Ecological and biogeomorphological modelling of brown trout ( Salmo trutta L.): Hints for improvements

The loss of biodiversity in freshwater environments is becoming an increasing problem globally. As a result, many tools have been developed and improved to reduce this decline. However, there is still a need for the identification and evaluation of precise restoration measures to improve habitats and preserve sentinel freshwater species, such as brown trout. This paper provides an up-to-date viewpoint about the life history, habitat characteristics, suitability conditions, and metapopulation dynamic modelling of brown trout, aiming to identify and discuss gaps and propose possible improvements based on collating and reinterpreting literature data. Results suggest that habitat suitability curves for environmental and hydraulic variables possess some degree of universality, for spawning habitat, fry, juvenile and adult trout. Further, an improved method to estimate the amount of suitable area by including the role of stream obstacles (i


| INTRODUCTION
Worldwide, river ecosystems have been experiencing increasing levels of anthropogenic pressure due to the construction of barriers and structures, the intensive use of water resources, and a growing level of pollutants.In turn, river regulation has caused considerable changes in natural flow regimes (Abe & Erinjery Joseph, 2015) that have then limited river geomorphic activity and contributed to reducing longitudinal (Branco et al., 2012), lateral (Liu et al., 2018), and vertical connectivity (Boulton, 2007).Acting as multiple stressors, the medium-to long-term persistence of such perturbations has endangered aquatic organisms, ultimately causing a considerable reduction in riverine biodiversity (Cazzolla Gatti, 2016).This decline is expected to be further exacerbated by climate change (McFadden et al., 2023), notably by effecting water temperature and altering streamflow variability as well as flow seasonality (Birsan et al., 2005).
Brown trout (Salmo trutta L.) are an important fish of the family Salmonidae in many freshwater ecosystems, native to most of Europe, West Asia and parts of North Africa, with high economic and social value (Massa-Gallucci et al., 2010).Specific causes endangering this fish include misinformed fisheries management (e.g., intensive stocking; Burkhardt-Holm et al., 2002), the increased presence and spreading of lethal diseases such as Proliferative Kidney Disease (Burkhardt-Holm et al., 2007;Carraro et al., 2017), and a decrease in water quality (Bergerot et al., 2015;Burkhardt-Holm & Zehnder, 2018).Furthermore, the increase in the frequency of extreme events and consequent alteration of habitat morphology, such as increased erosion of the riverbed, modification of river banks for flood protection, bed stabilisation, and regulation of water flow from hydropower plants, have led to clogging of inter-gravel spaces, reducing spawning habitats and endangering the hatching success of the eggs (Burkhardt-Holm et al., 2005;Scheurer et al., 2009).Lastly, the rise in mean water temperatures due to climate change also plays a crucial role in the degradation of freshwater environments, particularly for coldwater fishes that are forced to higher altitudes to meet habitat requirements (Burkhardt-Holm & Zehnder, 2018).
To preserve or restore the ecological status and functioning of riverine corridors, river scientists, over decades, have developed strategies to either prevent or mitigate the adverse effects caused by anthropogenic disturbances.It is clear today that healthy river ecosystems are defined by the amount of morphodynamic activity characterising the watercourse, whose basic drivers are flow and sediment dynamics (Camporeale et al., 2013).To this end, river restoration aims, firstly, to re-activate such dynamics, thereby developing and organising the long-term habitat complexity and richness of natural rivers (Wohl et al., 2015).Despite many examples of success (e.g., Gerner et al., 2018;Lorenz et al., 2013;Schirmer et al., 2014), scientists and experts continue to seek quantitative tools to evaluate the actual efficacy of restoration measures and thereby support the decisionmaking process.
The assessment of habitat conditions is not always an easy task but some important tools can be helpful to scientists and experts in river management; in particular, physical habitat models (Bockelmann et al., 2004).These models can help to evaluate the suitability of habitat for specific species and at different scales such as at the micro-scale (e.g., Bovee, 1986), meso-scale (e.g., at the scale of pools or riffles; Wegscheider et al., 2020), and macro-scale (e.g., river reach, river segment, etc., Radinger & Wolter, 2015;Lamouroux et al., 2005).Specifically including in models, consideration of physical characteristics of the study river (e.g., water depth, flow velocity, substrate grain size, etc.; Bovee et al., 1998) and how habitat suitability varies in time depending on fluctuations in river flow (Davey et al., 2011).These models can use different indicators to assess the degree of variability based on hydrological (Richter et al., 1997) and ecogeomorphological (Gostner et al., 2013) properties of a river in meeting species-specific requirements.Actual values of such important indicators pertain to the characteristics of the habitat, and changes in the value indicate possible alterations in population dynamics (Gong et al., 2012;Raleigh et al., 1984).However, there is still an open debate within the scientific community on whether these indicators are valuable towards predicting ecological status and population health (see Lancaster & Downes, 2010;Shenton et al., 2012, for further discussion).The Habitat Suitability Index (HSI) is a widespread species-specific index used to assess the suitability of a small part of the river (i.e., microhabitat; Bovee, 1986;Ahmadi-Nedushan et al., 2006).This index, which takes values from 0 to 1 in summarising the suitability of different river characteristics (mainly water depth, flow velocity, sediment grain size, and water temperature), is usually graphically displayed as a function of a physical variable (i.e., habitat suitability curve, HSC).The HSI can be used as a weighting factor to calculate two additional indicators: the weighted usable area (WUA) and the suitable area (SA).The WUA of a river reach is the summation of the composite HSI values of individually measured cross-sections, each multiplied by the corresponding area of the cross-section (Bovee et al., 1998;Nestler et al., 2019), while the suitable area (SA) is the summation of the areas of the river reach that have a HSI above a certain threshold (Muñoz-Mas et al., 2018).WUA and SA values are typically assessed based on average flow properties at the catchment scale.
In the literature, it is possible to find the normalised WUA under other names such as Percent Usable Area (PUA), which is the WUA normalised on the total surface area (Hung et al., 2022), or Hydraulic Habitat Suitability (HHS), which is the WUA normalised on the wetted area (Garbe et al., 2016;Schneider et al., 2010).
The constant increase in computational power makes the use of such indices particularly helpful if integrated within numerical biomorphodynamic models and either directly or indirectly coupled with population dynamic models.Metapopulation models, in particular, allow examination of the interactions and movement among different subpopulations across time and space (Borsuk et al., 2006;Chen et al., 2019;Judson, 1994;Ramos-Jiliberto et al., 2011;Riecke et al., 2019;Zhang et al., 2019).However, existing literature often focuses on specific cases worldwide, giving the impression that the diverse nature of riverine environments does not follow common rules.This challenges the development of universal restoration guidelines, emphasising the importance of putting more effort into defining globally applicable indicators for riverine ecosystems.This work aims to present an appraisal of previous works about food habits and habitat characteristics for brown trout by examining a broad sample of peer-reviewed articles on the subject (Figure 1) and to identify essential primary variables thought to be relevant for advancing future biogeomorphological and ecohydraulics modelling.
From this, a simple statistical aggregation method is then proposed to group all observations and extract a general HSI for each selected variable.Results from the literature identified four variables as primary metrics defining the habitat properties of a river reach for the maintenance of brown trout.These results suggest the existence of general habitat conditions where brown trout most likely occur.All indices support the existence of a universal range of optimal conditions for the examined habitats but with some important distinctions.These distinctions concerned the link between trout life stages and some habitat characteristics that may be typically generated by macroroughness elements with characteristic size comparable to the mean water depth (e.g., stepping stones, wood logs, etc.).The hydraulic role of macro-roughness elements will be discussed with a focus toward advanced ecohydraulic applications involving metapopulation and biomorphodynamic models.

