Certain ecosystems are known to be inherently more susceptible to the colonisation by a non-native species than others. At any one time within a population of N ecosystems (which could be different ecosystem types or different areas of a single ecosystem type), the rate of change in the number of Susceptible ecosystems (S) will be a function of the rate at which Susceptibles become infected and move to the Exposed class (λ, the force of infection), become resistant and move to the Resistant class (μS) , as well as the rates at which Infectious (ξI), Exposed (θE) and Resistant (νR) classes become Susceptible (Fig. 2, Eqn 1).

$\frac{dS}{dt}=-\lambda +\xi I+\theta E+vR-\mu S$ (1)

Susceptibility can be viewed at two levels: amongst different types of receptors (e.g. woodlands, grasslands and wetlands) and within a single receptor type (e.g. coniferous forest). Intriguingly, the balance of effort has differed between disease and invasion studies: the former have focused more strongly on intra-host variability (Fellous et al. 2012; Tack et al. 2014; Vale 2013), whereas the latter have largely addressed why some ecosystems are more vulnerable to invasion than others. This is understandable since many microparasites have a relatively-narrow host range (Loker and Hofkin 2015), but a single non-native species can often colonise a wide range of different ecosystem types (Affre et al. 2010). Nevertheless, similarities exist in the factors influencing the relative susceptibility of different host species to microparasites and ecosystems to non-native species. For example, the absence of specific tissue or cellular receptors for colonisation of hosts by microparasites (Doran et al. 2016; Toruno et al. 2016) is equivalent to the absence of suitable resources (e.g. diet, habitat, symbiont) for a non-native species (Gioria and Osborne 2014). Temperature of the host may limit microparasite growth (Fang et al. 2016), just as it can limit the establishment of poikilothermic non-native animals and frost-intolerant plants (Hulme 2017). A lack of the exact nutrient requirements to support microparasite growth or development (Johnson et al. 2010; Smith 2007) corresponds with the scarcity of non-native plants in nutrient-poor habitats. Even the dynamic nature of a host’s immune response through phagocytic defences may have its counterpart in the role of natural enemies in limiting non-native species to certain ecosystems (Schulz et al. 2019). External drivers of susceptibility, such as ecosystem fragmentation and land-use change, can similarly affect invasions by non-native species (Riitters et al. 2018), as well as the spread of infectious diseases (Gottdenker et al. 2014).

Analogous factors also exist that influence susceptibility to microparasites and non-native species within a specific host or ecosystem. Host age, homeostatic disturbance, intercurrent disease, microbial antagonism and MHC diversity have all been proposed to influence host susceptibility to microparasites (Casadevall and Pirofski 2018). A similar list can be generated for the susceptibility to non-native species of an individual ecosystem type that includes successional age, habitat disturbance, the presence of other non-native species, competition with resident species and native species diversity (Guo et al. 2015). The concept of “invasional meltdown”, where one non-native species facilitates the invasion by other species (Simberloff 2006), has similarities in the multiple opportunistic bacterial infections of individuals with HIV (Joos et al. 2007). Susceptibility is not necessarily an immutable characteristic of a receptor and external drivers, such as climate change, increases or decreases in resource supply, pollution etc., can lead to previously Resistant receptors becoming Susceptible (Guo et al. 2015; Johnson et al. 2010).

However, an important issue when examining ecosystem vulnerability to invasion is the need to control for variation in exposure to colonisation by non-native species (e.g. propagule pressure), because this is rarely independent of the type of ecosystem. When this has been taken into account, emerging hypotheses are that ecosystems that naturally experience recurrent disturbances and are rich in available nutrients are most susceptible to invasion (Aikio et al. 2012; Chytrý et al. 2008). The receptor-centred framework presented here requires that inherent susceptibility is assessed independently of exposure (e.g. propagule pressure and force of infection), since it provides the basis for clearer prioritisation of the ecosystems most at risk from biological invasions (Catterall et al. 2012).

The transitions between the Susceptible and Exposed and Infectious states have received considerable empirical and theoretical attention with reference to the factors shaping disease transmission (Johnson et al. 2019). The force of infection (λ) depends on the number of Susceptible receptors (S), the proportion of Infectious receptors (I/N) and the transmission rate (β) which is a function of the rate of contact between receptors and a per-contact probability of infection (Kleczkowski et al. 2019).

