Snapshot isolation and isolation history challenge the analogy between mountains and islands used to understand endemism

Aim: Mountains and islands are both well known for their high endemism. To explain this similarity, parallels have been drawn between the insularity of “true islands” (land surrounded by water) and the isolation of habitats within mountains (so-called “mountain islands”). However, parallels rarely go much beyond the observation that mountaintops are isolated from one another, as are true islands. Here, we challenge the analogy between mountains and true islands by re-evaluating the literature, focusing on isolation (the prime mechanism underlying species endemism by restricting gene flow) from a dynamic perspective over space and time. Framework: We base our conceptualization of “isolation” on the arguments that no biological system is completely isolated; instead, isolation has multiple spatial and temporal dimensions relating to biological and environmental processes. We distinguish four key dimensions of isolation: (a) environmental difference from surroundings; (b) geographical distance to equivalent environment [points (a) and (b) are combined as “snapshot isolation”]; (c) continuity of isolation in space and time; and (d) total time over which isolation has been present [points (c) and (d) are combined as “isolation history”]. We evaluate the importance of each dimension in different types of mountains and true islands, demonstrating that substantial differences exist in the nature of isolation between and within each type. In particular, different types differ in their initial isolation and in the dynamic trajectories they follow, with distinct phases of varying isolation that interact with species traits over time to form present-day patterns of endemism. Conclusions: Our spatio-temporal definition of isolation suggests that the analogy between true islands and mountain islands masks important variation of isolation over long time-scales. Our understanding of endemism in isolated systems can be greatly enriched as explanatory variables and if these models account for the trajectories of the history of a system.

Every continent, every country, and every island on the globe, offer similar problems of greater or less complexity and interest, and the time has now arrived when their solution can be attempted with some prospect of success. Many years of study of this class of subjects has convinced me that there is no short and easy method of dealing with them; because they are, in their very nature, the visible outcome and residual product of the whole past history of the earth. (Wallace, 1880)

| INTRODUC TI ON
Mountains are known for hosting about half of the biodiversity hotspots of the world (Barthlott, Rafiqpoor, Kier, & Kreft, 2005;Hoorn, Perrigo, & Antonelli, 2018;Myers, 1988;Orme et al., 2005), for their high levels of endemism (Hughes & Eastwood, 2006;Körner, 2004) and for their iconic radiations (Hughes & Atchison, 2015;Nürk et al., 2020). To explain the high concentrations of endemic species in mountain areas, parallels have long been drawn between "mountain islands" (see Glossary), which are surrounded by land, and "true islands", defined here as islands surrounded by (oceanic) water bodies. In fact, elevation-driven isolation and consequent endemism is a common situation for many mountain species, because many taxonomic groups show maximum species richness (Heaney et al., 2016;McCain, 2005McCain, , 2009McCain & Grytnes, 2010) and higher rates of endemism at higher elevations .
Besides these commonly quoted parallels, few studies directly compare the drivers of endemism (Box 1) in mountain islands and true islands (but see Itescu, 2019;Steinbauer et al., 2016).
Accordingly, comparisons of their intrinsic characteristics, including their geological ontogeny, life span, isolation characteristics and isolation history, and of the contribution of these characteristics to contemporary patterns of endemism, are uncommon. Here, we revisit the concept of isolation and its link with endemism by focusing on, and questioning, the postulate (and common assumption) that mountain islands and true islands are analogous systems. In comparing these two systems, we clarify what can be learned about islands as drivers of endemism. For convenience, we use the term "island" to refer to both mountain islands and true islands.