| STATE OF KNOWLEDGE: A BRIEF REVIEW
Information and data regarding brown trout diet, metapopulation modelling, and habitat characteristics have been collected from the literature.The analysis was carried out by considering the guidelines for data collection of the Preferred Reporting Items for Systematic Reviews and Meta-Analyses protocol (PRISMA; Page et al., 2021).
The entire research was conducted on Web of Science, Scopus, and Google Scholar, and the keywords were identified according to a preliminary analysis of reference works in the literature (e.g., Armstrong et al., 2003;Frost, 1938;Levins, 1969;Raleigh et al., 1984).In the first part of the research, information was gathered to define the most common food items consumed by brown trout and the types of models used in the literature to analyse population dynamics.In the second part, after the identification of the most used physical and hydraulic parameters for the construction of the habitat suitability curves, data on water velocity, water depth, sediment grain size, and water temperature were collected both from habitat suitability curves and preferential ranges for adults, juveniles, fry, alevins, rearing, spawning, nursery, eggs, and redds.The data were then summarised into four groups: Adults, Juveniles, Fry, and Spawning (see Section 2.2 for more details).When multiple ranges were available for a specific category, the absolute minimum and absolute maximum across all ranges were noted.
During the second part of the research, additional articles beyond those referenced in the manuscript were found.However, some were omitted based on the study methodology (e.g., laboratory or field study), location along the river, or availability of relevant data.Data from studies conducted in laboratory-controlled conditions (e.g., with constant temperatures), reporting only average river temperatures, or not considering the presence or absence of fish were excluded.Moreover, studies focusing on fish growth rates without considering the likelihood of finding individuals in a specific habitat, and studies conducted at river mouths or near lakes, where water depth and flow velocity data were not representative of fluvial environments were not accounted for.

