Despite a decades‐old empirical literature, little theoretical work has explored when natural selection may favor bequeathal. We present a simple mathematical model of the evolution of bequeathal in a stable environment, under both global and local dispersal. We find that natural selection favors bequeathal when adults are competitively advantaged over juveniles, baseline mortality is high, the environment is unsaturated, and when juveniles experience high dispersal mortality. However, frequently bequeathal may not evolve, because the fitness cost for the adult is too large relative to inclusive fitness benefits. Additionally, there are many situations for which bequeathal is an ESS, yet cannot invade the population. As bequeathal in real populations appears to be facultative, yet‐to‐be‐modeled factors like timing of birth in the breeding season may strongly influence the patterns seen in natural populations.Adults sometimes disperse, while philopatric offspring inherit the natal site, a pattern known as  Bequeathal is a type of breeding dispersal, which occurs when a parent disperses to a new site, leaving a philopatric offspring to inherit the natal site and its resources. We know bequeathal occurs in nature from field studies of four mammal species: Columbian ground squirrels, Urocitellus columbianus  juvenile offspring each breeding season. The life cycle proceeds in the following sequence: (a) birth of offspring, (b) dispersal of either the offspring or parent, (c) competition for site occupancy, and (d) probability of survival to the next breeding season.Imagine a population of organisms with overlapping generations, living at sA be the probability a resident adult (A) survives to the next breeding season. Let sJ be the corresponding juvenile survival probability. When sA = sJ = 1, all sites will remain occupied. The environment will be saturated. When either survival probability is less than one, some open sites may exist. Thus, these models allow us to examine the effects of saturation and open environments, as emergent properties of vital parameters, rather than exogenous assumptions.Juveniles reproductively mature in one breeding season. At the end of each breeding season, adults and juveniles may die, prior to reproduction in the next season. Let 2.2Bequeath (B) and Stay (S). Both strategies are expressed in adults. A bequeathing adult always disperses after reproduction, arriving at an “away” site. This leaves its offspring behind to compete to retain the natal “home” site. A staying adult always evicts its offspring, forcing it to compete for an “away” site, while the adult remains behind to compete to retain the “home” site.Assume reproduction is sexual and haploid. Also, assume two pure heritable strategies, Bequeath and pure Stay, using a heritable probability of bequeathing. The continuous strategy space produces the same results, in this case, owing to a lack of geometric mean fitness effects (bet hedging), stable internal equilibria, and evolutionary branching. Therefore, we stick to the discrete strategy case in this paper, for ease of understanding. The individual‐based simulation code we include in the Supplemental can be toggled to continuous strategy space for comparison.We have also analyzed an infinite alleles model that allows continuously varying strategies between pure 2.3We have analyzed two extreme dispersal models, a global model and a local model. In the global model, all sites are equidistant; consequently, dispersal from any site has an equal probability of arriving at any other site. In the local dispersal model, sites are arranged in a ring, and individuals can disperse only to one of two neighboring sites, at random. Real dispersal patterns are probably intermediate between these two extremes.dA be the probability that an adult survives dispersal and arrives at a new site. Let dJ be the probability that a juvenile survives dispersal. Typically, dA > dJ, and so we focus on that condition, considering whether it is necessary or not for bequeathal to be an ESS.We assume that dispersal is costly, carrying a chance of dispersal‐related mortality. These costs may be due to increased predation risk during dispersal, energetic costs, or limited knowledge of resource availability in new sites. Let 2.4CA > 1. The probability that an adult retains or occupies a site with nA other adult competitors and nJ juvenile competitors is as follows:Individuals must compete to retain or colonize sites. All individuals who disperse into or remain in a site compete for it. We assume a lottery‐type competitive model, in which all individuals arriving or residing at a site simultaneously compete for it. Adults have an advantage over juveniles in competition, and we express this advantage as a relative advantage After competition, a single individual survives to occupy each site.2.5 Bequeath, p, while the local model cannot. However, both models can be analyzed for the ESS conditions of both B and S.Using the assumptions above, we can write expected inclusive fitness expressions for B and S. We fully develop the global dispersal model first, before specifying how the local model differs. The global model can be derived for any population frequency of2.5.1p be the proportion of the population with strategy B. Let R be the proportion of sites with a resident adult, at the start of each breeding season. The goal is to compute the probability nA adults and nJ juveniles immigrate to a particular site. Under the assumption that dispersal events are independent of one another, the probability that nA adults and nJ juveniles arrive at a particular site will be multinomial with three categories  and N − 1 trials. As the number of sites N grows large, the distribution approaches a bivariate Poisson, just like a binomial distribution with low probability approaches univariate Poisson as the number of trials becomes large. Therefore, in the limit N → ∞:λ=RpdA+(1−p)dJ> is the average number of immigrants (either adult or juvenile) entering the site, n = nA + nJ, andnA, nJ) is just a special case of a multivariate Poisson process, with uncorrelated dimensions. But it can be motivated more easily by considering that dispersal events are independent Poisson samples that are equally likely to arrive at the focal site. Whether a disperser is adult or juvenile can then be viewed as a binomial process, independent of arrival. Note that were adults and juveniles to use different dispersal strategies, varying in distance or some other aspect, then some other function would be required.Let R is dynamic, but quickly reaches a steady‐state expectation. The steady state of R is defined implicitly by the recurrence:Rt is the proportion of sites that are occupied at time t, and Pr (A|O) is the probability an adult (A) wins a site that is occupied (O). Similarly, Pr (A|V) is the probability an adult wins a vacant (V) site. Pr (J|V) is the probability a juvenile (J) wins a vacant site. This recurrence cannot in general be solved explicitly for the steady‐state value of R, the value that makes Rt+1 = Rt. But it can be solved numerically. A Mathematica notebook  and Stay (S) alleles. There are two components to this fitness measure. The first is the probability of retaining the home  site. For a Bequeath individual, this is as follows:Using the above definitions, we can write the expected fitness of the nA adult immigrants and nJ juvenile immigrants. The juvenile survives the season with probability sJ.The juvenile stays at the site, competing with The other component of fitness is the probability of acquiring the away site to which the adult disperses. This is as follows:R of the time, in addition to another nA adult immigrants and nJ juvenile immigrants. Since the number of sites is very large, the distribution of immigrants here is the same as before, not conditional on the focal immigrant, because dispersal events are independent in the Poisson process. If the number of sites were small, or dispersal were local, this would not be true, as we explain later.If the bequeathing adult survives dispersal, it competes with a resident ρ is the coefficient of relatedness between the adult and juvenile. For a typical example, this would be ρ = 0.5. But for a maternally inherited trait, it might be ρ = 1.Finally, we devalue fitness from the offspring, due to imperfect inheritance. This gives us inclusive fitness:Stay strategy is constructed similarly:The fitness expression for the W(B) and W(S) are presented as inclusive fitness expressions, they are just expected growth rates. No weak selection approximation or other assumptions typical of other inclusive fitness models have been made.Note that, while the expressions 2.5.2nA, nJ) under local dispersal cannot be approximated by a Poisson distribution, even at N → ∞, because at most two sites (neighbors) contribute dispersers to any focal site. Additionally, the disperser pool is no longer independent of a focal disperser arriving at an away site. Furthermore, it is not easy to specify the distribution of immigrants for any population frequency of Bequeath, p, because local dispersal generates spatial correlations in genotypes—the population residency rate R will not tell us the relevant residency probability at every locale.The local dispersal model is analogous. However, the probability Pr , discounted by the probabilities of residency R and dispersal survival dA and dJ. In other words, each immigrant is a coin flip from a biased coin with probability of arrival of π = R(pdA + (1 − p)dJ).Constraining Whether there are one or two “coins” to flip depends upon our focus. When focusing on a home site, there are two neighbors who may contribute immigrants. But when focusing on an away site, the focal disperser counts as one of the neighbors, and so there is only one “coin” to flip. With these facts in mind, we can define inclusive fitness much as before. The expressions add little insight, and so we include them only in the 3Bequeath can be an ESS. The first is the comparative advantage that adults have in competition. This advantage favors Bequeath. The second force, opposed to the first, is the conflict of interest between parent and offspring that arises from sexual reproduction. Baseline survival, dispersal survival, and dispersal pattern  all interact with these two forces.There are two antagonistic forces that strongly influence when Even a model as simple as this one is very complex. Therefore, we explain these two antagonistic forces first, without reference to dispersal pattern or baseline and dispersal survival rates. We consider how local and global dispersal differ, through their effects on comparative advantage and conflict of interest. Then, we vary adult and juvenile survival rates to show how they interact with adult comparative advantage and parent–offspring conflict of interest.3.1sA = sJ = 1 and that dA = dJ = 1 so that there is no baseline nor dispersal mortality. As