| ISOL ATI ON A S A S TATE AND A PRO CE SS
"Isolation" is defined in common English as "the process or fact of isolating or being isolated", highlighting the ambiguity with respect to being a state or a process. What "being isolated" means is often biased by what humans intuitively perceive as isolated ("habitat bias"; Wiens, 1995), and this is reflected in the measures to quantify isolation (Box 2). An example is the Euclidean distance or Haversine distance between islands, which is easy to quantify and conceptualize, but may neglect ecological and evolutionary dimensions of isolation, | 3 FLANTUA eT AL. such as intermittent gene flow (for a review of isolation indices, see Itescu, Foufopoulos, Pafilis, & Meiri, 2020). Here, we advocate for a more sophisticated biogeographical conceptualization of "isolation" based on the arguments that: (a) no biological system is "isolated" in an absolute sense (Taylor, Fahrig, & With, 2006); and (b) isolation has multiple spatial and temporal dimensions that relate to isolating biological and environmental processes (Gillespie, Lim, & Rominger, 2020).
The effect of isolation on endemism results from multiple ecological and evolutionary processes of different intensities (Figure 1).
For instance, higher levels of isolation (Figure 1, right side) are reflected in reduced levels of gene flow, resulting in the potential for allopatric speciation and genetic drift (Gillespie et al., 2012;Heaney, 2000). Isolation changes over time, modulated by changing environments, direction, continuity and intensity of vectors (wind, ocean currents and human transport) and by species traits (Gillespie & Roderick, 2002;Gillespie et al., 2020;Pepke, Irestedt, Fjeldså, Rahbek, & Jønsson, 2019;Steinbauer, 2017). This means that through time, an island experiences different levels of isolation ( Figure 1, top) and, as a result of the different processes at play ( Figure 1, centre), present-day patterns of endemism carry a mix of the legacies from these processes (Figure 1, bottom). Accordingly, we define isolation of an island (i.e., island-like entity) as "a continuum of processes whose strengths vary in space and time, modulated by species traits and by environmental and geological conditions that influence the (spatial) characteristics of the island and, as a result, change the degree of gene flow". Based on this definition, a change in isolation represents a change in how influential processes that lead to reduced (e.g., cladogenetic/allopatric speciation, genetic drift) versus increased gene flow (e.g., "dispersification", Glossary; Moore & Donoghue, 2007; hybridization after secondary contact: Grant, 2014;Petit et al., 2003) are for the ecological and evolutionary pool of a focal species assemblage or, in this case, the percentage endemism (Figure 1). In our theoretical framework, "isolation" is always defined from the perspective of focal taxa or assemblages (Gillespie & Roderick, 2002;Wiens, 1995), which is also the case for endemism, and is best viewed as encompassing both patterns and processes. With this definition, we also embrace the complexity of patterns and processes as quantified by landscape "connectivity" in terrestrial systems (Box 2), where "isolation" is only one of several variables to quantify the spatial composition and arrangement of patches.
Building upon our redefinition of isolation, we develop a conceptual framework for mountain islands and true islands that takes into account the degree of isolation at a certain moment in time (i.e., "contemporary"), differences in isolation between species groups, and dynamic changes of isolation over time ( Figure 2). The framework allows testing how these variables jointly contribute to contemporary patterns of endemism. We start by discussing the main dimensions that influence what we call "snapshot isolation", which is the degree of isolation of mountain islands and true islands at any point in time (Figure 2a). We then address "isolation continuity", which considers the past dynamics of isolation (Figure 2b), and the record of past

BOX 1 Identifying and measuring endemism
There is a key distinction between endemism (see Glossary) as the proportion of species that are endemic (here "percentage endemism") and endemism as the number of species that are endemic (here "endemic species richness").
Herein, we focus primarily on percentage endemism.
Two main approaches exist in the literature to identify endemism spatially: one uses geographical units as reference entities, the other a gradual range size-based approach.
The first approach is binary and defines whether a species occurs only within a given entity or not (e.g., a single island, archipelago, mountain range or country) and is, therefore, often evolutionarily meaningless. According to this definition, endemism can be nested, that is, a single-island endemic is, by definition, also an archipelago endemic. In contrast, the second approach is continuous; the smaller a species' range size, the higher is its level of endemism.
The sum of "endemism values" of all species in a given area results in its overall level of endemism and can be related to the geographical extent of the area (i.e., endemics-area relationships).
On a temporal scale, endemics can be separated into two groups: "neoendemic" and "palaeoendemic" (Stebbins & Major, 1965). The former describes species formed by "recent" speciation (e.g., divergence and reproductive isolation, hybridization and polyploidy in plants) that failed to disperse out of the ancestral area (Laffan & Crisp, 2003;Morrone, 2008). Palaeoendemics are usually relict species whose ranges became spatially restricted over evolutionary time-scales (Gillespie, 2009;Mishler et al., 2014) but can also have persisted by dispersing between volcanic islands while they emerge and perish (Fernández-Palacios et al., 2011). Empirically distinguishing between these alternatives is often difficult. As alternatives, various authors have proposed "phylogenetic endemism" (Mishler et al., 2014;Rosauer, Laffan, Crisp, Donnellan, & Cook, 2009) and "weighted endemism" (Crisp et al., 2001;Laffan & Crisp, 2003). Although different in their approaches to capture endemism, each endemism metric is inherently related and strongly influenced by the spatial extent at which it is studied (Daru et al., 2020). isolation ("isolation history"), which combines isolation continuity with the overall duration of isolation ( Figure 2c). Together, current isolation and isolation history mediate the dominant isolation-related processes driving endemism (Figure 2d). We specifically discuss how endemism depends on the continuity of isolation through time and argue that the degree and dynamics of isolation differ substantially among types of mountain islands and true island systems.

