Island Rule Research Articles

Entanglement islands and the Page curve of Hawking radiation for rotating Kerr black holes

We initiate the study of the information paradox of rotating Kerr black holes by employing the recently proposed island rule. It is known that the scalar field theory near the Kerr black hole horizon can be reduced to the two-dimensional effective theory. Working within the framework of the two-dimensional effective theory and assuming the small angular momentum limit, we demonstrate that the entanglement entropy of Hawking radiation from the nonextremal Kerr black hole follows the Page curve and saturates the Bekenstein-Hawking entropy at late times. In addition, we also discuss the effect of the black hole rotation on the Page time and scrambling time. For the extreme Kerr black hole, the entanglement entropy at late times also approximates the Bekenstein-Hawking entropy of the extreme Kerr black hole. These results imply that entanglement islands can provide a semiclassical resolution of the information paradox for rotating Kerr black holes. Published by the American Physical Society 2024

Entanglement entropy, phase transition, and island rule for Reissner-Nordström-AdS black holes

This study focuses on the examination of the island rule within the context of four-dimensional Reissner-Nordström-anti-de Sitter (4D RN-AdS) black holes, illuminating the intricate relationship between the entanglement entropy and phase transitions of black holes. The entanglement entropy of 4D RN-AdS black holes follows the anticipated linear growth pattern before ultimately declining to a constant value, in accordance with the well-established Page curve. The novelty of this study lies in the examination of the influence, previously unexplored, of the first-order phase transition on the shape and evolution of the Page curve in situations involving both eternal and evaporating black holes. Despite the morphological alterations of the curve induced by the transition, the inherent unitarity of the system persists. As the evaporation progresses, the Page curve displays diverse configurations, unveiling phenomena that are novel and defies traditional expectations, thereby enriching our comprehension of the thermodynamics of black holes interlinked with quantum information. Published by the American Physical Society 2024

The Indonesian Throughflow circulation under solar geoengineering

Abstract. The Indonesia Throughflow (ITF) is the only low-latitude channel between the Pacific and Indian oceans, and its variability has important effects on global climate and biogeochemical cycles. Climate models consistently predict a decline in ITF transport under global warming, but it has not yet been examined under solar geoengineering scenarios. We use standard parameterized methods for estimating the ITF – the Amended Island Rule and buoyancy forcing – to investigate the ITF under the SSP2-4.5 and SSP5-8.5 greenhouse gas scenarios and the geoengineering experiments G6solar and G6sulfur, which reduce net global mean radiative forcing from SSP5-8.5 levels to SSP2-4.5 levels using solar dimming and sulfate aerosol injection strategies, respectively. Six-model ensemble-mean projections for 2080–2100 show reductions of 19 % under the G6solar scenario and 28 % under the G6sulfur scenario relative to the historical (1980–2014) ITF, which should be compared with reductions of 23 % and 27 % under SSP2-4.5 and SSP5-8.5. Despite standard deviations amounting to 5 %–8 % for each scenario, all scenarios are significantly different from each other (p<0.05) when the whole 2020–2100 simulation period is considered. Thus, significant weakening of the ITF occurs under all scenarios, but G6solar more closely approximates SSP2-4.5 than G6sulfur does. In contrast with the other three scenarios, which show only reductions in forcing due to ocean upwelling, the G6sulfur experiment shows a large reduction in ocean surface wind stress forcing accounting for 47 % (38 %–65 % across the model range) of the decline in wind + upwelling-driven ITF transport. There are also reductions in deep-sea upwelling in extratropical western boundary currents.

Quantum focusing conjecture and the Page curve

The focusing theorem fails for evaporating black holes because the null energy condition is violated by quantum effects. The quantum focusing conjecture is proposed so that it is satisfied even if the null energy condition is violated. The conjecture states that the derivative of the sum of the area of a cross-section of the null geodesic congruence and the entanglement entropy of matter outside it is non-increasing. Naively, it is expected that the quantum focusing conjecture is violated after the Page time as both the area of the horizon and the entanglement entropy of the Hawking radiation are decreasing. We calculate the entanglement entropy after the Page time by using the island rule, and find the following results: (i) the page time is given by an approximately null surface, (ii) the entanglement entropy is increasing along the outgoing null geodesic even after the Page time, and (iii) the quantum focusing conjecture is not violated.

Correction: ‘Strength of the “island rule” in birds is positively associated with absence of avian predators’ (2023), by Ponti et al.

