qst Here, we have defined the genetic Allee effect are calculated between all pairs of populations as a component Allee effect, that is an effect of within groups); (2) the component of fitness population size on fitness, triggered by genetic measured is a quantitative trait, with a continu- factors. Like any other component Allee effect, ous distribution, influenced by multiple loci with the genetic Allee effect can lower mean individ- small effects. If estimates ofF st and Qst are similar ual fitness in small populations, thereby causing

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Fig. 3. Extinction vortices driven by Allee effects. In ecological Allee effects, a decrease in population size directly causes a decrease in a component of individual fitness, which may in turn yield a decrease in population growth rate. A genetic Allee effect is a two-step­ process. A decrease in population size induces a change in the genetic variation of the population via inbreeding, drift/selection balance or migration (Step 1). This change yields inbreeding depression, drift load, or migration load, causing a decrease in the value of fitness components (Step 2). Both ecological and genetic component Allee effects can produce a demographic Allee effect, which, if strong, can generate an extinction vortex. a decrease in the population growth rate, that is Using an experimental approach, Newman and a demographic Allee effect (Lennartsson 2002; Pilson (1997) showed that populations founded Fig. 3; Angulo et al. 2007). In the case of strong by genetically related seedlings were subject demographic Allee effect with negative growth to inbreeding depression and/or drift load and rate, or if combined with detrimental environ- therefore had a lower growth rate than popula- mental factors, the genetic Allee effect can drive tions founded by unrelated seedlings. In several small populations to extinction and is thus at the other species, genetically eroded populations core of an extinction vortex. have been shown to have a lower growth rate A canonical example is provided by research (Fauvergue and Hopper 2009, Markert et al. on the Glanville fritillary butterfly,Melitaea cinxia. 2010, Wennersten et al. 2012, Turcotte et al. 2013, In this species, small subpopulations are less het- Vercken et al. 2013). Fitness components were erozygous than large subpopulations, and less not measured in these studies, but the dynamics heterozygous females produce larvae with lower observed may reflect genetic Allee effects. survival rates (Saccheri et al. 1998). The Glanville fritillary is therefore subject to a genetic Allee Genetic versus Ecological Allee Effects effect. Controlled crosses in the laboratory and in the field have confirmed the existence of inbreed- Temporal issues ing depression in this species (Nieminen et al. Genetic and ecological Allee effects are both 2001). The combination of inbreeding depres- component Allee effects capable of generating sion with poor availability causes the demographic Allee effects, but they differ in sev- extinction of small subpopulations of M. cinxia, eral ways, including the time scale. Genetic Allee as shown by the higher probability of extinction effects are characterized by a time lag between the for smaller and less heterozygous populations change in population size and its consequences for living in less favorable environmental conditions mean individual fitness, whereas an ecological (Saccheri et al. 1998). A genetic Allee effect also Allee effect may occur as soon as population size impacts demography in the plant Clarkia pulchella. decreases (e.g., mating success decreases together

v www.esajournals.org 8 July 2016 v Volume 7(7) v Article e01413 Synthesis & Integration Luque et al. with population density). The two steps of a the evolution of adaptations mitigating ­sensitivity genetic Allee effect may not occur over similar to population size (Courchamp et al. 2008). For time scales: a decrease in population size may instance, long-range­ volatile sex pheromones modify the genetic structure of the population may prevent mating failures (Fauvergue et al. over tens or thousands of generations, but fitness 2007). The same reasoning applies to genetic consequences may appear in the generation fol- Allee effects too. Inbreeding depression may lowing the change in genetic structure (Amos and have shaped the evolution of dispersal, inbreed- Balmford 