| S NAPS HOT ISOL ATION
Snapshot isolation is the degree of isolation of a location at a given the environmental difference of a location from its surroundings ("Difference sur "); and (b) the effective distance from an equivalent environment ("Distance equiv-env "). Here, "equivalent" means that an environment is similar enough to be within the environmental tolerance of a focal organism. Both dimensions depend on the pre-adaptations of a species, such as its environmental niche (Janzen, 1967) and dispersal ability, which could potentially evolve at the focal location. Life-history strategies of evolving clades affect success rates for colonization of islands and island-like environments (e.g., Pepke et al., 2019). Thus, the isolation of a given location varies between organisms according to the breadth of their environmental tolerance, dispersal capacity and adaptations to use existing dispersal vectors to establish in new locations (Gillespie & Roderick, 2002;Gillespie et al., 2020;Steinbauer, 2017).

| Environmental difference from surroundings (Difference sur )
This dimension is related to the concept of the inhospitable matrix and the patch-corridor-matrix contrast (Forman, 1995), but we question the notion of using a "habitat patch" to represent islands as units of analysis to understand species richness (also see Fahrig, 2013). Here, we assume that the difference in environmental conditions between a location and its surroundings, here termed Difference sur , is sufficient to impose ecophysiological constraints on a particular species' range, such as the prevention or the inhibition of gene flow through species dispersal and establishment. Differences in environmental conditions are easiest to identify when there is a sharp transition in space between two environments, such as between land and water at the coast of true islands. In such cases, the difference is so large for most organisms that isolation is often measured simply by the distance to another landmass (See section 3.2; Itescu et al., 2020).

BOX 2 Isolation, connectivity, connectedness and fragmentation
The way that isolation in island biogeography has commonly been defined and used is a solely distance-based measure. "Decreased isolation", meaning decreased distances between islands, is frequently equated with "increased connectivity" in the literature, suggesting a continuous gradient of isolation along which connectivity represents the other side of the same coin. This usage poorly represents the concept of "connectivity" as formalized originally in landscape ecology. Connectivity in a landscape as defined by Taylor et al. (1993;Glossary) was always intended to include both the physical structure and arrangement of patches and also the behaviour of organisms within the landscape in response to these physical characteristics and the surroundings. The former was described to be the "structural connectivity" (Glossary), often quantified by interpatch distances alone (e.g., straight-line distance, nearest-neighbour measures), but can also include the surface area of the patch, type of habitat and suitability of the patch for focal species [nicely summarized by the "intrapatch connectivity" within the concept of "habitat availability" or "reachability" by Pascual-Hortal & Saura (2006) and Saura & Pascual-Hortal (2007)]. "Connectedness" (Glossary) refers only to the degree of physical connection between patches. Isolation as usually defined in island biogeography is thus one aspect of structural connectivity. However, "connectivity" is not properly captured by an index of linear distances alone.
The variability in the movement and behaviour of taxa (e.g., resulting from influences of dispersal capacities and directional dispersal vectors) is represented by "functional connectivity" (Glossary). In landscape ecology, the importance of an organism-centred approach to quantification of connectivity has been much emphasized (e.g., Pearson, Turner, Gardner, & O'Neill, 1996;Saura & Rubio, 2010;Taylor et al., 2006;Wiens, 1995); this is ignored when considering only structural connectivity. The functional connectivity explains why a given arrangement of patches/ islands can be perceived as being both connected and disconnected by two species with different dispersal capabilities and opportunities (Taylor et al., 2006). Thus, "connectivity" is an inherent description and integration of the landscape characteristics and the behaviour of taxa within this landscape (Tischendorf & Fahrig, 2000).

Numerous connectivity indices have been developed and
later on compared and reviewed by Tischendorf and Fahrig (2000) and by Saura and Pascual-Hortal (2007), who also ecotones, such as the upper forest line (highest elevation of con- Although clearly bounded by a water body, true islands also feature a mix of transitions, because they are often environmentally heterogeneous (e.g., large spatial variety in soils, topography and microclimates). For true islands, this results in different degrees of snapshot isolation, both within islands and between islands within a (meta-)archipelago. The Hawaiian Islands, for instance, show a high environmental heterogeneity (Seijmonsbergen, Guldenaar, & Rijsdijk, 2018). Hawai'i is the youngest island of the archipelago Some aspects of the abiotic diversity are low attributable to the relative youth of the mountain, whereas its elevation creates high variability in microclimatic zonation and orographic rainfall, producing a wide range of vegetation zones and, as such, represents a sky island within a true island . In contrast, one of the oldest islands of the archipelago, Kauai (c. 5.3 Myr old; 1,598 m a.s.l.) displays high abiotic environmental variability and limited microclimatic zonation. Thus, although Difference sur can be characterized by a sharp boundary, this dimension is better regarded as a continuum ranging from abrupt (e.g., water and land at the coast of a true island) to gradual transitions (e.g., gentle slopes), or combinations of the two, and is applicable to a wider range of systems with island-like properties (Gillespie & Roderick, 2002).