Correction: ‘Strength of the “island rule” in birds is positively associated with absence of avian predators’ (2023), by Ponti <i>et al.</i>

Fish body size influenced by multiple drivers

There is evidence that organisms have become smaller during the past periods of global warming. Global change has substantial effects on biodiversity, with body size reduction being the third most common response to global warming. Body size allometry in ectotherms needs to be explored further; the objectives of this study were to better understand the mechanisms regulating body size in fish by testing: 1) Bergmann's rule with temperature and elevation, 2) additional environmental drivers, 3) the role of isolation, 4) ecoevolutionary hypotheses comparing native and exotic species and 5) the role of migration propensity in comparing migratory and resident species. We analyzed an extensive dataset of Chilean fish composed of 75 198 records which included 25 species from 12 different families between latitudes −28.80 to −51.42 using linear mixed models to discern the best environmental variables contributing to body size changes, as well as incorporating factors related to dispersal capabilities, biogeographic isolation and levels of exotic/native interactions. Bergmann's rule is supported by changes in elevation, and our study shows that freshwater fish body size also increases with increasing environmental heterogeneity and productivity. In general, inland native fish tend to be smaller than coastal ones, supporting the island rule with evidence of gigantism or dwarfism in selected species. Ecological variables affecting fish body size do not differ between native and exotic fish unless other factors are considered, such as dispersal capacity (migrating vs resident fish) or mechanisms related to their isolation. Although temperature is not a direct driver of body size in Chilean fish, heterogeneity, productivity, geography, migratory ability and species origin may affect body size. A better understanding of the mechanisms driving body size in ectotherms will aid in determining management priorities in the face of global climate disruption.

Insular aurochs (Mammalia, Bovidae) from the Pleistocene of Kythera Island, Greece

Islands are renowned for their remarkable biotas and have been widely recognised as natural laboratories for the study of evolution, speciation, and extinction. Large mammals in insular environments typically evolve to dwarfs and small ones to giants, a trend known as the island rule. Despite their dominance in the continental European mammal faunas of Middle-Late Pleistocene, Bison and Bos are usually lacking from the neighbouring endemic insular assemblages. Here, we report the first insular bovin from the Late Pleistocene of Kythera Island, Greece and we carry out a detailed morphometrical analysis with emphasis on its adaptations and palaeogeographic implications. Based on both dental and postcranial qualitative and quantitative comparisons, we attribute the studied material from Kythera to Bos primigenius. Significant differences from both its continental Pleistocene relative and the endemic bovins from Mediterranean islands, allow us to recognize it as a new subspecies, Bos primigenius thrinacius n. ssp., the third known insular dwarf of this taxon in Europe. Our main hypothesis is that the gradual disconnection of Kythera Island from the neighbouring Peloponnese peninsula just after MIS 6 (late Middle Pleistocene, ∼180 ka) resulted in the isolation of a mainland Bos primigenius population in the rocky and predator free environment of palaeo-Kythera Island. Under these particular conditions the population underwent some remarkable changes and gained some peculiar features, especially on metapodials. The timing and reasons of Bos primigenius thrinacius extinction remain unknown.

Implication of the island rule for inflation and primordial perturbations

It is usually thought that the efolds number of inflation must be bounded by its de Sitter entropy, otherwise we will have an information paradox. However, in light of the island rule for computing the entanglement entropy, we show that such a bound might be nonexistent, while the information flux of primordial perturbation modes the observer after inflation is able to detect follows a Page curve. In corresponding eternally inflating spacetime, it seems that our slow-roll inflation patch is accompanied with a neighbourly collapsed patch (eventually developing into a black hole) so that its Hawking radiation might be just our primordial perturbations. Accordingly, the perturbation spectrum we observed will present a ``Page-like" suppression at large scale.

Evolution: The rise and fall of island dwarfs and giants

Islands are arenas for a range of striking evolutionary phenomena, including the island rule- the tendency for larger animals to shrink and smaller animals to enlarge. A new study of insular mammals finds such body size shifts predispose these evolutionary marvels to greater extinction risk.

La regla de islas y el tamaño corporal del poliplacóforo Plaxiphora mercatoris en Rapa Nui

To test the island rule, the body size of P. mercatoris and P. aurata was measured, then statistical test and generalized linear models (GLM) were performed to explore changes in body length of both species. A smaller body length was evidenced in P. mercatoris supporting insular dwarfism. Additionally, P. mercatoris showed a trend of decreasing body size over time. This is the first report of the island rule in polyplacophorans. The temporal decrease in the size of P. mercatoris suggests a possible increase anthropogenic pressure, which should be studied to facilitate conservation and monitoring strategies.