$\lambda =\frac{\beta St}{N}$ (2)

Epidemiological approaches have tended to focus on the spread of a disease following its establishment in the host population (Diekmann et al. 2013), whereas the study of biological invasions has stressed the role of propagule pressure (i.e. the number and frequency with which individuals of a particular non-native species are introduced) in determining whether or not the agent will establish itself in a specific ecosystem (Simberloff 2009). However, estimation of propagule pressure has largely focused on the raw numbers of individuals of a particular non-native species arriving into an ecosystem (equivalent to the contact rate) and less on the likelihood of establishment per contact (equivalent to the per-contact probability of infection). Vectors often facilitate the transmission of agents of disease and non-native species. Yet, although the terminology is the same, the processes by which vectors transmit microparasites and spread non-native species are often quite different. In epidemiology, a vector is usually an alternative host, whose demography and status (Susceptible, Exposed, Infectious etc.) is a fundamental component of disease dynamics. Furthermore, living vectors may exhibit specific host-seeking behaviour that will increase transmission rates (Wynne et al. 2020). In contrast, the most important vectors of non-native species are humans and human-driven instruments (e.g. boats, trains, cars) that may provide passive transport between locations (Hulme et al. 2008). The extent to which such passive vectors link similar ecosystems and facilitate transmission has yet to be explored in detail. There are, of course, exceptions to this dichotomy, such as the role played by unclean needles in the spread of HIV amongst intravenous drug users (Smith et al. 2005), the deliberate mailing of anthrax spores to unfortunate victims (Arora et al. 2012)), the role of frugivores in the dispersal of non-native plants (Dawson et al. 2011) and the many occasions where humans have selected, bred and deliberately released non-native species for hunting, fishing or biological control. It is becoming increasingly clear that, just as in the case of non-native species, complex vector components and multiple hosts are often involved in the transmission of emerging zoonotic diseases (Engering et al. 2013; Hulme 2014).

In the case of local direct transmission or spread of diseases, the simplest model assumes that exposure is a product of the numbers of Susceptible and Infectious receptors linked by a transmission function (Diekmann et al. 2013; Kleczkowski et al. 2019). Epidemiological SEIR models often assume homogenous mixing of Susceptible and Infectious receptors as a result of random movement of the receptors, but ecosystems cannot be assumed to “mix” in the same way as mobile hosts. The assumption of homogeneous mixing can provide general insights once an epidemic is well established, but can lead to errors if incorrectly assumed at the earliest stages (Del Valle et al. 2013). Instead, invasion models have focused on the agents’ dispersal kernel (Sullivan et al. 2017). Models of the dispersal of non-native species have moved from simple diffusion processes to explore stratified dispersal (multiple functions) and integro-difference equation approaches in order to capture the importance of rare long-distance dispersal events (Kot et al. 2012). Such dispersal models may be equally appropriate for microparasites, as in the case of foot and mouth disease in the UK, where local spread was from aerial plumes and typically modelled via a transmission kernel, based on Euclidean distance, but long distance movement occurred via vehicles (Keeling et al. 2003). Indeed, there is an increasing push to model microparasite transmission and non-native species dispersal in similar ways (Lindström et al. 2011).

Where mixing is known to be non-random but the variation in individual contact rates is poorly known, lattice models, in which random connections between neighbouring sites facilitate transmission, have been used to assess the role of connectivity and spatial heterogeneity in disease epidemics (Liccardo and Fierro 2015). However, when the movement of agents is facilitated by human activity (e.g. shipping, airfreight, railroads) and the origins and destinations of the activity are known, gravity models can be used to assess the potential spread of disease (Charu et al. 2017) and non-native species (Drake and Mandrak 2014). These models estimate rates of transmission as a function of the distance between receptors. Where additional data are available on contact rates between receptors, network models are appropriate to predict future disease and non-native threats (Silk et al. 2017). Receptors have transmission contacts only along the links in a specified network of hosts or ecosystems. The existence of a connection predisposes the receptors to infection, but does not guarantee it. The number of connections each receptor has with others can be modelled by choosing a particular degree distribution for the network (e.g. a power-law would describe most receptors having few connections but a small number having many). In these models, the agent usually originates in one or more randomly-selected Infectious nodes in a population that is otherwise made up of Susceptible receptors. For discrete time models, in every time-step, all the Susceptible neighbours of the Infectious nodes become infected with probability β (the transmission rate) per Infectious neighbour (Enright and Kao 2018).