| Effective distance from equivalent environment (Distance equiv-env )
The geographical distance between landmasses is often the only dimension of isolation accounted for in models of island biogeography and is traditionally measured as straight-line distances to other landmasses (Itescu et al., 2020;Whittaker & Fernandez-Palacios, 2007).
In simulation models, this has proved valuable to test hypotheses on the influences of distance to the mainland and island size on proposed an approach that is potentially useful for comparing mountain islands and true islands (further details in Supporting Information Appendix S1).
The concept of "fragmentation" (Glossary) has gone through a similar process of becoming increasingly diffuse and ambiguous in its usage since its original formulation [see reviews by Franklin et al. (2002) and Fahrig (2019)]. Often (mis)used in the literature as analogous to the opposite of "landscape connectivity", originally it described only the breaking up of habitat that results in reduction of surface area, increase of patch numbers and increase of isolation, without accounting for the responses of organisms.

BOX 2 (Continued)
F I G U R E 1 Isolation is a continuum of different processes that interact with species traits to result in particular levels of endemism. Darker/warmer and lighter/colder colours in the bars indicate high and low levels, respectively. The degree of isolation of an island or other insular system changes, often resulting in different processes influencing the species composition and thus the degree of endemism in an island. A lesser degree of isolation (left) is not a synonym for higher "connectivity" (see Box 2). Percentage endemism is the percentage of native species that are endemic. For definitions of the terms "endemism", "taxon cycle" and "dispersification", see Glossary endemism (Rosindell & Phillimore, 2011). However, the effective isolation captured by measures of straight-line distances can vary between species and higher-level taxonomic groups (Gillespie & Roderick, 2002;Weigelt & Kreft, 2013). Defining isolation only by distances between landmasses ignores the role of the environmental tolerances of species or assumes that all landmasses are homogeneous. It also ignores differences between species in their ability to use existing dispersal vectors and the directionality of many vectors (e.g., wind or water currents; biotic agents; Gillespie et al., 2012Gillespie et al., , 2020. Thus, we argue that Distance equiv-env is more meaningful as a species-specific measure, which can differ between co-existing species Steinbauer, Irl, & Beierkuhnlein, 2013;Weigelt & Kreft, 2013). The equivalent environments may be within the same island, archipelago or mountain range, or beyond.
Despite pronounced gradients, delimiting mountain islands and quantifying Distance equiv-env can be challenging in the absence of clear boundaries between habitats that vary in suitability for focal species (Fahrig, 2013). For "alpine islands" (Glossary), the upper forest line might serve as a simplified equivalent to the coastline of true islands in defining relatively pronounced boundaries, making it possible to use connectivity metrics that require clearly delimited units of analysis (Supporting Information Appendix S1). However, such landscape ecological measures of "connectivity" (Box 2) are rarely used in marine archipelagos (but see Cabral, Weigelt, Kissling, & Kreft, 2014). Comparing connectivity (ideally from the perspective of a focal species) between archipelagos of mountain islands and true islands (Table 1) could help in estimation of the importance of the spatial organization of islands in shaping endemism, especially when integrated over time-scales as long as the Quaternary (section 4). Additionally, the use of directional network models that take into account island age (Carvalho, Cardoso, Rigal, Triantis, & Borges, 2015) and randomized simulations to test the effect of archipelago configuration on richness in "oceanic archipelagos" (Glossary; Jõks & Pärtel, 2019) can provide additional common ground to compare mountains and true islands.

| ISOL ATION CONTINUIT Y
The dimensions that define snapshot isolation are dynamic and change through time. Isolation continuity ( Figure 2b) comprises two main components: (a) the temporal variability of snapshot isolation, and (b) the initial level of isolation when the island is formed.
Isolation history (isolation continuity combined with the overall duration of isolation) is addressed in Section 5.  Table 2; Norder et al., 2018Norder et al., , 2019Voris, 2001). Higher sea levels during interglacials (Figure 3a) caused many true islands to become smaller and more isolated, whereas during glacial periods they were larger and sometimes connected to other islands or continents ( Figure 4a). Some archipelagos, such as the continental islands of the Seychelles (Figure 4a), the atolls of Phoenix and Aldabra, largely submerged for a short period in the last interglacial F I G U R E 2 A framework for endemism in mountain islands and true islands, derived from bringing together key aspects of the overall isolation of these islands and its dynamics through time. This scheme highlights both similarities and differences between mountain islands and true islands and between different types of islands and mountains. We separate important dimensions of isolation, each of which is expected to affect the amount and nature of contemporary endemism at any given place. (a) Snapshot isolation is the degree of isolation at any given moment in time, depending on species traits. (b) Isolation continuity describes the temporal aspect of isolation in terms of its dynamics through time and the degree of isolation when the island arose. Note the reversed axis for temporal variability of isolation. (c) Isolation history considers the total duration of isolation (time) alongside isolation continuity. (d) These aspects of isolation history together shape current patterns of endemism, in conjunction with current levels of isolation of the island, which in most cases can be considered to represent the last c. 2,500 years (Lambeck et al., 2014). The considerable variation within the types of insular systems depicted is not shown; instead, each type is located according to what we suggest might be representative of that type overall and integrated across the full range of organisms. For definitions of the terms, including "oceanic islands", "continental shelf islands" and "continental fragments", see Glossary (LIG, c. 129-116 ka;Felde et al., 2020;Norder et al., 2018). The consequences of sea-level changes on isolation were less drastic for remote "hotspot volcanic oceanic islands" (Glossary), such as