Island and Rensch’s rules do not apply to cave vs. surface populations of Asellus aquaticus

Body size is a trait of fundamental ecological and evolutionary importance that is often different between males and females (sexual size dimorphism; SSD). The island rule predicts that small-bodied species tend to evolve larger following a release from interspecific competition and predation in insular environments. According to Rensch’s rule, male body size relative to female body size increases with increasing mean body size. This allometric body size – SSD scaling is explained by male-driven body size evolution. These ecogeographical rules are rarely tested within species, and has not been addressed in a cave–surface context, even though caves represent insular environments (small and isolated with simple communities). By analyzing six cave and nine surface populations of the widespread, primarily surface-dwelling freshwater isopod Asellus aquaticus with male-biased SSD, we tested whether cave populations evolved larger and showed higher SSD than the surface populations. We found extensive between-population variation in body size (maximum divergence being 74%) and SSD (males being 15%–50% larger than females). However, habitat type did not explain the body size and SSD variation and we could not reject isometry in the male–female body size relationship. Hence, we found no support for the island or Rensch’s rules. We conclude that local selective forces stemming from environmental factors other than island vs. mainland or the general surface vs. cave characteristics are responsible for the reported population variation.

A global assessment of the ‘island rule’ in bats based on functionally distinct measures of body size

AbstractAimThe ‘island rule’ postulates that on islands large continental animals become smaller, and small continental animals become larger. Its generality has been supported by some studies but contested by others. Bats are cosmopolitan and speciose mammals thus are ideal to test ecogeographic patterns. Based on three functionally distinct measures of body size, I compare mainland and island variation in bats at the order to subspecies level.LocationGlobally.TaxonChiroptera.MethodsI compiled information from literature on the skull length, forearm length, and body mass of 251 bat species in 840 locations. For conspecific bats from different locations, I calculated size divergences, and categorized them as within‐mainland (M–M), mainland‐to‐island (M–I), or island‐to‐island (I–I). I used a modified size ratio to quantify divergences, analysis of variance, non‐parametric tests, and effect sizes to complement statistical significances.ResultsOn islands, cranial size increases, wing length becomes more uniform, and body mass decreases more often than not. The first trend would support the island rule, but had a small effect size. Families differ considerably in how they vary geographically. Species are ranked very differently based on functionally distinct size measures. Divergences are uniform across M–M, M–I, and I–I ranges, and large between bats of different subspecies.Main ConclusionsLikely owing to limitations imposed by flight and echolocation, bats do not follow the island rule. The absence of correlation between how bats are ranked based on them indicates that functionally distinct size measures are not necessarily coadaptive. High vagilities may lead to low local differentiation, but interfamilial variation shows this differentiation to also depend on other factors. Body sizes converge to species‐specific optima, not to supraspecific optima as predicted by theoretical studies. Size differences are reflected in taxonomy more often if observed across M–I ranges.

When Rensch meets Foster: insular gigantism may reduce sexual dimorphism in anurans

According to the Island rule, insular populations exhibit gigantism in small species and dwarfism in large species. These contexts offer opportunities to test for complementary aspects pertaining to the evolution of body size, and particularly sexual size dimorphism (SSD). ‘Rensch's rule' states that SSD should vary with increasing body size, depending on the larger sex. As a consequence, it is expected that dwarfism or gigantism occurring in insular populations should influence the magnitude of SSD. Using anuran amphibians as a study system (because most anuran species express a female‐biased SSD and a marked lability in size), we investigated our hypothesis both in a specific comparison of continental and insular populations of a widespread coastal amphibian, and using a large‐scale analysis across anurans (10 species across 62 sites). Both datasets yielded similar results, with increasing body size in insular populations reducing the magnitude of SSD through an increase of male body size, as expected by Rensch's rule. Detailed data on insular populations considering both sexes are scarce, and future studies are required to complement the existing literature in order to test for the validity of our hypothesis at a wider scale and to infer the mechanistic causes of size variations, which remain unknown. In addition, further investigations are required to explore the consequences of insularity on the magnitude of SSD including various taxa (e.g. mammals, birds, lizards and snakes) in which the Island rule has found support, and considering taxa in which males are the larger sex.Keywords: amphibians, body size, insularity, Island rule, Rensch's rule, sexual dimorphism

Stowaways: Maritime ecology of the oldest commensal ship rats (Rattus rattus) found on a Mediterranean shipwreck