can be seen by substituting these values in Equation R = 1), a saturated environment. Figure Assume for the moment that Bequeath's stability (a) and invasion (b) under the global dispersal model. When B is common (top), a lone S adult (A) remains at its home site, while evicting a juvenile (J) to disperse to an away site. The home site receives dispersers from other sites, all of which are occupied by B, and so all of the immigrants to the home site are adults (A). At the away site, the juvenile S individual is joined by adults dispersing from other sites to compete with a resident juvenile B individual. The distributions of immigrants at both the home and away sites are the same Poisson distribution, with a mean of 1, because of the global dispersal pattern.Consider only the top two diagrams for now, (a) and (b). These diagrams represent CA > 1). So, Stay sends its juvenile to an away site at which it must compete against, on average, one additional juvenile. Also, any competitive advantage of adults hurts Stay, because as CA increases, the chance of acquiring the away site decreases. For very large CA, the only way for a S juvenile to acquire an away site is for no adults to immigrate.Now consider the amount of competition at home and away. To retain the home site, the adult S individual competes with, on average, one other adult. Any competitive advantage of adults has no effect here, because all immigrants are adult, when B is common. In contrast, to acquire the away site, the lone juvenile disperser competes with a juvenile resident and, on average, one adult immigrant. Therefore, there is one additional competitor at the away site, and the juvenile must contend with its disadvantage against an adult  is again irrelevant for the invader retaining the home site. But at the away site, the dispersing B adult does better as CA increases, since its competitive advantage reduces the impact of any immigrant juveniles. If CA = 1, the dispersing adult acquires the away site one‐third of the time, on average. But for very large CA, it will acquire the away site one‐half of the time.The situation is nearly reversed when Bequeath can be an adaptation is that it uses the comparative advantage of adults by allocating the better warrior, the adult, to the worse battlefield, the away site. In contrast, Stay allocates the worse warrior, the juvenile, to the worse battlefield. In the mathematical CA > 1 and ρ = 1), Bequeath is always an ESS and Stay is never an ESS.Considering Figure ρ = 1. B is still favored by comparative advantage and uniquely an ESS. So, we postpone discussion of local dispersal until the next section.The same principle applies to the local dispersal model, illustrated by Figure 3.2ρ = 1, there is no conflict of interest, and selection favors allocating the adult to the more dangerous away site. The adult and juvenile always agree. But for ρ < 1, there is a conflict of interest, with bequeathal representing a costly action by the adult. As ρ gets smaller, selection favors adults choosing the easier battle, which is always the home site. However, large CA can compensate, allowing B to continue to be stable, even when ρ is so small that B can no longer invade the population.The principle of comparative advantage will not uniquely determine the evolutionary result, unless the juvenile and adult have no conflict of interest. When ρ and CA. Focus for now on only the upper left, panel (a), the enlarged plot with labeled regions. The horizontal axis is the magnitude of CA, expressed as the base‐2 logarithm, a “fold” value. If you folded a piece of paper in half 10 times, then its thickness would be 210 layers, a 10‐fold increase in thickness. Likewise, you can read the value log 2CA = 10 as a 10‐fold increase in adult competitive ability, relative to a juvenile. The vertical axis is ρ, from complete conflict at the bottom to complete agreement at the top. The colored regions represent different combinations of ρ and CA for which B and S are not evolutionarily stable. In the orange regions, S is not an ESS. In the blue regions, B is not an ESS. In the white region, both B and S are evolutionarily stable. The red and blue curves show the boundaries for the different dispersal models, with global dispersal represented by the solid curves and local by the dashed.To appreciate how conflict of interest and comparative advantage interact, in Figure Bequeath an ESS (and Stay not an ESS) for all CA > 1 (log 2CA > 0). But as ρ decreases, the orange regions become increasingly restricted to large CA values. By the time ρ reaches 0.5, corresponding to sexual reproduction, either only S is an ESS (blue regions) or both B and S are ESSs. At the limit ρ = 0, B is never an ESS, although if CA is large enough, even tiny amounts of relatedness are sufficient for B to be an ESS. We prove this result in the In Figure Stay to be a “selfish” strategy while Bequeath is “cooperative.” A Bequeath adult disperses at a personal cost, because there is more competition at the away site, leaving the easier home site for the juvenile to defend. When ρ = 1, the interests of the adult and juvenile are completely aligned, and so the adult favors the strategy that results in the greatest joint success (family growth). But when ρ < 1, the adult and juvenile will disagree.To understand these results, consider CA is large enough, B can remain stable. But for small CA, B may not be an ESS. The reason B can be stable even when it cannot invade is because of positive frequency dependence. When B is rare, the adult is dispersing into a site with a resident S adult, in addition to any juvenile immigrants from other sites. For an adult, competing against another adult for the away site is much harder than defending the home site from invading juveniles. But as B increases in frequency, more and more away sites are occupied by juveniles left behind by B adults. It is simultaneously true that more adults enter the dispersal pool, and so adults invade the away site. But this effect happens at both the home and away site and so does not affect the relative cost of adult dispersal. This means that Bequeath does better the more common it becomes, because the away site becomes easier to win, reducing the costliness of adult dispersal.Provided The boundaries for global and local dispersal, shown by the solid and dashed curves, sometimes differ greatly. The major effect of local dispersal is to make it harder for either strategy to invade the population. Local dispersal makes the white region larger, and so more combinations of parameters lead to both B and S being evolutionarily stable. To understand why, it is helpful to refer again to Figure Bequeath, by reducing the effective cost of adult dispersal. It is still true that average competition at the away site is greater than average competition at home. But a smaller difference under local dispersal means that B can be stable for smaller values of ρ than it can under global dispersal. Simultaneously, Stay becomes stable under local dispersal for larger values of ρ. The sword of local dispersal cuts both ways: A smaller cost for a dispersing adult is also a smaller benefit for a resident juvenile. This means that Bequeath gains less under local dispersal than it does under global, resulting in both dashed boundaries in Figure This reduced competition at the away site and increased competition at the home site help ρ and CA under different values of dispersal and baseline survival. In Figure sA, and juveniles, sJ, is reduced by 25%. This creates open habitat, effectively reducing competition at the away site. Under global dispersal, the steady‐state residency becomes R ≈ 0.56. Under local dispersal, R ≈ 0.61. Competition at the home site is also reduced, as fewer other sites have residents to produce immigrants. But this reduction in the disperser pool applies equally to home and away sites. In aggregate, lowered baseline survival benefits Bequeath, by reducing the relative intensity of competition at the away site. This results in an increased orange region, a reduction in the region in which Stay can be an ESS.The other plots in Figure dA = dJ = 0.75. Dispersal mortality has the opposite effect, to aid Stay over Bequeath. Unlike a reduction in baseline survival, a reduction in dispersal survival does not necessarily result in open habitat. Here, the environment remains saturated at R = 1. Since residents always survive, as long as any individual arrives at a site, the site will remain occupied, eventually filling the environment. Now the cost of dispersal is greatly increased. If ρ = 1, this has no effect, because the adult will still agree to disperse, since both the adult and juvenile must pay the same dispersal cost (25%). But as long as ρ < 1, the cost quickly becomes too great for the adult, favoring Stay. The region in which B can be an ESS is greatly reduced.In Figure ρ = 0.5, representing sexual reproduction, and allowing adult and juvenile survival rates to vary independently.Combining 25% baseline and dispersal mortality, in panel (d), demonstrates a strong interaction between these two forms of mortality. To further understand the effects of the mortality parameters, we proceed in the next sections by fixing 3.3CA (left and right columns). Relatedness is set to ρ = 0.5. Colors have the same meanings as before. The purple region in the lower left of Figure Stay individuals is nonviable, approaching a residency rate R = 0. The conditions for viability are sA + pJsJ > 1, for a monomorphic population of Stay, and sJ + pAsA > 1, for a monomorphic population of Bequeath. Note that Stay can be both an ESS and nonviable, as sometimes happens in models with both ecological and evolutionary dynamics. Also, note that the conditions for viability refer to expectations. Many parameter combinations will lead to extirpation with high probability, even when they strictly satisfy the conditions above. Populations near the purple region are highly endangered.Figure Bequeath does best when adult survival, sA, is low while juvenile survival, sJ, is high. When adult survival is low, the residual reproductive value of an adult is also low. This effectively reduces the cost to the adult of bequeathing the home site. Since the adult will likely die anyway, better for it to provide a benefit to the offspring. However, unless sJ is also sufficiently large, the juvenile will not live to enjoy any bequeathed benefit. As a result, the orange regions lie in the upper left corner of each plot in Figure Perhaps counterintuitively, Bequeath can be stable. But large CA can compensate, increasing both the region in which B is the only ESS (orange) and especially the region in which both B and S are ESSs (white). The effect of increasing CA on the stability of Bequeath is pronounced for the local dispersal model, as seen in Figure Adding dispersal mortality (bottom row) and increasing adult competitive advantage (right column) have