| Temporal variability of isolation
Hawai'i, the Canary Islands, Azores and Galápagos, which mainly lost land but maintained much of their original geographical con-

True island examples
Stepping stone archipelago between two or more large surface areas Stepping stone archipelago between mountain ranges: Stepping stone archipelago between a large island and the mainland or between two large islands: Note: Here, we draw parallels between archipelago configurations as proposed by Warschall (1994; mountain island examples) and true islands. Further research could assess similarities and differences in patterns of endemism among and within each type of archipelago, and among and between mountain islands and true islands, also considering their isolation histories; the archipelago types proposed by Warschall represent only present-day snapshot isolation (Figures 3 and 4). The effects of past climatic fluctuations on processes related to endemism have likewise been substantial on mountain islands (Table 1; e.g., Adams, 1985;Simpson, 1974;Sklenář & Balslev, 2005). average (set here at 0°C), based on EPICA Dome C Ice Core (Jouzel et al., 2007). "[×0.5]" refers to the calculated factor of polar temperature to global mean surface temperature. Adjusted from Fergus (2018). (d) The percentage of time over the last c. 800 kyr that temperatures were within each interval (0.5°C bins). The intervals marked with asterisks correspond to the configurations displayed in Figure 4 where glacial periods are associated with a greater connectivity, a long-persisting notion for alpine islands has been that glacial periods induced increased isolation because extensive glaciers reduced alpine habitat to smaller islands along the outer ridges of the mountains, the so-called "glacial refugia" (Hewitt, 2000;Schönswetter, Stehlik, Holderegger, & Tribsch, 2005;Willis & Whittaker, 2000; Figure 4b, Alps). Based on this notion, high temporal variability of isolation would lead to higher extinction and lower phylogenetic diversity and would have a negative influence on endemism, especially when it involves fragmentation and loss of area (Svenning, Eiserhardt, Normand, Ordonez, & Sandel, 2015). Current endemism patterns would, therefore, result more from range contractions of formerly widespread species and less from in situ speciation (Tribsch & Schönswetter, 2003). However, many high-elevation ecosystems  & Filatov, 2018;Rull, 2005). This strengthens the support for hypotheses on Quaternary diversification that move beyond refugial speciation alone (Rull, 2020). In summary, in mountain islands high temporal variability of isolation has been suggested to be both a strong driver of extinction with a negative influence on endemism   (Rull & Nogué, 2007); East African rift (Chala et al., 2017;Sklenář et al., 2014) Ryukyu islands (Wepfer, Guénard, & Economo, 2016); Azores (Rijsdijk et al., 2014) previously part of another landmass from which it separated (i.e., initially not isolated, "fragment islands" sensu Gillespie & Roderick, 2002) is important for understanding the patterns of endemism (Sondaar & Van der Geer, 2005). When the initial level of isolation is high and persists throughout history, evolution has a limited set of lineages to work on. Here, the species composition will mostly become neoendemic through time as a result of cladogenesis (Gillespie & Roderick, 2002;Emerson & Gillespie, 2008: figure 1). Initial arrival of species is through rare dispersal (e.g., Whittaker, Bush, & Richards, 1989) of airborne or seaborne species with high dispersal capabilities. Depending on the distance to continents or pre-existing true islands, this set of species corresponds to a filtered subset of the regional species to the dispersal capacity of species and to their ability to colonize island environments successfully (Gillespie et al., 2020;Kisel & Barraclough, 2010;Weigelt et al., 2015), also described as the attenuation of species composition across islands and archipelagos (Lomolino & Brown, 2009;Whitehead & Jones, 1969). It results in phylogenetically clustered island assemblages and "disharmonic" species assemblages (Glossary; König et al., 2019), with taxa and/ or entire groups from the regional pool missing (Carlquist, 1974;Emerson & Gillespie, 2008;Gillespie & Roderick, 2002;Whittaker & Fernandez-Palacios, 2007).