2001, but see Hufbauer et al. 2013). ing avoidance and self-incompatibility­ systems Conversely, if population size increases, ecological (Penn and Potts 1999, Perrin and Mazalov 2000). Allee effects should die down almost immediately, whereas genetic Allee effects will not. For instance, Conclusion: Why is all this Important? after several generations of genetic drift, a popula- tion cannot recover its initial level of genetic varia- The focus on genetic Allee effects does not sim- tion unless new alleles arise by or ply add a new semantic layer to processes that migration. This implies that a population can be have been thoroughly discussed in the last few rescued from a demographic threat, but, if the decades. On the contrary, it is essential, for sev- underlying genetic variation is not also restored, it eral reasons. may still suffer from a genetic Allee effect and be First, although a genetic Allee effect has been prone to extinction (what has been referred to as mentioned in a few articles (starting with Fischer an ; Vercken et al. 2013). et al. 2000), no formal definition has ever been provided. We show here that a genetic Allee Two steps for the genetic Allee effect effect is not merely an Allee effect underpinned The two steps of genetic Allee effects are idio- by genetic mechanisms. The formal definition syncratic: each step can occur independently of we provide here includes two successive steps: the other, but the occurrence of the two steps in a decrease in population size modifying the succession is necessary to create (and demon- within-­population genetic structure, in turn strate) a genetic Allee effect. The first step, a causing a decrease in the mean value of a com- change in genetic structure caused by a decrease ponent of individual fitness. The requirement of in population size, can occur with no decrease in these two steps differentiates genetic Allee effects mean fitness (Step 1, but not Step 2). For instance, from ecological Allee effects. Genetic Allee effects inbred individuals do not necessarily suffer from are unique in terms of their potentially long inbreeding depression. Indeed, although coun- time scale (particularly for the change in genetic terintuitive at first glance, inbreeding can even structure in response to a decrease in population result in the purging of deleterious alleles, lead- size) and their entropy (by contrast to ecolog- ing to an increase in mean fitness (Glémin 2003, ical Allee effects, a population cannot recover Facon et al. 2011). Similarly, drift can randomly instantly from a genetic Allee effect). According eliminate detrimental alleles and fix beneficial to the formal definition proposed here, some ones, and immigration in small populations can reported findings refer to a genetic Allee effect lower the negative impact of drift and inbreeding (including from our own research; Fauvergue by bringing new adapted alleles and increasing and Hopper 2009, Vercken et al. 2013), but with- heterozygosity. The second step, in which a out providing explicit evidence for such an effect. change in the genetic structure of a population Alternatively, some specific types of Allee effect, triggers a decrease in a component of fitness, is such as the so-­called S-Allee­ effect (Wagenius not necessarily induced by the first step, because et al. 2007, Hoebee et al. 2012, Busch et al. 2014), genetic structure can change independently of may be seen as genetic Allee effects. The pro- population size, under the influences of muta- vision of a clear definition of the genetic Allee tion, migration, or the mating system. effect should prompt a better examination of the genetic mechanisms affecting fitness and demog- Evolutionary consequences raphy in small populations. We identified only 15 The effects on individual fitness of ecological demonstrations of this particular type of compo- Allee effects could act as a selective force, driving nent Allee effect in the literature, but we predict