the same effects as before. Dispersal mortality reduces the region in which 3.4CA (left and right columns). Again, ρ = 0.5 in all four plots. Intuitively, Bequeath does best when adult dispersal survival, dA, is large and juvenile dispersal survival, dJ, is low. Such an asymmetry further improves the adult's comparative advantage, by increasing the relative probability that the adult will reach the away site. However, as long as CA is large enough, there are many combinations dA < dJ at which Bequeath is stable, even though it cannot invade (white regions in the figure).Figure 3.5Bequeath or Stay or both are evolutionarily stable. There are no mixed, internal equilibria at which both B and S may coexist. But when adult dispersal survival is relatively high and adult baseline survival relatively low, it is possible for the orange and blue regions to overlap, for neither B nor S to be an ESS. At these parameter combinations, natural selection favors a stable mix of B and S.For the vast majority of the parameter space, either sA and dA, fixing juvenile survival to sJ = 0.8 and dJ = 0.55. The orange and blue regions have the same meaning as in previous figures: Orange indicates combinations of parameters for which Stay is not an ESS, and blue indicates combinations for which Bequeath is not an ESS. However, now there is a thin wedge where the orange and blue regions overlap. In this region of overlap, neither B nor S is evolutionarily stable. Notice that the region of overlap comprises combinations of relatively low adult baseline survival, sA, and relatively high adult dispersal survival, dA. Put plainly, when adults disperse well but survive poorly , neither B nor S may be an ESS.Figure Rt and p, at the parameter values indicated by the circle inside Figure p isocline, combinations of p and Rt at which Δp = 0. Below the orange curve, p increases. Above it, p decreases. The black curve is similarly the Rt isocline, where ΔR = Rt+1 − Rt = 0. An internal equilibrium lies at the intersection of these two isoclines, near p = 0.3, Rt = 0.28.The analytical model predicts a stable mixture of B and S under these conditions. Figure We are not sure what to predict, given the existence of these mixed equilibria. On the one hand, this dynamic may be an unlikely outcome in natural populations, as the parameter combinations that make it possible are rare. On the other hand, nature does not randomly sample from parameter spaces. Instead, dispersal costs and baseline mortality evolve. In addition, drift may be a substantial force in natural populations, and drift will interact with selection in these models, because selection alters the habitat saturation and may decrease effective population size.Regardless, the existence of these mixed equilibria sheds light on the general conditions that favor both B and S, and therefore aids in understanding dispersal strategy more generally. Specifically, we are struck by how hard we had to search to find mixed equilibria in these models. Unless dispersal and mortality are tuned in precise ways, selection will not favor a mix of B and S.4We have developed and analyzed two very simple models of bequeathal. In the first, dispersal is global and random. In the second, dispersal is local and random. In both models, a single adult breeder occupies a site and produces a single juvenile offspring. Genes in the adult determine whether it evicts the juvenile, forcing it to disperse, or rather bequeaths the site to the juvenile, dispersing itself. Both adults and juveniles must compete with nonrelated individuals to retain or acquire breeding sites, and adults are advantaged in such competition. Adults and juveniles experience mortality during dispersal and at the end of each breeding season. Depending upon survival parameters, the habitat may or may not be saturated, but it is always uniform and static, with respect to the number and productivity of breeding sites.In unsaturated habitat. An unsaturated environment, with vacant breeding sites, reduces the competition a bequeathing adult faces.When adults easily defeat juveniles in contests for breeding sites. Our models make no distinction between experience‐related and size‐related competitive advantages.When adults are superior to juveniles in dispersal survival. Our models do not address whether superior survival is due to greater knowledge of the habitat or greater experience avoiding predation or even greater body size.When adults have less residual reproductive value than their offspring. This can be true, for example, when an adult is less likely to survive to breed a second time than a juvenile is to survive to adulthood.Based on our results, bequeathal is most likely to be adaptive under the following conditions. These conditions do not seem too restrictive, and indeed, all of them have been suggested in the empirical literature as conditions that may favor bequeathal. As described in Section 3, these conditions are interactive and can sometimes counteract one another.Our analysis also finds many situations in which bequeathal does not evolve, even when these conditions are satisfied (for empirical examples that fail to detect bequeathal, see Lambin, Prediction is made more challenging once we remember that models of this sort are rarely valuable for their direct quantitative predictions. As the first formal models of bequeathal, these had to be simple to be productive. Despite their simplicity, they exhibit complex dynamics that demonstrate the basic trade‐offs inherent in bequeathal, trade‐offs that are likely to operate in more complex models as well as in real populations.4.1The strategies we have modeled so far are inflexible. Bequeathal in nature, like other modes of resource inheritance, is more likely part of a portfolio of dispersal strategies that individuals deploy facultatively, as conditions change Myles, . Models CA, is constant across individuals. If instead adults vary in competitive ability and have some knowledge of it, then dispersal strategy may be contingent. We found that bequeathal is favored and easier to maintain when CA is large, suggesting that larger and more aggressive individuals might do better pursuing bequeathal. There is also the possibility that individuals who already occupy a site have a prior residency advantage over immigrant intruders (Kokko, López‐Sepulcre, & Morrell, We have assumed that adult competitive ability, An animal using bequeathal facultatively should be more likely to bequeath in unsaturated habitat than in a saturated one (Boutin et al., Bequeathal may also be a facultative strategy at end of life (Descamps et al., Another aspect of life history that may lead to facultative bequeathal is timing of birth Price, . When feFinally, we have treated habitat saturation as a uniform factor. In reality, local saturation matters more than global saturation. Adults who know their range and are aware of open sites may do better bequeathing, even though the same individuals might do better to evict offspring, if the local environment were more saturated. Along similar lines, the models could be expanded to include a flexible search strategy during dispersal (McCarthy, 4.2Conspicuously absent strategies in our models are site sharing and floating. In the wider literature, for example, Brown and Brown , and in Stay and Bequeath sites, it is unclear exactly how this would influence bequeathal and would depend on the assumptions made about the survival and competitive abilities of floaters.Similarly, our models could be expanded to include the possibility of floating, or waiting in interstitial habitat for breeding sites to become available (Penteriani, Ferrer, & Delgado, Our models deliberately studied reproduction of a single offspring, so that we could study bequeathal in the absence of sibling rivalry and the greatly enlarged strategy space that must arise once families can be of any size. Some of the species for which bequeathal has been observed do tend to have small litters frequently with only a single offspring surviving each season (e.g., woodrats; McEachern, McElreath, Van Vuren, & Eadie, kA for adults and kJ for juveniles, where kA < kJ. We think this model could be analytically specified under global dispersal, generating a three‐dimensional dynamical system in which the frequency of bequeathal, the residency rate, and the proportion of sites with dens would all evolve together.A feature of bequeathal in many species is that a durable resource—often a den, burrow, or cache—is bequeathed together with the territory. Our models ignored the construction and persistence of such resources. Presumably, there is some cost of building a den, and if adults are better able to afford these costs, then our models may underestimate bequeathal's adaptiveness. As a first sketch of a model with dynamic site resources, suppose that each site is also characterized by the presence or absence of a den. When a site has a resident, a den can be maintained. In the absence of a resident, a den has a probability of decaying. A den can be constructed at a site at a fitness cost Our models have ignored males, treating them as ambient and causally inert. Provided that males are carriers of the bequeathal allele and that there is no shortage of males, this assumption may be harmless. However, suppose instead that males also depend upon the same sites for survival. Then, different dispersal strategies may be favored, depending upon both an individual's sex and the sex of its offspring. As observed instances of bequeathal appear to be sex‐biased toward both females (Fisher et al., Lastly, observed instances of bequeathal are heavily biased toward mammals, particularly rodents. However, there is no reason to believe that this is a uniquely mammalian phenomenon. Instances of bequeathal may be overlooked and attributed to adult mortality if the juvenile remains in the natal territory and adult movement is not tracked or detected. Bequeathal may be observed in other solitary breeding species with overlapping generations who depend on discreet resources such as dens, burrows, nests, or caches to survive—particularly if these resources are limited or costly to build. We encourage researchers studying dispersal in other taxa that fit these criteria to entertain bequeathal as an alternative dispersal hypothesis– especially in commonly known breeding dispersers like birds. This requires researchers to track the relatedness of juveniles and adults in a population, location of adults and juveniles after breeding, and availability of potential territories in space across several breeding seasons to adequately identify and test the predictions of our model.None declared.Parry M. R. Clarke contributed to the theoretical analysis and interpretation, and helped draft earlier versions of the manuscript. Mary Brooke McElreath contributed to the original design and concept of the study, analysis and interpretation of the models, and helped draft the manuscript. Brendan J Barrett contributed to the interpretation of the models, maintenance of R code and supplemental materials, and the writing and revision of the final manuscript. Karen E. Mabry contributed to the original design and concept of the study, and helped draft the manuscript. Richard McElreath contributed to the original design and concept of the study, supervised the theoretical analysis and interpretation, and helped draft the manuscript.https://github.com/bjbarrett/bequeathalA Mathematica notebook (Wolfram Research Inc.  Click here for additional data file.