Ship rats (Rattus rattus) have successfully colonized six continents and 80% of islands worldwide by stowing-away on anthropogenic vessels. Numerous zooarchaeological and metagenomic studies have contributed to tracing the western dispersal of ship rats out of the Indian subcontinent and into the Mediterranean Basin, North Africa, and Europe. This has increased understanding of historical maritime mobility, trade contacts, and the spread of pandemic disease such as the plague. Moreover, considerable research has been conducted on the behavior, ecology, and population dynamics of ship rats in invaded areas, which supports conservation and eradication efforts. However, few studies have shed light on the mode of travel in between the geographic origins and destinations of ship rats, such as ships and boats, which act as mobile, commensal habitat for this cosmopolitan species. We address this lacuna here, by analyzing an assemblage of ship rat remains from an early Islamic period shipwreck, the Ma‘agan Mikhael B, located on the Carmel coast of modern Israel. Using zooarchaeological, biometrical, and palaeogenetic (aDNA) methodologies, we investigated the maritime ecology of ship rats regarding dispersal behavior, habitat selection, source–sink dynamics, and relative body size. The results of this study suggest that ship rats actively inhabited the Ma‘agan Mikhael B as part of their habitat selection processes, that conditions onboard provided high-quality habitat (adequate food and harborage, likely absence of predators and disease), and that they appear to have exhibited a degree of gigantism, possibly due to ‘island rule’. This study has implications for future metapopulation genetic studies on ship rats, as well as shows the value of zooarchaeological analysis in understanding the ecological circumstances of the maritime mobility of ship rats in the Mediterranean region.

The island rule with multiple islands and its application to the Indonesian Throughflow

The island rule theory in the case of complex geometry with multiple islands referring to the Indo-Pacific Maritime Continent is investigated on the basis of Godfrey’s island rule theory. The bottom friction and lateral friction of multiple channels are considered by employing the Munk and Stommel boundary layer models. Five idealized cases with various spatial distributions of islands are designed to examine the influence of shape and size of the islands. The analytical solutions of the streamfunctions of the through-flows among the islands are obtained and the volume transport through each channel is estimated. The Indonesian Throughflow (ITF) transport is then calculated using the analytical solutions with wind stress and compared with observations and previous theoretical results. The ITF transport from the multiple island rule is about 14.5 Sv during 2004–2006, which is close to the observed ITF transport (about 15.0 Sv) from the International Nusantara Stratification and Transport. We find that the multiple islands rule reproduces well the mean value and interannual variability of the observed ITF transport, and inclusion of wind stress in the North Pacific Ocean may improve the estimate of ITF transport. Sensitivity experiments indicate that frictional boundary layer thickness and channel size influence the estimated ITF transport under the multiple island framework. These results imply that the multiple island rule shows improvements in estimating the ITF transport relative to previous studies, and the multiple island rule can be used to produce long time series of ITF transport and might have implications for paleo-ITF study.

Changes in body size in some bird species from the Yucatán peninsula since the Late Pleistocene

AbstractDuring the Pleistocene, the Yucatán Peninsula reached its greatest geographic extension, with 457,650 km2, but the rise of sea level after the Last Glacial Maximum (ca. 20,000–12,000 years ago) reduced its area to 225,182 km2(50.8% reduction). These geographic extension changes likely modified the extension of different habitats throughout the peninsula, which may have also promoted morphological changes in the species that inhabit this region. Here, we tested if the reduction of the geographic size of the Yucatán Peninsula may have promoted changes in the body size of three fossil bird species and two modern bird species. We compared Late Pleistocene bird fossils specimens from Loltún, Yucatán, Mexico (ca. 28,000–11,700 ya), San Josecito Cave and Tlapacoya, and study skins of collected specimens. To assess the area‐scale ratio and to establish if body size changes occurred over time from a large to a small body size, we relied on the “island rule” as a framework; we also relied on Bergmann's rule, which postulates a decreasing in size from north to south in homeothermic species to recognize if these birds show a north to south cline. Based on body mass and measurements of the tarsometatarsi, a reliable proxy for the estimation of body size, we performed statistical analyses to test for differences between fossil and non‐fossil birds, as well as to test a gradient in body mass north to south. We found a statistically significant trend in body size changes through time, from small body sizes in fossil birds to larger body sizes in non‐fossil birds. These results suggest that relatively recent ecological factors related to the environmental carrying capacity may have promoted body size variations in birds from the Yucatán Peninsula. We also found that modern population of bird species follow Bergmann's rule.

Strength of the 'island rule' in birds is positively associated with absence of avian predators.