Network models have been used to model the connections between individuals linked to the spread of sexually-transmitted diseases (Beyrer et al. 2012), the spread of COVID-19 in cities (Xue et al. 2020), the global movement of shipping that enables the spread of non-native species (Seebens et al. 2019), the dissemination of plant pathogens through international horticultural trade (Moslonka-Lefebvre et al. 2011) and parasite transmission in wildlife (White et al. 2017). Different network topologies have a significant impact on disease dynamics and can have a stronger impact on outbreak magnitude than fundamental microparasite features such as transmission rate, infection duration and immunisation ability with important implications for management and control (Strona et al. 2018). In both gravity and network models, key considerations underpinning the likelihood of transmission include the life-history traits of the agent, such as how likely it is to survive and/or increase in prevalence during transport, the ease of detection of the agent or its symptoms, as well as attributes of the pathways (or connections) themselves. These attributes include the duration and condition of transport and the probability of transfer to suitable receptors on arrival. As the importance of landscape and spatial heterogeneity in the transmission and dispersal of disease and non-native species is recognised, so it is likely that these fields will increasingly converge on common modelling approaches (Claflin et al. 2017; de la Fuente et al. 2018; Kirby et al. 2017).

Once it has been infected or colonised by an agent and assuming there is growth of the agent population, a Susceptible receptor enters the Exposed state. The transition of Exposed receptors to the Infectious state is determined by the latent period or lag-phase (determined by 1/σ), that reflects the time elapsed before the emergence of symptoms of disease or noticeable impacts of the non-native species. For many diseases, the “latent period” is so brief that the Exposed state is not incorporated into compartment models, although the human prion disease, kuru, has an incubation period of between 40 and 60 years (Collinge et al. 2006). In contrast, the temporal dynamics of many non-native species show a marked “lag-phase” between initial colonisation and subsequent spread that can span several decades (Aikio et al. 2010; Coutts et al. 2018; Rouget et al. 2016). Drake (2005) compared the latent-period of bovine tuberculosis (Mycobacterium bovis) infection and the lag-phase in the spread of coypu (Myocastor coypus) in the UK and concluded that their different durations may be explained by the demographic stochasticity associated with small founder populations. Thus, the transition from the Exposed state reflects the turnover of agents within the receptor, which is determined by their rates of immigration, establishment, reproduction and mortality. In contrast to most microparasite SEIR models, epidemiological invasion models require knowledge of the population dynamics of the agent within the receptor. These mathematical models will need to track the population size of the non-native species within each particular ecosystem that has become Exposed, rather than simply their presence or absence. Allee dynamics, where populations experience low or negative per capita growth rates at low densities can result in longer lag-phases, slower spread and decreased establishment likelihood of both non-native species and microparasites (Tobin et al. 2011). During this phase, the agent may become extinct as a result of demographic stochasticity, in which case the receptor will revert to the Susceptible state (Fig. 2). The latent-period or lag-phase may also result from genetic processes including: selection and adaptation of agent genotypes to the receptor environment, purging of genetic load responsible for inbreeding depression, accumulation of additive genetic variation and recovery from loss of genetic diversity (Pysek and Hulme 2005; Vieira et al. 2019). Under these circumstances, the duration of the Exposed state may reflect the strength of selection pressures, generation time of the agent and the genetic diversity of the inoculum.

Once exposed and possibly following a latent period or lag-phase, a receptor may become Infectious. Whether or not an Exposed receptor transitions to the Infectious state will depend on the ability of the agent population to produce migrants or propagules that can colonise other receptors. This ability will be affected by the nature of density-dependence (including Allee effects) and the generation time of the agent (Cassey et al. 2014; Drake and Lodge 2006). Transmission of agents from one receptor to another may be passive (e.g. virus shedding, oocytes in faeces, wind-dispersed seeds) or via a vector (e.g. mosquito, frugivore, vehicle). For microparasites, the length of the infectious period, during which migrants or propagules are generated, can range from only a few days (e.g. COVID-19) to a decade or more (e.g. HIV). In contrast, without intervention, many non-native species can persist in ecosystems for centuries (Hulme 2020) and which therefore remain Infectious almost indefinitely. It might be expected that the likelihood of transmission to other receptors will be a function of local (within-receptor) population size, as it is in many macroparasites (Hollingsworth et al. 2015). Nevertheless, population size is only one factor influencing transmission rates since agents need to be dispersed and make contact with Susceptible receptors. Contact rates will reflect the attraction of receptors to agents or their vectors. This attraction and the availability of suitable vectors will influence both the spread of disease and non-native species. This is equally true for the host feeding preference of mosquitoes (Takken and Verhulst 2013) or the suitability of lake ecosystems for recreational anglers (Oh et al. 2018). In addition, the ultimate probability of transmission should increase as the duration of the infectious period lengthens.