| Initial level of isolation
In contrast, fragment islands that were initially connected to existing ecosystems before separating from them (e.g., continental island systems) start out with species sets that are more representative (i.e., more harmonic) of the regional pool (Gillespie & Roderick, 2002). This, in turn, affects how, and how fast, endemism develops if isolation is strong enough and persists long enough (see isolation history in section 5). When isolation continues, species richness "relaxes" to a new equilibrium (Diamond, 1972). Over time, speciation can lead to new species, and some of the initial island species might become relicts of extinct mainland species, forming palaeoendemics of once widely distributed taxa (Gillespie, 2009 et al., 2017). Equivalent examples exist for many insect groups (Gillespie & Roderick, 2002).
The level of disharmony not only affects functional diversity by causing whole groups of species and sets of traits to be present or absent, but also has knock-on effects on the speed and direction of evolution of the taxa that are present. For example, on Luzon (Philippines) only two endemic mammal clades have given rise to c. 50 species that have evolved via repeated elevation-driven isolation on different mountains within the island (Heaney et al., 2016).
The overall lack of terrestrial mammals on many oceanic islands typically reduces selection for anti-predator defences (e.g., tameness; Cooper, Pyron, & Garland, 2014) and unpalatability of plants to herbivores (Cubas et al., 2019). Good colonizers repeatedly lose dispersal capacity (e.g., flightless birds) and start to occupy niches typically occupied by "missing" species groups from mainlands (e.  (2019)]. Such directional evolution to exploit available opportunities is not only so common as to be predictable but may also happen rapidly (e.g., Knope, Morden, Funk, & Fukami, 2012;Linder, 2008). When this evolution involves loss of dispersal capacity, it can increase speciation rates by increasing the effective isolation of populations (Jocque, Field, Brendonck, & de Meester, 2010).
In contrast to true islands, the species composition of mountain islands is likely to be more harmonic with the regional pool than that of oceanic islands, especially Darwinian islands, because the isolation of mountain islands was initially low (because they developed on a continent) and increased gradually over geological time. Most of the regional species pool was consequently available to contribute to the build-up of mountain taxa diversity, and vice versa (mountains as "cradles" of biodiversity; see several chapters by Hoorn et al., 2018). The "birth" of alpine islands is related to the geo-ecophysiological processes that initiate the isolation of a mountain island situated on a continent. In general, mountains develop from a lower (or less topographically varied) landscape, and the initially low elevational isolation increases as uplift continues during the orogenic phase . If uplift continuously exceeds erosion rates, and elevations thereby increase, the limit of the physiological tolerances of trees can be reached, and novel al- and Cleef (1986); Wijninga (1996).

Duration of isolation (time)
General dynamic model of oceanic island biogeography (GDM) and ATT 2 (i.e.,  (2018) and references therein; Wijninga (1996). In the páramos of the Northern Andes, for example, the early species-poor páramo (the "proto-páramo"; Hooghiemstra, 1984;Van der Hammen & Cleef, 1986;Van der Hammen et al., 1973) was later enriched by the numerous immigrating genera from Neotropical and temperate zones (Cleef, 1979;Sklenář, Dušková, & Balslev, 2011;Wallace, 1880). Present-day páramo endemism, therefore, consists of a mix of taxa originating from páramo ancestors and more recent immigrants, both of which contributed to endemism through evolutionary radiations during the Pleistocene (Morrone, 2018;Nürk et al., 2020). Thus, the initial isolation of mountain islands is often less than for true islands, with an increase in disharmony and endemism with respect to the regional species pool through time.

| ISOL ATION HIS TORY
The length of time over which isolation has operated (duration of isolation) is the final key dimension in our framework for understanding patterns of endemism. We combine isolation continuity with the duration of isolation to discuss "isolation history" (Figure 2c).
The first models of island biogeography, including the equilibrium  (Table 3; Borregaard et al., 2017;Borregaard, Matthews, Whittaker, & Field, 2016). Processes such as volcanic activity, uplift and erosion influence the processes that generate and maintain endemic species on these islands through time. The duration of isolation (from island emergence to submergence) is considered to have a positive influence on the presence of endemics such as those observed in ancient continental fragments, including New Caledonia and Madagascar (Kier et al., 2009). Similar patterns are observed in ancient mountain areas, such as southwestern Cape (South Africa) and southeastern Australia (Goldblatt & Manning, 2002;Antonelli et al., 2018: Supporting Information). The total duration of isolation that species experience can be increased effectively in oceanic archipelagos through the progression rule (e.g., Shaw & Gillespie, 2016), according to which island lineages may persist for longer than the islands they inhabit because they colonize new islands in the archipelago before the original islands disappear.
For most mountain islands and true islands, accurate data on the timing of isolation based on the age of the island setting are scarce. In mountainous settings, relief formation can be estimated by various radiometric dating techniques of island substrates or using thermochronometric data that measure the time at which certain minerals crossed thermal boundaries in the upper 10 km of the crust . However, these estimates of age do not necessarily represent when a mountain reached the necessary elevation for elevationl zones of ecosystems to form. Such radiometrically dated emergence ages are likewise problematic for true islands to estimate when an island emerged fully from the sea (Borregaard et al., 2017). Palaeoaltimetric approaches are often complex and highly debated, and new ones are under development (Table 3; see overview table by Perrigo, Hoorn, & Antonelli, 2020).
The influence of island ontogeny on evolutionary dynamics has been assessed for individual islands (Lim & Marshall, 2017). However, to date, a global synthesis of palaeoaltimetric data that contains both uplift rate and palaeoaltitude with a high degree of fidelity is still lacking, hindering our ability to infer the age of a mountain range and thus the time-scales over which geo-evolutionary processes have influenced endemism in isolated conditions. Multi-proxy studies that integrate different palaeoaltimetry proxies (Perrigo et al., 2020) with adequately calibrated phylogenies would be of great value (also see Pennington, Richardson, & Lavin, 2006).