The similar characteristics shared by island environments have been shown to lead to common patterns of adaptations in island species, commonly referred to as the 'insularity syndrome'. A well-known example is the 'island rule', where large species become smaller on islands and small species become larger, leading to well-known cases of dwarfism and gigantism. This pattern was recently verified on a global scale, but the mechanisms underlying it have been poorly investigated. Here, we focused on the role of released pressure from predation and competition experienced by island birds. Using 120 pairs of endemic island species and their mainland sister relatives, we first verified that the island rule was detected in our dataset, and then evaluated the effects of the numbers of raptors and interspecific competitors on the evolution of the insular species' body mass. We found a strong effect of predation on body mass evolution, with a stronger island rule for species occurring on islands with no raptors, while the pattern disappears in their presence. However, we did not find an effect of competition on this pattern. Our study shows the importance of considering ecological interactions for understanding patterns of body size evolution, and the exceptions to those patterns.

Geographic variation and biogeography of the greater Japanese shrew mole Urotrichus talpoides (Eulipotyphla: Talpidae)

The island rule has been generally studied as a morphological evolution between continents and islands. Recently, an evolution between islands of the larger main islands and smaller peripheral islands in Japan has been implied. This study revealed island–island biogeography and examined the island rule between islands. We studied the skull morphology of the greater Japanese shrew mole Urotrichus talpoides Temminck, 1841 (Eulipotyphla: Talpidae). Univariate and multivariate analyses were conducted on the basis of 20 measurements obtained from 296 specimens. Our results revealed morphological differences among islands, in the overall skull size, distance of the fourth premolar to the third molar in the upper and lower jaws (P4M3 and P4M3), and the slender–robust proportion of the rostrum and braincase. P4M3 and P4M3 were commonly larger in the peripheral island populations than in the main island populations. By contrast, the overall skull size and proportion of the rostrum and braincase diverged among the peripheral islands. Therefore, gigantism of P4M3 and P4M3 was suggested in the peripheral island populations, and the island rule was partially supported; however, the island–island morphological evolution should be considered to have a different direction from the island rule due to divergent morphology in small–large skull size and slender–robust proportion among peripheral island populations.

Baron Franz Nopcsa: the man who would be king of Albania

"Franz Nopcsa, a polymath who was a founder of palaeophysiology, in addition to making great contributions on palaeontology, geography, philology and Balkan ethnography with a special focus on Albania. Coming from an aristocratic family in Transylvania, he was one of the first palaeobiologists, promoted the idea of tectonic plate movement and what is now known as the island rule, in addition to discovering 25 reptile genera and five dinosaurs. He was, however, a difficult personality with a rudeness and arrogance that antagonised many colleagues and left him marginalised. Nopcsa spent long periods in Albania, then a wild and isolated country for the West, staying with the hill people of Shkodra and travelling widely, making him a leading ethologist and expert on the languages, culture and tribal law. Nopsca challenged conventional attitudes towards sex as well, having a relationship with Bajazid Doda, which lasted till the end of their lives. Nopcsa’s financially-comfortable life ended after World War 1 and it was a struggle to support himself after that. Nevertheless, he continued to travel and put out publications. Unwell, struggling financially and depressed, on 25 April 1933 he killed Doda and himself, leaving a suicide note. Franz Nopcsa came from the last days of the Habsburg Empire with so many other radiant talents. He was one of the last ‘gifted amateurs’ who adapted poorly to the new classless world of professional academics, but his phenomenal creativity and output should not be forgotten."

Planar black holes in holographic axion gravity: Islands, Page times, and scrambling times

The present work investigates the entanglement entropies of the Hawking radiations, the Page times, and the scrambling times, for the eternal planar black holes in the holographic axion gravity. The solutions correspond to a new class of charged black holes, because the boundary diffeomorphism is broken due to the graviton mass induced by the axion fields in the bulk. The information theoretical aspects of these black hole solutions is determined upon applying the island rule for the entanglement entropy. Like non-extremal charged black holes, the radiation entropy grows linearly in the no-island configurations, while is saturated at late times by asymptotic values set by the Bekenstein-Hawking entropy in the island configurations, with the boundary being located slightly outside the outer horizon. In particular, for the extremal black planes of holographic axion gravity, we find that: (a) the entanglement entropy of the Hawking radiation is ill-defined at the early times when the island is absent; (b) it tends to a distinctive constant at the late times; (c) the late-time location of the island is indeed universal. Moreover, we investigate how the Page time is affected by the holographic massive gravity deformation. For neutral solutions at the small deformation parameter, and for charged solutions with almost-extremal deformation parameter, we find that the Page transition happens at earlier times.