Reductions in the thickness and extent of Antarctic ice shelves are triggering increased discharge of marine-terminating glaciers. While the impacts of recent changes are well documented, their role in modulating past ice-sheet dynamics remains poorly constrained. This reflects two persistent issues; first, the effective discrimination of sediments and landforms solely attributable to sub-ice-shelf deposition, and second, challenges in dating these records. Recent progress in deciphering the geological imprint of Antarctic ice shelves is summarised, including advances in dating methods and proxies to reconstruct drivers of change. Finally, we identify several challenges to overcome to fully exploit the paleo record. The recent collapses of ice shelves in Antarctica due to warming make it essential to understand past ice shelf conditions and mechanisms. Here Smith and colleagues review the latest progress in deciphering the geological imprint of Antarctic ice shelves via sediments, landforms and proxy indicators. The rapid collapse of the Larsen B Ice Shelf in 2002 not only demonstrated the sensitivity of the Antarctic cryosphere to recent warming3, but also confirmed earlier theoretical work that ice shelves act to buttress inland ice4. The near-instantaneous acceleration of outlet glaciers following collapse resulted in greater land-ice discharge and contribution to sea-level rise6. Breakup of ice shelves along the Antarctic Peninsula has been linked to atmospheric warming since the late 1800s together with specific mechanisms, e.g., hydrofracture in water-filled crevasses9. Some Peninsula ice shelves, together with those along the West Antarctic Ice Sheet (WAIS) Pacific margin 13, suggesting that this region is also susceptible to rapid and large-scale ice loss14, and together with contributions from the Antarctic Peninsula and WAIS could drive significant future sea-level rise15.The majority of grounded ice in Antarctica drains through the ice sheet’s peripheral ice shelves making them a critical component of its mass balance16 and in some cases, ice shelves might have been pre-conditioned to collapse through many thousands of years of thinning17. This has highlighted the need for detailed reconstruction of ice-shelf history at a range of time scales so that the relative roles of contemporaneous ocean–atmosphere forced-change and/or a continuing response to an earlier perturbation in driving ice shelf loss can be fully assessed. Furthermore, the geological record can serve as an important analogue for recent and future changes and particularly dynamic thinning, where the impacts of ice-shelf removal on grounded ice further upstream can be fully explored and used to constrain model simulations. Such records will not only help decipher the drivers of change but are also important for initialising models which aim to predict future change15. The more important the long-term behaviour, the more likely the model will be required to run over longer time scales18.In addition to an improved understanding of the sensitivity of Antarctic ice shelves to ocean and atmospheric forcing, there is a growing awareness that some currently observed changes were instigated in the recent past22 and the considerable theoretical and observational advances that have been made by studying recently exposed and former sub-ice-shelf environments23. We consider how this information can constrain key boundary conditions relevant for modelling studies, such as ice shelf extent, thickness and cavity geometry, and review the methods currently available to assess the rates and drivers of past retreat. Finally, key gaps in our understanding of these systems are identified as areas for future research. Past or ‘paleo’ largely refers to changes since the Last Glacial Maximum  because, unlike previous glaciations, the sediments and landforms are comparatively well-preserved and consequently easier to interpret and date accurately. The concepts and applications are also relevant to more ancient glaciations, which is particularly important as future climate conditions might differ from the LGM/Holocene.In this review, we examine sediments, landforms and available proxy indicators associated with ice-shelf presence, absence and collapse, by utilising new information obtained from direct access24 beneath Mackay Glacier Tongue, fed by an outlet glacier of the EAIS flowing into the Ross Sea . This contrasts with Arctic systems where meltwater-related processes are much more common27. Concentrations of suspended particulate matter increased near the GL, originating from either meltwater at the ice-bed interface or by re-suspension of seafloor sediments caused by increasing current velocities within a confined cavity. Up to 300 m away from the GL, a soft glacimarine drape consisting of clast-rich sandy-mud (shelfstone mud28) and diamicton with a poorly sorted texture similar to that of its basal debris source was imaged. The poor sorting indicated little subsequent sorting during rain-out from the ice shelf base. A key observation was that the drape is also locally patchy reflecting variations in rainout process and modification by ocean currents and/or by meltwater discharge.The processes operating beneath modern ice shelves Fig.  are critSea Fig. , remain 29. An exception to this are the AUV missions beneath Pine Island Glacier (PIG) ice shelf using Autosub, which not only revealed detailed information about the properties of the ocean and cavity geometry10 but also the morphology of the seafloor and ice base30. Inflowing CDW is warm and salty and contrasts with the melt-laden outflow that has been cooled and diluted by the addition of fresh water  missions have prioritised the measurement and characterisation of ocean-water properties31 and seafloor. Measurements include sediment sampling20 and analyses of the biological communities living under the ice34, in the water column35, and on and within the seabed37. Early work on sub-ice shelf environments considered these regions unlikely to support living biota due to the absence of primary producers in settings devoid of light. Photographs from beneath the Ross Ice Shelf provided the first evidence for living biota beneath an Antarctic ice shelf hundreds of kilometres landward of ocean water, but also confirmed the low productivity of this environment with a relatively depauperate benthic assemblage comprised solely of mobile scavengers38. Fossilised benthic organisms in debris bands on the surface of the McMurdo Ice Shelf were used to infer the existence of a living benthic community beneath this ice shelf40, with a relatively impoverished community more recently imaged from the seaward part of this ice shelf41. In contrast, video footage collected 100 km from the calving front of the Amery Ice Shelf revealed a more diverse epifauna assemblage, including 29 distinct benthic taxa, mostly sedentary filter feeders, within an area of only 1–2 m2 (ref. 36)  Fig. . Lower d 42 Fig. . This wo48 are not covered here (see instead ref. 49).A fundamental requirement for paleo-ice shelf studies is to reconstruct their geometry, including extent and thickness, together with temporal changes in these properties. In this section, we summarise the key sediment types, proxies and landforms used to determine ice shelf presence, absence and collapse Fig. . Epishel23. Idealised models for sedimentation beneath Antarctic ice shelves57 tend to consider a retreating GL and calving line, and typically comprise a basal diamicton , sediments in sub-ice-shelf environments are characterised by low depositional rates (relative to other glacimarine environments) and low amounts of biogenic matter. Sedimentation is controlled by proximity to the sediment sources—the GL and calving line Fig. —but is a59. Ultimately, any of the aforementioned sedimentary units may be muted, amplified or entirely absent, and the formation/preservation of a particular unit depends on the time scales over which the various depositional processes operate as well as the size of the ice shelf. Sediments associated with short-lived phases of ice shelf cover will differ from those deposited beneath a large ice shelf system that exists for many thousands of years. It is also worth noting the potential differences between glacier tongues vs. ice shelves. Although many of the processes, facies and landforms are likely to be similar, their lateral extent and overall footprint will differ, as will the biogenic signature within the sediments. For example, because ocean currents are more likely to circulate freely under a glacier tongue, sediments deposited away from the GL will be similar to outer parts of a larger ice shelf system.While subsequent work has demonstrated the general applicability of these stratigraphic models, especially as a robust framework to infer GL proximal to distal sedimentation, it has also highlighted the variable and heterogeneous nature of sub-ice-shelf sediments60. The latter reflects limited subglacial meltwater discharge (relative to Arctic ice shelves51) potentially allowing effective discrimination between polar ice-shelf and more temperate or sub-polar tidewater glacimarine regimes. However, coarse-grained facies occur directly above subglacial tills across much of the Antarctic shelf and do not necessarily reflect ice shelf cover. In this context, several authors ascribe ‘granulated facies’, consisting of muddy-gravel, rich in granules or ‘till pellets’ (pelletized-mud53)  and a lack or paucity of subaqueous outwash53) Fig. , solely 16. The presence of cross-bedded sands directly above the coarse-grained facies has been interpreted to reflect strong traction currents in a widening, but relatively narrow ocean cavity 64. On large ice shelves, where the GL and calving line can be separated by >100 km, the laminated muds grade into massive muds with progressive distance from the GL before eventually reaching a theoretical zone where sedimentation is almost zero .The transition from coarse- to fine-grained sediments typically reflects increasing distance from the GL, and on a retrograde seabed, an enlarging sub-ice cavityty Figs.  and 520,50. However, several studies have described poorly sorted debris at the surface of and within large ice shelves68 which either remains on the ice shelf surface and is later deposited as IRD at the calving