| CON CLUS IONS
Present-day conditions provide only a snapshot within the life span of mountains and islands, and the past is bound to have left a strong legacy on modern patterns of endemism (Rull, 2020;Wallace, 1880;Whittaker, Willis, & Field, 2001). How much the present is representative of the past depends on "isolation continuity" and "isolation history", which are driven by geological and environmental changes through time. Islands and archipelagos (sensu lato) have taken numerous spatial configurations, with changes in surface area, connectivity and environmental conditions. As discussed throughout this contri- Isolation is key to understanding patterns of endemism, but it is a complex phenomenon that varies greatly between taxa and among and within islands, and even more so for mountain systems, depending on their surrounding landscape matrix. Arguably, the strongest commonality between true islands and mountain islands is their high variability of isolation in space and time. Although we acknowledge that the "sky island" and "mountain/alpine islands" analogy is useful to some extent, we argue that a more nuanced spatio-temporal approach will improve our understanding of endemism in both mountains and true islands, in addition to other biogeographical patterns.
Such an approach is equally applicable to any type of island-like system (Whittaker & Fernandez-Palacios, 2007). We argue that it is essential to embrace the manifold dimensions of isolation that may affect endemism (and other biogeographical and ecological patterns) in different ways, and we provide a framework to do so. Similar levels of endemism in island and mountain systems may result from different pathways in response to changing environmental conditions ( Figure 2), emphasizing the need for better representation of historical processes in models of contemporary biodiversity. We suggest that research on endemism needs to move beyond the focus on processes that promote allopatry and to explore other drivers of diversification, such as isolation history and shifting degrees of archipelago connectivity, while acknowledging differences between species.