v www.esajournals.org 9 July 2016 v Volume 7(7) v Article e01413 Synthesis & Integration Luque et al. that widespread evidence of its existence will be Literature Cited obtained if the methods we propose are used to identify genetic Allee effects and to distinguish Amos, W., and A. Balmford. 2001. When does conser- them from ecological Allee effects occurring in vation genetics matter? Heredity 87:257–265. the same populations. Amos, W., J. W. Wilmer, and H. Kokko. 2001. Do female Second, a definition of the genetic Allee effect grey seals select genetically diverse mates? Animal should promote a more comprehensive approach Behaviour 62:157–164. to the biology of small populations. The integra- Angulo, E., G. W. Roemer, L. Berec, J. Gascoigne, tion of demography and genetics has long been and F. Courchamp. 2007. Double allee effects and extinction in the island . Conservation Biology recognized as an important endeavor, but tangi- 21:1082–1091. ble progress is still required, particularly for the Bell, G., and A. Gonzalez. 2009. Evolutionary rescue management of declining and/or bottlenecked can prevent extinction following environmental populations (e.g., Robert et al. 2007, Fauvergue change. Ecology Letters 12:942–948. et al. 2012). Indeed, early developments in popu- Berec, L., E. Angulo, and F. Courchamp. 2007. Multiple lation viability analyses clearly assumed a feed- Allee effects and population management. Trends back between demographic and genetic processes in Ecology and Evolution 22:185–191. at the core of extinction vortices (Gilpin and Bolnick, D. I., and P. Nosil. 2007. Natural selection in Soulé 1986, Caughley 1994), and, more recently, populations subject to a migration load. Evolution the concept of evolutionary rescue has emerged 61:2229–2243. as a race between demographic and evolutionary Bonsall, M. B., C. A. Dooley, A. Kasparson, T. Brereton, D. B. Roy, and J. A. Thomas. 2014. Allee effects and processes (Bell and Gonzalez 2009, Gonzalez et al. the spatial dynamics of a locally endangered but- 2013). However, these concepts have generally terfly, the high brown fritillary (Argynnis adippe). been restricted to the analysis of demographic Ecological Applications 24:108–120. and environmental stochasticity, resulting in the Brys, R., H. Jacquemyn, L. De Bruyn, and M. Hermy. neglect of the Allee effect as an important mecha- 2007. Pollination success and reproductive out- nism for small populations. Conversely, the Allee put in experimental populations of the self-­ effect is attracting the attention of an increasing incompatible Primula vulgaris. International Jour- number of scientists with a general interest in the nal of Plant Sciences 168:571–578. biology of small populations and extinction vor- Busch, J. W., T. Witthuhn, and M. Joseph. 2014. Fewer tices. However, despite widespread evidence for S-­alleles are maintained in plant populations with the significant role of genetic processes, it is only sporophytic as opposed to gametophytic self-­ incompatibility. Plant Species Biology 29:34–46. very recently that theoretical works have started Caughley, G. 1994. Directions in conservation biology. to combine Allee effects with genetic processes Journal of Animal Ecology 63:215–244. (Kanarek and Webb 2010, Roques et al. 2012, Charlesworth, D. 2006. Balancing selection and its Shaw and Kokko 2014, Wittmann et al. 2014a, b, effects on sequences in nearby genome regions. Kanarek et al. 2015). The genetic Allee effect, as Plos Genetics 2:379–384. defined here, is at the very intersection of demog- Charlesworth, D., and J. H. Willis. 2009. The genetics raphy and genetics and should serve as a unify- of inbreeding depression. Nature Reviews Genet- ing paradigm. In the long term, the genetic Allee ics 10:783–796. effect should contribute to improving the dialog Charlesworth, D., M. T. Morgan, and B. Charlesworth. between genetics and demography. 1993. Mutation accumulation in finite outbreeding and inbreeding populations. Genetical Research Acknowledgments 61:39–56. Courchamp, F., T. Clutton-Brock, and B. ­Grenfell. This work was supported by the Agence Nationale de 1999. Inverse and the ­Allee la Recherche (Sextinction project ANR-2010-­ ­BLAN-­1717 ­effect. Trends in Ecology and Evolution 14:405–410. and RARE project ANR-­2009-­PEXT-01001)­ and the Courchamp, F., L. Berec, and J. Gascoigne. 2008. Allee Fondation de Recherche sur la Biodiversité (VORTEX proj- effects in ecology and conservation. Oxford Uni- ect APP-­IN-2009-­ ­052). We thank four anonymous versity Press, Oxford, UK. reviewers for valuable insights on previous versions of Davis, H. G., C. M. Taylor, J. G. Lambrinos, and D. this manuscript and Nathan Fauvergue for fresh R. Strong. 2004. Pollen limitation causes an Allee thoughts. effect in a wind-­pollinated invasive grass (Spartina

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