line67 or is entrained into the ice shelf by inflowing glaciers69 before melting out at its base. Coarse-grained debris can also freeze to the base of an ice shelf as it grounds on pinning points during phases of advance, ice shelf thickening or locally lowering sea-level56. This debris is subsequently redistributed as the ice shelf unpins and is exposed to basal melting56 or, in some unique cases, can migrate to the surface as a result of high rates of surface ablation40. An expected corollary of this is that the sediment flux and grain size will vary over time, depending on which ice layer is being melted at the base24. However, debris incorporated into the ice shelf englacially or from freeze-on is likely to be locally sourced, making it distinguishable from calving-line diamictons, where IRD can be sourced from icebergs originating from a wide area53.The absence of IRD within the largely terrigenous laminated to massive muds has traditionally been used as an important indicator for ice shelf cover based on the assumption that larger ice-stream fed ice shelves are devoid of coarse particle sizes beyond the GL63)—productivity indicators, e.g., total organic carbon (TOC), ratios of carbon and nitrogen (C/N), absolute diatom abundances (ADA) and biogenic silica, are assumed to be low, and widely employed to differentiate between ice shelf, tidewater and open-marine depositional settings . In contrast, a tidewater calving front would allow both GL proximal and diatom sedimentation to occur contemporaneously, giving rise to higher ADA/biogenic content, if the related siliciclastic sedimentation rates are low. Consistently low TOC content and ADA throughout sediment cores recovered from the seafloor below the former Larsen B Ice Shelf were used to demonstrate its persistence during the Holocene17  values in benthic and planktic foraminifera tend to be lower in shells calcifying in sub-ice shelf waters72 relative to open-marine settings. Recent work in the Amundsen Sea suggests that a switch from a benthic foraminifera assemblage dominated by Nonionella bradii and Globocassidulina species  to one composed of various Angulogerina species, and specifically Angulogerina angulosa, reflects a change from sub-ice-shelf to open-marine deposition  is associated with an ice-shelf edge environment in the Larsen Ice Shelf area78. Sub-ice-shelf sediments in the Whales Deep Basin, eastern Ross Sea  as well as spinose and costate morphotype of T. earlandi77. The pustulose morphotype of G. biora appears to be most prominent in GL-proximal sediments and particularly those associated with GZW foresets , which the authors related to advection beneath the ice shelf and subsequent mortality before reaching the terminal life stage72. Minzoni et al.74 also propose advection to explain increases in N. pachyderma sin. in glacier proximal sediments deposited beneath an expanded Cosgrove Ice Shelf. Arenaceous benthic foraminifera are also common in ice shelf covered areas although their taxonomy and ecology is poorly known compared to other groups79, and their relative abundance in some settings might relate to preservation potential80. Nevertheless, Miliammina arenacea and Portatrochammina sp. have been documented in sub-ice-shelf sediments in Marguerite Bay59, Whales Deep Basin77 and Lallemand Fjord81, while Portatrochammina pseudotriceramata and Cyclammina pusilla have specifically been linked to grounding line-proximal sub-ice-shelf sediments59 . Landforms associated with ice shelf presence include grounding zone wedges (GZWs), various scours, corrugation ridges and moraines Figs. ; Table 185 yet are only preserved in a handful of ice free terrestrial settings. Push moraines with similar dimensions to those observed beneath Mackay Glacier (~2 m) have also been imaged on deglaciated parts of the western Ross Sea shelf . Their formation has been associated with push and squeeze in basal crevasses as well as delivery and deposition from sub- or englacial material86 although no clear association between these features and the presence of an ice canopy was found86. As such it remains unclear, if such moraines are diagnostic of ice shelf presence or simply indicate a specific GL configuration and/or retreat pattern.Ice shelf moraines—formed where debris is deposited or redistributed around the ice-shelf margins—provide constraints on ice shelf presence and thinning history88. Their vertical restriction and asymmetry implies limited accommodation for sediments above the grounding zone, due to the low seaward slope of an extending, floating ice tongue88. In the absence of a restricting ice shelf, flux of subglacial sediments will more likely construct morainal banks or proglacial grounding-line fans, both of which are distinct in their morphology and internal facies from GZWs28.GZWs form when the GL remains near-stationary allowing the accumulation and forward progradation of sediment to build a wedge geometry Figs.  and 6a8690. It is likely that ice shelf keels regularly interacted with the tops of GZWs, where GL migrations occurred. Such ‘keel’ expressions are perhaps the most prominent landform signature discerning past ice shelf extents and create both indirect and direct evidence for ice shelves in the form of melange scours and sub-ice shelf keel scours. Melange scours 93. Multiple lines of evidence indicate that, at least beneath PIG, corrugations record sub-ice shelf keel interaction with the seabed and not past iceberg grounding in open water  bathymetry from beneath an extant ice shelf, where such a lift-off is known to have occurred, were obtained with Autosub from the top of Jenkins Ridge beneath PIG ice shelf. Graham et al.er Table 30. Indeence Fig.  although94 due to deposition of sediment from the ice shelf surface and increased rainout of englacial and basal debris from the ice-shelf base  to survive under the outer limits of an ice shelf34. Biogenic detritus reaching the seabed after collapse was dominated by diatoms, and concomittant increases of chlorophyll pigments65. Sub-ice-shelf sediments, on the other hand, contain older and more refractory organic matter thought to be related to advection65. In this context, geochemical analyses that can distinguish different organic carbon compounds may provide a more powerful discriminator in reconstructing ice shelf cover and absence in the geological record. There is also untapped potential in using sponge spicules to help distinguish phases of ice shelf presence/absence—and particularly collapse—as sponges rapidly colonise the seabed following ice shelf disintegration99. In addition, work from the eastern Ross Sea also noted an increased abundance of freshwater diatoms (Chrysophytes) in sediments associated with a post-LGM ice-shelf breakup73. This was interrupted as a biotic signature of freshwater melt ponds which existed on the ice-shelf surface prior to the ice-shelf disintegration. Fursenkoina fusiformis, which is an opportunistic  benthic foraminfera often associated with organic-rich sediment and oxygen-depleted waters, has been documented in ice shelf collapse facies recovered from Marguerite Bay59. Majewski et al.77 also document a strong association between the two morphotypes of T. earlandi and the ice shelf breakup facies described from Whales Deep Basin  vary between subglacial, sub-ice shelf and open marine sediments  6 ka110. Here, the amplitude of the glacial–interglacial δ18O shift in the deep-sea benthic foraminifera record predicts more ice volume than available sea-level records indicate, a discrepancy that can be explained if 16O is stored in a large ice shelf that, once melted, has only a minor effect on sea level111.The potential of offshore sedimentary successions  for reconstructing ice shelf history is comparatively understudied, due to the complexity in interpreting ice-distal records. Accumulation rates112. However, these landforms are still being created in Antarctica today, making it difficult to discern “fossil” from modern ploughmark populations, particularly in shallower shelf regions, whose water depths overlap with keel depths of icebergs calved from modern ice shelves (<650 m113).A defining characteristic of landforms associated with retreating ice shelves is the interaction of ice keels with the seafloor Fig. . Some su114. These bedforms are generally restricted to sea beds that shoal gradually seaward from the ice front. Their relationship to ice-shelf retreat is linked to the idea that a distinct population of plough ridges form near synchronously during a single event, but the ridges are usually distal to the inferred calving front and only occur under circumstances in which the retreating ice shelf front is thick enough to calve icebergs with keels of suitable draft to ground at the sea floor. Therefore, ice plough ridges may not always be created, even during large ice-shelf collapse events.A more useful set of diagnostic landforms occurring in the shallow shelf areas have been termed ‘ice plough ridges’ Fig. . Ice plo93. Unlike other streamlined subglacial bedforms, these ‘mega-berg furrows’ have a pronounced relief (>20 m), and are characterised by clear downward incisions at irregular spacings, indicating they did not form subglacially. Jakobsson et al.93 interpreted these scours as having formed by an armada of grounded icebergs discharged during ice shelf breakup and retreat. Where found, these landforms may represent the proglacial signature of ice shelf collapse and may indicate ice-shelf extent and width, ice-shelf thickness during retreat, keel spacing and configuration, and even relative timing of the evolution of the collapse event in cases where they crosscut pre-existing morphological features. Corrugation ridges have also been used as diagnostic landforms of ice-shelf retreat and absence .Similar glacial features to linear melange scours described previously have been associated with episodes of past ice-shelf breakup on the middle continental shelf of Pine Island Troughnce Fig. . In Pinence Fig. . The ass93. Subsequently, this mechanism has been discussed and expanded upon in theoretical studies: where ice-shelf retreat leads to the exposure of thicker inland ice without a buttressing floating tongue, a positive feedback of structural failure of the ice cliff has been proposed . MICI has been incorporated into ice sheet models and constitutes a key physical process by which ice sheets rapidly disintegrate15. Wise et al.112 showed that this mechanism may have occurred during post-LGM retreat of collapsing ice shelves in the Amundsen Sea, with its signature preserved in the shapes of ploughmarks carved into the sea floor. Structural physics of ice shelves suggests that the landform signatures of MICI should only be present at discrete water depths112. However, the mechanism remains poorly studied and presents a challenge for geoscientists to discover, if MICI leaves additional landform signals at the sea floor.Part of the model