ACK N OWLED G M ENTS
We would like to thank Editor-in-Chief Brian McGill for supporting the submission of this paper to Global Ecology and Biogeography.  Connectedness, The degree of physical connection between patches/islands. Related to "structural connectivity" that corresponds to spatial relationships (continuity and adjacency) between patches or islands. It is a structural attribute of a landscape and can be mapped [Farina (2000) citing Baudry, 1984].; Connectivity, (a) The degree to which the landscape facilitates or impedes movement among resource patches (Taylor, Fahrig, Henein, & Merriam, 1993). This definition emphasizes how the types, amounts and arrangement of habitat or land use on the landscape influence movement and, ultimately, population dynamics and community structure (Taylor et al., 2006). (b) The process by which subpopulations are interconnected in demographic functional units (Farina, 2000). (c) The functional relationship among habitat patches, owing to the spatial contagion of habitat and the movement responses of organisms to landscape structure (With, Gardner, & Turner, 1997); Connectivity, functional, The degree of reachability of suitable habitat based on the dispersal abilities of a species. For example, valleys and sea constrain functional connectivity more for amphibians than for birds (also see Supporting Information Appendix S1).; Connectivity, structural, Corresponds to spatial relationships (continuity and adjacency) between the structural elements of a system. A decrease of structural connectivity, for example, owing to a change in sea level, implicates fragmentation of previously connected islands (increase of number of islands), loss of surface area (habitat loss) and increase of inter-island distance (isolation). This concept is independent of the ecological characteristics of the species (see "functional connectivity"; also see Supporting Information Appendix S1 Disharmony, (a) Taxonomic "imbalance" of island biotas (Carlquist, 1965(Carlquist, , 1974. (b) Biased representation of higher taxa (e.g., families) in island biotas compared with their mainland source regions (Whittaker & Fernandez-Palacios, 2007) as the result of selective assembly (see review by König et al., 2019). Disharmony represents a case of phylogenetic clustering that arises from nonrandom distribution of traits that foster island colonization among the evolutionary lineages in the source species pool.; Dispersification, Increased rates of diversification associated with biogeographical movements into newly formed environments (Moore & Donoghue, 2007).; Endemism, (a) A species (or other taxon) is defined as endemic if its natural range is restricted to a confined area (Anderson, 1994). (b) Species that have a relatively narrow geographical range, such as on/in a particular island, habitat or region (Moorcroft, 2009: p. 445). (c) Species with small geographical ranges (Hughes, 2009: p. 482). The more range restricted a species is, that is, the smaller its range size or the smaller the reference area in which a species occurs (e.g., mountain range versus single mountain top or archipelago versus single island), the higher its endemicity, that is, the more "endemic" it is ( (a) The breaking up of a habitat, ecosystem or type of land use into smaller parcels (Curtis, 1956;Forman, 1995;Moore, 1962; see reviews by Fahrig, 2003Fahrig, , 2019. The definition of habitat fragmentation implies four effects of the process of fragmentation on habitat pattern: (i) reduction in habitat amount, (ii) increase in number of habitat patches, (iii) decrease in sizes of habitat patches, and (iv) increase in isolation of patches (Fahrig, 2003). (b) The state of habitat fragmentation as discontinuity, resulting from a given set of mechanisms in the spatial distribution of resources and conditions present in an area at a given scale that affects occupancy, reproduction or survival in a particular species (Franklin, Noon, & George, 2002). (c) The process of habitat fragmentation as the set of mechanisms leading to that state of discontinuity (Franklin et al., 2002). For a full list of definitions of fragmentation, see Isolation history, Considers the historical dynamics of isolation of an island/archipelago in terms of: (a) "isolation continuity", and (b) the overall duration of isolation.; Mountain islands, Mountains or biomes within mountains (or mountain ranges) in which the geological features, species composition, habitat and ecosystem are distinct from the surrounding landscape, often characterized by sharp gradients that accentuate the "island" boundaries. Used in this paper as a general term to describe "alpine islands", "habitat islands in mountains" and "sky islands".; Mountain island archipelagos, Biogeographical coherence of an assemblage of mountain islands resembling limited species dispersion and in situ evolutionary processes seen in true island archipelagos.; Oceanic islands/ archipelagos, (Clusters of) islands located on oceanic crust, either at plate boundaries near subduction zones (arc islands) or those which were formed by hotspot volcanism (see hotspot volcanic oceanic islands). The geodynamics of islands are highly complex, and more detailed geological classifications are provided by Ali (2017) and Nunn, Kumar, Eliot, and McLean (2016).; Patch, (a) A relatively homogeneous area within a landscape that differs markedly from its surroundings (Fischer, Lindenmayer, & Hobbs, 2009: p. 431). (b) A discrete, bounded area of any spatial scale that differs from its surroundings in its biotic and abiotic structure and composition (Peters, Gosz, & Collins, 2009: p. 458).; Percentage endemism, The proportion of species that are endemic. At large scales, percentage endemism can reflect speciation , whereas at smaller scales (e.g., on the plot scale) percentage endemism describes compositional uniqueness (e.g., and species composition that are as different from their surroundings as if they rose from some remote sea (Heald, 1951(Heald, , 1967. (c) Geological features with a species composition or ecosystem distinct from the surrounding landscape, often with steep gradients that accentuate the "island" boundaries, for example, table-top mountains in Venezuela and Colombia (Rull, 2010) and the Madrean archipelago (see Table 1). More recently, the term has been expanded also to describe mountain top islands, such as the high-elevation páramos of the Northern Andes (e.g., Diazgranados & Barber, 2017) and the Hengduan sky islands (e.g., He & Jiang, 2014). As such, true islands can also include sky islands with numerous endemics, for example, Sulawesi and Luzon.; Snapshot isolation, The degree of isolation of mountain islands and true islands at a point in time. The degree of isolation of mountain islands and true islands at a point in time.; Taxon cycle, (a) Temporal sequence of geographical distribution of species from (i) colonizing through (ii) differentiating and (iii) fragmenting to (iv) specializing (Gillespie, 2009: p. 144). (b) Taxon cycles are sequential phases of expansion and contraction of the ranges of species, usually associated with shifts in ecological distribution and adaptations to changing ecological relationships through the cycle (Ricklefs & Bermingham, 2002, citing Wilson, 1959, 1961.; Vicariant speciation, A mode of allopatric speciation that involves a physical barrier, such as an ocean channel or mountain range, that subdivides a range and prevents gene flow between the two resulting populations (Phillimore, 2013)..

AUTH O R CO NTR I B UTI O N S
Initial ideas for this paper were developed at the Macroecology meeting in Vienna (2017)  Richard Field's main interests are macroecology, biogeography, islands, geodiversity and plant ecology, with particular focus on biodiversity and the forces that structure ecological communities.