While metapopulation models have been used to understand the spatial dynamics of disease (Grenfell and Harwood 1997; Parratt et al. 2016; Wang and Wu 2018) and non-native species (Pichlmueller and Russell 2018; Tamburello et al. 2019), attention has primarily focused on the demographic attributes of the agent rather than the infectivity of receptors. Within the Epidemiological Framework for Biological Invasions, Infectious receptors are those within which an agent can reproduce and from which it can disperse, either naturally or with human assistance. Not all receptors are equally likely to play a role in the spread of an agent, a number will act as sources (where agent population growth is positive) and others as sinks (where agent population growth is negative or dispersal is prevented) of varying strengths (Geoghegan et al. 2016). The importance of an Infectious receptor to the spread of an agent will be a function of its connectivity (e.g. existence of invasion corridors, proximity to Susceptible receptors) and of the agent’s life-history.

The minimum evidence for classifying a receptor as Infectious is the persistence of the microparasite or non-native species. Such evidence is usually obtained through expression of symptoms or impacts on the receptor or detection of a persistent population of the agent using serological techniques or field surveys. Nevertheless, not all receptors classified as Infectious in this way may actually be capable of infecting Susceptible receptors. Furthermore, not all Infectious receptors will be symptomatic. As has been seen with COVID-19, asymptomatic hosts can contribute to the spread of disease, but go largely undetected and can therefore undermine efforts to control transmission (Gandhi et al. 2020). Although the ability to distinguish the occurrence of symptoms from an Infectious status has proved invaluable in the management of disease, such a classification of ecosystems remains in its infancy with respect to biological invasions. Non-native species may occur in an ecosystem without having a significant impact on native biodiversity or ecosystem function, yet that ecosystem may still contribute to the spread of the species. An “asymptomatic” Infectious state may also occur where non-native species possess covert resting stages (e.g. seeds, rhizomes, spores, cysts and eggs) that remain viable in the receptor without developing into adults, but may be dispersed passively by the transport of soil between ecosystems.

In microparasitic diseases, the Infectious state comes to an end through the recovery or death of the host. Recovery may result from a natural acquired immune response and may render a receptor Resistant to further infection, either permanently (e.g. measles) or temporarily, in which the receptor becomes Susceptible at some time in the future (e.g. common cold). Alternatively, human intervention such as chemotherapy (e.g. antiviral drugs, antibiotics, fungicides, pesticides etc.) can lead to recovery, but only to the Susceptible rather than Resistant state. Evidence for natural recovery of ecosystems following invasion is scarce, although several cases of boom and bust dynamics of non-native species, where formerly widespread populations collapse, have been documented (Strayer et al. 2017). However, there is no general equivalent of acquired immunity to non-native species. While there is evidence that native insects and pathogens may adapt to non-native plant hosts and may even inflict severe damage, there is limited evidence that these natural enemies impede invasions or result in ecosystems no longer being Susceptible (Crous et al. 2017). In most cases, ecosystem recovery is the result of human intervention. Evidence of interventions resulting in successful recovery from biological invasions is mixed with about half of all non-native arthropod eradications being successful, while for non-native plant species most programmes have failed to deliver eradication (Hulme 2020) or promote ecosystem recovery (Prior et al. 2018) due to re-invasion. Nevertheless, possibly with the exception of a few classical biological control programmes, there are no studies suggesting that, even where eradication is completely successful, the ecosystems concerned are subsequently more resistant to future invasion. Therefore, it is likely that, for non-native species invasions, the rates at which Susceptible (μ) or Infectious (γ) receptors become Resistant will be negligible (Fig. 2).