for the formation of corrugation ridges, and of the signature of collapsing ice shelves, involves the scenario that icebergs can calve to full-depth near the GL Fig. 93. Subse115 coupled with depths of GZW crests at the sea floor. Relative elevations of GZW  also indirectly indicate past ice-sheet surface profiles, which in turn can be used to infer paleo-ice-shelf surface profiles. At the Pine Island-Thwaites paleo-ice stream bed, the GL was elevated by only ~80 m during a retreat of more than 100 km, implying a very low-gradient ice stream. GZWs do not give a clear indication of the calving-line location of an ice shelf but this can be inferred by analysis of the sedimentary record if the density of sediment cores is sufficient to map the spatial distribution of ice shelf/calving line facies. However, with the exception of a few targeted areas, such datasets are rare on the Antarctic shelf. Establishing the extent of ice shelves using the sedimentary record also requires good-dating control to ensure that sediments were deposited contemporaneously, and this often represents the biggest challenge.Establishing the thickness and extent of former ice shelves is critical for ice sheet mass balance calculations because the flux of ice across the GL increases strongly as a function of its thickness. Ice shelf thickness at the GL is quantifiable (for a single point in time) using past sea-level estimates that are corrected for isostatic rebound10, and hence knowledge of its shape is important for understanding the processes that determine melt and thus ice-shelf sensitivity to external forcing. As an ice shelf base limits the height of a GZW, cavity size can be estimated if the bathymetry seaward of the GZW is known.Constraints on past cavity geometry come from both seabed sediments and geomorphology, and by necessity require detailed bathymetric data which are currently unavailable for large areas of the Antarctic seabed, less so beneath extant ice shelves. Cavity geometry strongly influences the transfer of heat to the ice sheet24, meaning that the transition from coarse-grained GL-proximal sediments to more distal finer-grained muds can be used as a crude yet meaningful estimate for former positions of the GL16, and by inference cavity geometry. Cross-bedded and/or laminated muds directly above the coarse-grained facies also indicates deposition in a shallow cavity. Because tidal pumping creates traction currents that influence particle sorting, changes in current strength(inferred from sortable silt) may be indirectly associated with the change in cavity shape and associated weakening of tidal-pumping processes63.Indirect information about the evolution of the cavity can be inferred from the distribution of sedimentary facies seaward of a GZW. On a landward sloping bed, GL retreat results in a gradual enlargement of a sub-ice-shelf cavity. Although governed by several interacting variables, modern observations indicate that the majority of debris melts out from the ice shelf base within 1.5–10 km of the GL116. In instances where the sedimentary and/or landform record is sparse or inconclusive, modelling might offer additional support for former ice shelf cover117.Finally, it is worth reiterating that there exists no single diagnostic tool for identifying ice shelf presence, rather a succession of sedimentary facies and proxies that are linked to the proximity of the GL and calving line and the interplay between inflowing and outflowing currents. Likewise, the landform record is often patchy and in some instances poly-genetic, whereby certain landforms  can form in more than one setting. This highlights the need to apply a multi-proxy approach and integrate the geomorphological context in order to reconstruct ice shelf presence, collapse or re-growth210Pb, have helped constrain GL retreat, as well as recent sedimentation rates118. While fallout of atmospheric lead is typically preserved around Antarctica119, concentrations of other radioisotopes, such as 137Cs and 241Am, which are required to validate 210Pb decay profiles, are highly variable and often below analytical detection limits. 137Cs—injected into the atmosphere during nuclear bomb testing in the 1950s and 1960s—has a half-life of only 30 years, and in many Antarctic settings has already decayed below detectable levels. Furthermore, 137Cs is especially problematic in the Southern Hemisphere because fallout levels were approximately four times lower than in the Northern Hemisphere120. Smith et al.16 demonstrated the potential of using Pu-isotopes to validate 210Pb age models in sub-ice-shelf sediments. Plutonium isotopes, in contrast to other bomb-test products, have a much longer half-life and are expected to adsorb more readily than Cs to both coarse- and fine-grained detrital particles, with little chance of chemical re-mobilisation once the Pu is buried121.Establishing the duration of past ice shelf cover, timing and rates of ice-shelf retreat requires accurate chronologies. Unfortunately, the variable but predominantly terrigenous nature of sediments deposited in a sub-ice-shelf setting combined with low concentrations of biogenic material  represent significant challenges for conventional dating methods. On short times scales (<200 years), measurements of the concentrations of short-lived radioisotopes, such as 14C dating of calcareous microfossils provides the most reliable chronologies from marine sediments116 and can now be performed on very small sample sizes122. Unfortunately, the scarcity of such microfossils (even in low concentrations) in many sub-ice-shelf sediments has forced researchers to rely on dating other fractions124. Bulk organic matter or its acid-insoluble fraction (AIOM) can yield reliable and reproducible chronologies (see ref. 124), but it is often viewed as a last resort owing to the potential for large error caused by “contamination” with reworked fossil carbon125. Recent advances in Ramped Pyrolysis (RP) 14C dating minimises the effect of contamination by combusting sediments at gradually increasing temperatures to thermally break down the bulk organic matter127. The gradual temperature increase allows for the separation of the more thermochemically reactive younger constituents, which are preferably combusted under lower temperatures, from the reworked more stable older constituents, so that separate components can be dated independently127. Similarly, chemical compound-specific radiocarbon dating enables specific organic compounds  to be isolated, and thereby avoiding fossil carbon. Fatty acids in the surface waters of the Southern Ocean are primarily produced by diatoms and because their decomposition is relatively fast in both the sediment and water column129 they rarely stem from relict organic matter. Therefore, the majority of fatty acids extracted from sediments are formed just before deposition, rather than being derived from relict organic matter130.On longer times scales  AMS 131. However, this method is susceptible to changes in magnetic mineralogy and magnetic grain size, and thus to sediment provenance and physical grain size, both of which can vary considerably in sub-ice shelf sediments. Nevertheless, Brachfeld et al.71 used this technique successfully to constrain the timing of Holocene retreat of the Larsen A Ice Shelf, demonstrating its potential for dating mainly fine-grained terrigenous sediments deposited beneath an ice shelf. Finally, in regions where aeolian sand and silt accumulates at the calving line and on the ice shelf surface until being released during collapse  using δ18O measurements in diatom silica, although problems remain with disentangling ice shelf melt from other sources of glacial/freshwater discharge or chemical processes. δ18O data from planktic foraminifera have been used to infer water column freshening due to the long-term thinning of the Larsen B Ice Shelf17. Needless to say the usefulness of this proxy—together with benthic foraminiferal assemblages and trace metal and stable isotope data from calcareous shells—is dependent on preservation of foraminifera, which is often poor in sub-ice-shelf environments.Other attempts to reconstruct CDW intrusions have focussed on its geochemical fingerprint97. Together with recent advances in dating64 and multi-proxy approaches72 this work holds the potential to usher in a new era of deciphering former ice shelf cover together with the rates and drivers of change. To enable this, there needs to be a concerted effort to link the often disparate strands of research, including constraints on ice shelf thickness and extent from the geomorphological record together with detailed sedimentology, proxy reconstructions and accurate dating. Furthermore, because Antarctic continental shelf sediments are often lacking biogenic material , greater progress can be made by re-visiting areas where the sediments are known to be suitable for re-analysis using the latest proxies and dating methods and where the geomorphological footprint of former ice shelf cover is well-preserved .The past decade has witnessed significant progress in our understanding of sub-ice-shelf environments, resulting in a comprehensive ‘toolbox’ with which to identify past ice shelf cover as well as passive retreat and/or breakup events. This not only reflects technological advances in remote access but also detailed analyses of sediments Fig.  and land143 but also reveal fundamental information about the processes occurring beneath ice shelves, particularly those close to the GL. In this context, much of our knowledge of sub-ice-shelf sedimentary processes, particularly those operating at or close to the GL, has been obtained from a limited number of studies in the Ross Sea, which is almost certainly not representative of all ice shelf systems. Future work, while ambitious in scope, should aim to combine transects of sub-ice-shelf sediment cores from the GL to calving line, with down-hole oceanography and dedicated ROV/AUV missions  that image the seafloor, ice base and processes operating near the GL. Only by investigating the ocean cavity and seafloor beneath ice shelves of different sizes, experiencing different rates of change, and forced by different oceanic and atmospheric drivers, will it be possible to capture the full-range of processes operating there. The areas requiring further focus should include, but not be limited to, the spatial distribution of sediment facies/facies geometries, sediment and meltwater fluxes, seafloor benthos, circulation patterns and advection of detrital and biogenic particles as well as processes which form enigmatic landforms . With planned multi-national expeditions to the Eastern Ice Shelf of Thwaites Glacier as well as further work on the Amery and Ross ice shelves over the coming years, our knowledge of these processes is set to expand considerably.Despite this progress, sub-ice-shelf settings remain one of the least explored environments