In the case of microparasites, a high rate of transition to the Resistant state shortens the duration of the Infectious state, thus lowering the opportunities for transmission (Diekmann et al. 2013). To ensure the spread of disease under such circumstances, agents require a high transmission rate and short latent period. This points to a major difference from biological invasions in that, without a significant scope for ecosystem recovery, non-native species can persist even in the face of low transmission rates and long lag-phases. An understanding of the role of the Resistant state in the dynamics of disease is essential to the design of effective immunisation programmes. Therefore, more effort should be invested in research on ecosystem resistance to invasion and the development of tools that could be used to increase the resistance of ecosystems following the eradication on a non-native species.

The incorporation of host vital rates (births and deaths) into microparasite models can have dramatic implications for disease dynamics (Gallos and Fefferman 2015), but it is difficult to conceive of birth and death processes for entire ecosystems. Non-native species can dramatically impact species diversity and ecosystem functions following invasion and they may even transform ecosystems from one state to another (e.g. non-native rabbits impeding woody succession), but the spatial unit itself does not usually disappear (Vilà and Hulme 2017). Even if it is transformed to another ecosystem state (Cobb et al. 2017; Jarnevich et al. 2019; Perry et al. 2015; Stein et al. 2016), the receptor may remain Susceptible to further colonisation by non-native species and it may even continue to be Infectious. Human activities can, of course, create and destroy entire ecosystems. For example, the establishment of new forest plantations or their harvest can influence the spread and persistence of phytophagous non-native arthropods (Be et al. 2017); and newly-created reservoirs (Smith et al. 2015) or coastal marinas (Floerl et al. 2009) may act as stepping stones for the spread of non-native aquatic species. The potential importance of the addition or removal of ecosystems from a landscape for the spread of non-native species has received relatively little attention. but it may be a powerful driver of biological invasions, as well as a useful tool for management (Alharbi and Petrovskii 2019).

The Epidemiological Framework for Biological Invasions is receptor-focused and, although complementary to more traditional agent-focused demographic models, it provides new opportunities to understand biological invasions. The agent-centred approach to biological invasions assumes the probability of successful invasion is a function of the intrinsic rate of population increase when a non-native species is rare (Grainger et al. 2019). However, the receptor-centred approach suggests that an estimate of the mean number of Susceptible receptors likely to be colonised from the first Infectious receptor may be a better indicator of invasion risk, since it explicitly includes both population growth and spread. This parameter is equivalent to the basic reproductive ratio (R₀) which is defined as the expected number of secondary infections in a population of Susceptible receptors arising from a single individual during their entire infectious period and it often serves as a threshold parameter that predicts whether an infection will spread. The basic reproductive ratio (R₀) is the product of the transmission rate and the average amount of time a receptor spends in the Infectious state and, the larger its value, the harder it will be to eradicate the microparasite or non-native species (Blackwood and Childs 2018). For non-native species, the duration of the Infectious state can be many decades so even if transmission rates are low, R₀ will be much greater than 1.0 and the invasion will persist. Therefore, the rate at which a non-native species is eradicated from ecosystems must be higher than the rate at which new ecosystems are colonised. If, as is likely, there are often few options for creating Resistant ecosystems and once a non-native species has been eradicated from an Infectious ecosystem, it reverts to being Susceptible, then the proportion of ecosystems from which invasion must be prevented will be close to 1.0 (Fine et al. 2011). This undoubtedly explains why, once a non-native species is widely established, it becomes almost impossible to eradicate. Perhaps the primary application of R₀ is not in predicting the difficulty of eradicating an established non-native species, but in assessing the potential risk posed by species that have yet to be introduced. Under this scenario, rather than derive an arbitrary score or probability on invasion likelihood, risk assessment tools could be designed to estimate R₀.