on Earth, and there is a clear need to access and sample the seafloor and ocean cavity beneath contemporary ice shelves. This will not only help answer debates about ice shelf and GL histories at a range of time scales144. This includes information on key boundary conditions  as well as accurate constraints on the rates and drivers of ice shelf and ice sheet changes. However, integration of data and models is often intended but not always realised, which calls for a concerted effort to provide relevant paleo data in a form that can be easily utilised by modellers144. By producing detailed information on known past ice sheet-ice shelf configurations—such as complete loss of buttressing due to ice shelf collapse or stabilisation of a grounding line due to sediment deposition , eastern Ross Sea116. The study shows retreat was underway from the shelf edge prior to 14.7 ± 0.4 cal. kyr B.P. A paleo-ice-shelf collapse occurred at 12.3 ± 0.2 cal. kyr B.P. The GL was maintained on the outer-continental shelf until at least 11.5 ± 0.3 cal. kyr B.P before experiencing a 200-km retreat. GL retreat lagged ice-shelf collapse by at least two centuries and by as much as 14 centuries. This delay was due to rapid aggradation of sediment (GZW 5-7) as ice-stream discharge accelerated following ice-shelf collapse which helped stabilise the ice-sheet. This study serves as an example of how targeted coring, geomorphological mapping and reliable dating can provide well-constrained palaeodata with which to test the predictive skill of ice-sheet models and explore key processes, e.g., the dynamic response of ice-streams to ice shelf collapse and de-buttressing. One element that is missing from this study is information related to external and/or internal forcing which could be explored via numerical modelling and/or by applying multi-proxy analyses of nearby sediment cores to reconstruct key environmental variables .


Ice-binding proteins (IBPs) permit their hosts to thrive in the presence of ice. The ability of IBPs to control ice growth makes them potential additives in industries ranging from food storage and cryopreservation to anti-icing systems. For IBPs to be used in commercial applications, however, methods are needed to produce sufficient quantities of high-quality proteins. Here, we describe a new method for IBP purification, termed falling water ice affinity purification (FWIP). The method is based on the affinity of IBPs for ice and does not require molecular tags. A crude IBP solution is allowed to flow over a chilled vertical surface of a commercial ice machine. The temperature of the surface is lowered gradually until ice crystals are produced, to which the IBPs bind but other solutes do not. We found that a maximum of 35 mg of IBP was incorporated in 1 kg of ice. Two rounds of FWIP resulted in >95% purity. An ice machine that produces 60 kg of ice per day can be used to purify one gram of IBP per day. In combination with efficient concentration of the protein solution by tangential flow filtration the FWIP method is suitable for the purification of grams of IBPs for research purposes and applications. IBPs have several functions in nature, such as freezing point depression7, ice recrystallization inhibition8, and ice nucleation9. IBPs that function as freezing point depressants are usually termed antifreeze proteins (AFPs). All IBPs bind directly to the surfaces of ice crystals. The ice binding capacity of an IBP grants it the ability to control ice growth and shape, leading to a variety of potential applications in fields that require ice growth control10. IBPs are useful in the frozen food industry, agriculture, medicine, biotechnology, and in the cryopreservation of cells, tissues and organs13. Research studies have shown that IBPs act as cryoprotectants in the cryogenic and hypothermic storage of isolated organs, tissues, cells, sperm, oocytes, embryos, and red blood cells20. IBPs can also be used to design ice templates in material science and in coatings to prevent ice formation22. Interestingly, these proteins have not yet been used significantly in most of these industries. The gap between the evident potential of IBPs and their actual applications arises from a lack of sufficient protein quantities and the high cost of the proteins. The availability of large amounts of purified IBPs is indispensable for research, especially in cryopreservation, where low protein quantity hinders the development of practical technologies and limits basic research.Ice-binding proteins (IBPs) are produced by many organisms that need to survive in cold environments. These include vertebrates24. Purification can be conducted using standard chromatographic methods. The affinity of IBPs to ice can be used as a purification tool for the selective extraction of IBPs from unpurified solutions. The first ice affinity purification was described by Raymond and Fritsen25. Ice active substances were semi-purified from cyanobacteria, green algae and moss crude extracts. The extracts were partly frozen and then centrifuged to partition ice and liquid fractions. Later, two more efficient methods for IBP purification based on ice growth were developed. The basic principle of these methods is that if the ice grows slowly enough, supercooling is minimized, and the engulfment of impurities into the crystal is low. Solution mixing is needed to exclude solutes from the ice26. One method is the ice affinity purification technique, in which ice grows slowly on a cold finger immersed in a protein solution. Constant stirring of the solution prevents non-IBPs from the growing ice26. The second method is ice shell purification, in which ice is grown on the interior surface of a rotating round-bottom flask submerged in a cool bath27. In both methods, an IBP solution in a container is mixed while the temperature is lowered by a programmed water bath. The purified protein is extracted by melting the ice.IBPs can be extracted from natural sources  or produced by common recombinant technologiesIn this study, we present a new ice affinity purification method using a commercial clear ice-producing machine. Our method, termed falling water ice affinity purification (FWIP), is an effective, high-yield system. The amount of protein obtained by the FWIP method permits experiments to be performed on the scale of a half liter to hundreds of liters of IBP solution. FWIP is applicable to production of gram quantities of IBP, and thus, can advance IBP research and the use of IBP in cryopreservation, medicine, and other fields.The FWIP method relies on a commercially available ice-making machine  designed to produce clear ice cubes. The machine includes two large metal plates on which ice grows. The metal plates feature columns and rows that produce separate ice cubes. Water supplied to the machine reservoir is elevated by a pump to the top of the metal plates and flows on their surface back to the reservoir. The water is circulated as the temperature of the plates is gradually lowered. Once nucleation occurs below the freezing point, ice begins to grow slowly until the water level decreases or until a time limit is reached. After a batch of ice is produced, the electronic controller initiates a defrost step, the metal plate is heated, and ice cubes drop into the collecting bin. This process constitutes one “cycle” Fig. . At this2 in the smallest KM machine (model 35A). This surface area is 10 times larger than the surface of a typical cold finger (90 cm2 for a finger 10 cm in length). It is also more than twice the surface area of the 1 L round-bottom flasks typically used for ice shell purification27. The large surface area provides larger volumes of ice per cycle compared to the cold finger and the ice shell methods. The cold finger and ice shell methods are typically suitable for <1 L volumes, and one cycle requires several hours to complete. After each cycle, the operator must begin the process from the start. By comparison, an ice machine can load 2.5 L within a single 40 min cycle, producing 0.7 L of ice. The machine is designed to work in an automatic mode, repeating freeze cycles one after another. During regular use, a model KM 35 A ice machine consumes 143 L of water and yields 35 kg of clear ice cubes per 24 h without the need for intervention. The ice machine can also be adapted to the purification of smaller volumes. The minimum volume required for one cycle is 0.6 L of loading solution. In this case, a cycle requires only 12 min and produces 0.15 L ice.The gradual temperature drop and the constant water circulation exclude solutes and air bubbles from the growing ice front, yielding clear ice. Any ice-binding substances present are incorporated into the ice. This process is similar to other ice affinity purification methods; however, the metal plate on which the ice grows has a surface area of 900 cmWe modified the KM machine to allow insertion of a liquid from a pressure tank  instead of using water from a regular tap system. Loss of protein via drainage was avoided by collecting the drain liquid after a freezing cycle had completed. This solution was then re-loaded for use in additional purification cycles. The FWIP process is illustrated in Fig. −1) was run through one cycle of the process, similarly to the examination of the ice shell purification method27. Less than 0.1% of the dye, as measured by absorption, was incorporated into the ice fraction, whereas the drain fraction contained concentrated dye . The total protein concentrations in the loading solution and in the ice fractions were measured. These two values could be described according to a non-linear relationship , recombinant Tenebrio molitor AFP (TmAFP) fused to maltose binding protein (MBP-TmAFP), and TmAFP extracted from Tenebrio molitor larvae. We conducted 4–6 consecutive cycles as a first round of FWIP and collected the ice for a second round of purification . The purities of the ice fractions obtained from the first and second purification rounds were assessed using BCA concentration assay, SDS-PAGE, silver staining, fluorescence measurements, and mass spectrometry. Figures RiAFP purified by FWIP. Following consecutive cycles of FWIP, the amount of IBP in the loading solution was reduced, leading to a reduction in the fluorescence of the ice cubes .The FWIP method was developed for the efficient purification of large amounts of IBPs. As in other ice affinity purification methods, the FWIP method did not require protein affinity tags and is applicable to different types of IBP solutions, including hemolymph fluid. In all cases in which we used diluted solutions containing 0.16 mg/mL non-IBPs or less Fig. , we obtaThe yield that can be obtained from a single round could be increased by performing more FWIP cycles Fig. , and the29. This concentration corresponded to 4.5 μM, indicating a volume of 70 × 70 × 70 nm3 per molecule. Drori et al. performed accumulation experiments of IBP