In models of biological invasions, Infectious receptors act as sources that are capable of infecting Susceptible receptors, but can also maintain non-native species populations in Exposed receptors that would otherwise become extinct without immigration. Sink ecosystems have been observed for non-native fish (Dauphinais et al. 2018) and plants (Seipel et al. 2016) while microparasites in dead-end hosts are unable to achieve further transmission (Geoghegan et al. 2016). Similarly, measles in small rural villages is often sustained by the influx of infectious individuals from neighbouring major urban centres (Grenfell and Bolker 1998). In many disease systems, < 20% of Infectious receptors may be involved in 80% of transmission (Stein 2011). The receptors that make up this 20% are usually referred to as super-spreaders and their identification and subsequent targeting is a fundamental goal in disease management. It is unclear if the same 80/20 rule holds for non-native species, but identifying Infectious receptors that are super-spreaders could be an important component of the management of biological invasions. How can managers identify these super-spreaders? Managers surveying the distribution of non-native species may face difficulties in distinguishing between the stochastic population dynamics that may occur during the latent/lag phase in source receptors and the transient dynamics of agents in sink receptors where populations are maintained by immigration. The former scenario requires greater vigilance from managers to ensure the Exposed state does not progress to become Infectious (Fig. 2 σ). In contrast, sink receptors play little further part in invasion dynamics, but may divert management resources away from more important targets. The stochastic population dynamics that occur during the lag-phase following infection makes it difficult for managers to distinguish sources from sinks. However, Runge et al. (2006) provide some useful guidance on how this may be done. Transient populations of non-native species are frequently recorded (e.g. as casual alien plants), but the dynamics of these populations are rarely documented (Iles et al. 2016; Brock and Daehler 2020). Distinguishing between sources and sinks is an essential component in managing diseases and biological invasions (Hulme 2020). Unfortunately, data relating to biological invasions tend to score ecosystems as invaded (i.e. Exposed or Infectious) or uninvaded (i.e. Susceptible or Resistant), but rarely quantify the distribution of agents amongst receptors or address the equivalent of the infectivity of a receptor. This issue could be addressed if epidemiological states and transitions were incorporated into spatio-temporal models representing the spread of non-native species through heterogeneous landscapes (Catterall et al. 2012; Mang et al. 2018).

A much-debated approach for the management of microparasitic diseases is “ring vaccination” that targets immunisation to particular groups of Infectious receptors in order to prevent the spread of disease agents (Deen and von Seidlein 2018; Merler et al. 2016). A similar approach, which might be called “ring eradication” has been put forward for biological invasions, whereby non-native species eradication programmes may initially target small, isolated “satellites” first, rather than a single large core population, since many satellites will contribute disproportionally more to population expansion in a homogeneous environment (Hulme 2006; Kovacs et al. 2011; Panetta and Cacho 2014). However, in contrast to the management of diseases, quantitative assessments of the likelihood of containment of invasion through the targeted control of satellite populations through ring eradication have yet to be undertaken.

A more dramatic form of intervention is the establishment of a cordon sanitaire where locations containing high risk hosts are almost sealed from the outside world with severe restrictions placed on the movement in or out of the cordon sanitaire (Gostin et al. 2020). A dramatic example, recognised as the largest quarantine in history, was the cordon sanitaire imposed on Wuhan, a city of 11 million residents, with closure of all transport in and out of the city for 76 days to limit the spread of COVID-19 (Wan et al. 2020). Similar approaches have been used to prevent the spread of non-native species, including the establishment of movement controls, such as the Fruit Fly Exclusion Zone in Australia (Dominiak and Mapson 2017) and buffer zones around protected areas to prevent the spread of non-native weeds (Foxcroft et al. 2011).

The concept of “herd immunity” in which there may be a critical community size, beneath which persistence of metapopulations is not possible, has been influential in microparasitic disease management, since it suggests that only a proportion (albeit often high) of receptors needs to be managed (immunised) to prevent the persistence of disease (Metcalf et al. 2015). If applicable to non-native species, the concept of herd immunity could significantly assist control efforts. If a non-native species exhibited a metapopulation structure and was confined to a specific ecosystem type that was patchily distributed (e.g. lake ecosystems), then population persistence would depend on local dynamics and connectivity (Hastings 2014). In theory, reducing local population growth and eradicating the non-native species from a progressively greater proportion of patches to reduce connectivity could lead to the collapse of the metapopulation. Unfortunately, such an approach, while fine in theory, appears difficult to achieve in practice (Garcia-Diaz et al. 2019). Given that for many biological invasions, R₀ is much greater than 1.0, herd immunity would require most ecosystems to be or become Resistant which is unlikely since there is limited knowledge on what makes an ecosystem Resistant. Taken together this suggests that, for most biological invasions, it is currently impractical to attempt the equivalent of herd immunity for ecosystems.