on ice surfaces which revealed that IBPs accumulated on stationary ice surfaces to reach surface densities of 7–35 nm between IBPs with a typical accumulation time of several seconds30. In our experiments, the ice cube grew to a thickness of 13 mm in 30 minutes; thus, the ice grew at a rate of approximately 7 μm/s. It is reasonable to assume that ice grew in layers on which the IBPs accumulated at the saturation level.In the course of determining the effectiveness of the system, we found an interesting nonlinear correlation between the amount of impurities present in the loading solution and the amount of impurities incorporated into the ice. This phenomenon is related to the temperature profile near the ice surface and the flow rate of the water. These parameters could be physically manipulated if needed. A maximum concentration of 0.037 mg/mL type III AFP could be incorporated into the ice. This maximum level probably arose from the saturation of the IBPs on the ice and is a function of the IBP type, because different IBPs have different binding kinetics and different binding sites on iceOur analysis of the IBP concentrations in the ice relative to the total protein concentration in the loading solution revealed that the amounts of non-IBPs present in the loading solution did not affect the amounts of IBPs extracted into the ice. This is an important fact when considering the reproducibility of the purification process. The insensitivity of the purification process to impurities relied on the fact that ice excludes solutes in a colligative manner.FWIP is suitable for purification of both recombinant and native IBPs, however, like other ice affinity purification methods, it cannot separate different native isoforms of the specific type of IBP. FWIP is advantageous over other ice affinity methods because it is suitable for large-scale protein purification over short time frames. The largest KM machine available commercially by Hoshizaki produces 600 kg of ice in 24 h. With simple adjustments, this machine may be used to purify grams of IBPs per day. To concentrate the large amount of solution from the melted ice that includes pure IBPs (II fractions), tangential flow filtration (TFF) system can be used. For example, 300 L of solution can be concentrated in 24 hours by a commercially available membrane. The FWIP system does not require resins and does not produce chemical waste. These factors render the FWIP method readily suitable for IBP purification for use in the food and medical industries. The FWIP method can also be used for small-scale purification. We anticipate that the FWIP method has a potential to advance the practical use of IBPs in research and medicine.31. A plasmid containing the recombinant eGFP-RiAFP gene was generously donated by Aaron Hakim 32. A plasmid containing recombinant MBP-TmAFP was obtained from the lab of Deborah Fass 33. A plasmid bearing MBP-TmAFP was transformed using the heat shock method34 into the Origami-B E. coli strain (Novagen). All other plasmids were transformed by heat shock into BL21-DE3-PlysS E. coli strain. A stirred tank fermentor of 1 or 5 L  was used for a fed-batch fermentation process to produce all recombinant proteins. Bacteria were grown under controlled physical and chemical parameters . The feed and medium components  were supplied during the fermentation process by direct injection into the vessel. Air was supplied at a rate of 0.15–2 vvm (i.e. volume of air per volume of medium per minute) to maintain the dissolved oxygen concentration greater than 20% of air saturation. pH was maintained at 7 by the titration of either 2M H2SO4 or 3 M NaOH. The cultivation temperature was 37 °C and then lowered to 15–20 °C prior to induction with 1 mM of IPTG. Typical fermentation time duration was 20–24 hours, final OD values reached 60. Cells were harvested, pelleted by centrifugation at 4 °C at 4500 rpm for 45 min, and stored at −80 °C until purification. Five grams of wet cell pellet were resuspended in 50 mL 50 mM sodium phosphate buffer (pH 7.5) supplemented with protease inhibitors, precooled to 4 °C. The resuspended cells were lysed by sonication and centrifuged at 4 °C at 15000 rpm for 45 min. The supernatant of the lysate was diluted to 2.5 L and a final concentration of 25 mM of sodium phosphate buffer .A plasmid containing a type III AFP, QAE isoform from ocean pout, was obtained from Peter L. Davies Two and a half liters of the crude starting solution were chilled to 4 °C and loaded in a pressure tank under a pressure of 2.5 bar. We slightly reduced the water flow to improve the efficiency of purification. The machine was then turned on and a cycle of ice formation was started, as explained in the results section. During the cycle, ~30% of the solution gradually froze. At the end of the cycle, before the defrost step, the ice cubes were subjected to dry air flow to remove residual liquid from the ice surface. We found that air was more effective than rinsing for this purpose. The ice cubes were collected and stored. During the second cycle, the unfrozen liquid (drain) was collected and diluted using double distilled water to reach the initial buffer concentration of 25 mM and a volume of 2.5 L. This solution was loaded into the pressure tank and the system was turned on again. After completing the desired number of cycles, all ice fractions were collected and mixed. The series of FWIP cycles was termed the first round of FWIP. To improve the protein purity, the ice collected from the first round was melted in a 20 °C water bath, and 1M sodium phosphate buffer was added to a final concentration of 25 mM. The melted ice was used as a starting solution for a second round of purification. A schematic diagram of the process is shown in Fig. 31. A total of 132 mg of type III AFP was diluted in a crude lysate solution that did not contain any IBP at a concentration of 0.16 mg/mL to a final volume of 2.5 L. We conducted 10 cycles of FWIP to extract all IBP from the solution, which gave 7 L of ice. The 10th cycle contained only 0.6 mg of protein, indicating that >99.5% of type III AFP had been extracted. We verified that the drain did not contain any AFPs using SDS-PAGE of the concentrated drain solution. The purity level was calculated by measuring the amount of total protein present in the ice fractions. A total of 147 mg of protein was present in the ice, 132 mg of which was type III AFP. The 15 mg of non-IBPs were impurities. Given that this amount was divided among 7 L, and that the amount of impurities remained constant in all cycles, as shown, 0.002 mg/mL of impurities were present in the final solution.The type III AFP was purified by FWIP in previous experiments and a purity of >95% was verified using silver staining and thermal hysteresis measurements based on known activity valuesThe SDS-PAGE and protein concentration analyses were conducted using samples obtained from the ice and drain fractions. The ice fraction sample was obtained by collecting 5 cubes of ice from 5 different rows of the metal plate to avoid possible bias due to temperature gradients on the metal plate. Equal volume samples (20–40 mL) of the fractions were collected from each cycle and were concentrated to the same volume using the Vivaspin 20 . Large ice fractions up to 5 L were concentrated using a 2.5 L ultrafiltration stirred cell . Ice fractions of >5 L were concentrated using a TFF system , with a 3 or 10 kDa cutoff. TFF systems can be obtained with a concentration rate capacity per hour that matches the amounts of ice produced by the ice machine.Two and a half liters of a 0.05% (w/v) bromophenol blue dye solution (750 µM) was loaded into the ice machine and allowed to run for one cycle. The ice obtained was analyzed by absorbance spectroscopy at 600 nm .E. coli cells (not transformed with a plasmid bearing an IBP gene) were cultured in a fed-batch as described above. The soluble fraction obtained from a 16.5 g pellet was diluted to 2.5 L with a final concentration of 25 mM sodium phosphate buffer (pH 7.5). This starting solution contained 0.55 mg/mL proteins (note that the proteins do not include  IBPs). The starting solution was loaded in the ice machine and allowed to run. At the end of the process, all ice fractions were collected and melted. Samples from the starting solution, the ice, and the drain fractions were analyzed. The same process was repeated after dilution of the loading solution to 3.9 L, 5.3 L, 6.7 L, 8.1 L, and 11.5 L, giving diluted starting solutions with the same amount of proteins but at lower concentrations. The protein concentration of the fraction was measured using the micro BCA protein assay (described below).The BL21-DE3-PlysS Tenebrio molitor larvae were treated as described previously35. Briefly, the larvae were acclimated for 1 month at 4 °C and stored at −80 °C. Ten grams of the larvae were crushed and homogenized in 100 mL of a 100 mM ammonium bicarbonate (pH 8) buffer supplemented with 0.1 M phenylthiocarbamide and protease inhibitors. The homogenate was centrifuged at 4 °C and 50,000 rpm  for 1 h. The supernatant was diluted to a final volume of 2.5 L and final concentration of 25 mM ammonium bicarbonate (pH 8) and loaded into the pressure tank. After 4 cycles of purification, 60 mg of TmAFP (including low amounts of impurities) were obtained in the ice fractions. After the second round of purification (4 cycles), a total of 45 mg TmAFP were isolated. The protein content in the II fractions was assessed by mass spectrometry  using HCCA  as a matrix, according to the manufacturer’s recommendations. Protein Standard I  and Protein Standard II  were used to calibrate the respective mass ranges. Mass spectrometry measurements were performed in a microflex MALDI-TOF . The spectra fell within the mass range 5–60 kDa.36. Protein concentration was determined using the Micro BCA Protein Assay  against a bovine serum albumin (BSA) standard. The absorbance was read at 550 nm using an ELx808 ultra microplate reader . Sodium phosphate buffer 25 mM was used as a blank.SDS-PAGE was performed in a 6% stacking gel, 18% resolving gel following common proceduresRiAFP concentration was estimated using GFP fluorescence measurements with 485/20 nm excitation and 528/20 nm emission filters. All samples were concentrated to the same volume.The fluorescence was quantified using a Biotek Synergy-2 plate reader fluorometer . The total protein concentration was determined using the Micro BCA Protein Assay  according to the manufacturer’s instructions, with the absorbance read at a wavelength of 562 nm. The eGFP-37.The thermal hysteresis measurements were conducted using a computer-controlled nanoliter osmometer as described elsewhereAlmost all data generated and analysed during this study are included in this published article (and its Supplementary Information files). All datasets are available from the corresponding author on reasonable request.Supplementary figures