| General diet
Feeding primarily sustains metabolic activity and growth.Hence, trout are expected to select prey to maximise their energy intake (Elliott, 1975b;Sánchez-Hernández et al., 2011).Nonetheless, there are some morphological constraints (e.g., gape-limitations) closely related to the size, age, and sex of the individual, that can lead to variations in the prey eaten (Montori et al., 2006;Pentelow, 1932).
Accordingly, the diet of brown trout is affected by several factors, which are linked to the habitat they live in (e.g., water temperature, flow velocity), the age and size of individuals (Elliott, 1975a;Swynnerton & Worthington, 1940), and the time of the year.For this reason, the diet may be highly variable among trout inhabiting different rivers.Note: Only the main items in the diet were reported.An 'r' next to the author's name refers to data from different rivers retrieved from the same article.
Literature studies confirm that the diet of brown trout is predominantly insects, both aquatic and terrestrial, with a major component of insects belonging to the orders Ephemeroptera, Trichoptera, Diptera, and Plecoptera (e.g., see Table 1), either as larvae, pupae, or adults (Allan, 1978;Evans, 1952;Frost, 1938;Idyll, 1942;Lehane et al., 2001;Orzavol et al., 2011;Pentelow, 1932;Southern, 1934;Swynnerton & Worthington, 1940).These insects are predominantly from drift-feeding (Elliott, 1973), but trout can also feed on organisms living on the substrate.Additionally, it has been noted that large individuals often select other food types such as molluscs, crustaceans, or fish in addition to or as a substitute for insects (Kelly-Quinn et al., 1990).
The diversity of food found in the diet supports the known opportunistic behaviour of brown trout with respect to prey consumption, even including cannibalism (Sánchez-Hernández, 2020).
However, by regrouping the information in Table 1 into broader categories such as Insecta, Crustacea, Mollusca, Fish and other food residuals, and crossing it with the frequency with which a certain type of food was found in the stomachs of brown trout (Kelly-Quinn et al., 1990;Lehane et al., 2001;Southern, 1934), a pattern for diet composition emerges, highlighting the importance of insects in the diet (Figure 2).The link with habitat modelling will be further discussed in Section 3.

| Age and size
There are some differences in the diets of juveniles and adults, mostly linked to the fact that smaller fish tend to eat smaller prey.However, other studies reported that at the age of 2 years, the dietary differences between juveniles and adults are reduced to a minimum (Montori et al., 2006;Vøllestad et al., 1985).The diet of both life stages is to a large degree dominated by aquatic insects, but fry, given their smaller size, mouth gape limitations, and higher risk of predation (e.g., through cannibalism) tend to feed on smaller insect larvae, such as chironomids, smaller species, or instars of EPT taxa, thus less on the surface.It is not uncommon to find insect larvae in the stomachs of adult trout as well (Montori et al., 2006;Sánchez-Hernández et al., 2011).
Many studies reported that in the stomach of adult brown trout, it was usual to find pieces of molluscs and crustaceans (common crustaceans were Asellus aquaticus and Gammarus pulex; Hunt et al., 1972) together with the expected insect taxa (Figure 2).Large individuals switched from an invertebrate-based diet (Allan, 1978) to one based mainly on crayfish and fish, where the reported fish components were, for example, trout, other salmonids, and sticklebacks (Idyll, 1942).The size at which the transition occurred was variable, and the reported range at which the shift usually occurred was from 23 to 45.5 cm (Bachmann, 1991;Idyll, 1942;Metzelaar, 1929).

| Sex
Sex, along with the age of the individual, seems to be a discriminating factor in the diet of brown trout.Adult trout often exhibit territorial behaviour (Bohlin et al., 2002;Burnet, 1969), especially males during the reproductive season (Johnsson et al., 2001), leading to increased aggressiveness and occupation of river pools, where prey could be more accessible.This territorial behaviour is more prominent in trout inhabiting small streams with limited food resources since it causes the segregation of females and younger individuals into marginal microhabitats, resulting in differences both in the number of taxa and the proportion of terrestrial-aquatic prey eaten by the different groups (Johnsson et al., 2001).

| Habitat
Given the richness of dietary items described above, it is not surprising that the diet of brown trout is also influenced by habitat characteristics (e.g., substrate grain size, flow velocity, water depth, temperature; Elliott et al., 1995;Belica, 2007).Changes in diet can be caused by changes in environmental conditions such as seasonal variations of temperature and streamflow as well as water pH.
Brown trout individuals can be classified, depending on the habitat they use and the time that they spend in it, as movers (i.e., fish that move between different habitats), or stayers (i.e., individuals that stay within the same habitat; Giller et al., 2015).Stayers can be further divided into two subcategories (Greenberg & Giller, 2001) depending if they prefer to live in pools (generally males), or riffle areas, and these differences in habitat are reflected in the diet.Some studies highlighted that there is higher insect diversity in the pools, with a higher percentage of terrestrial prey (Giller et al., 2015), while riffle zones are characterized by a higher abundance of aquatic prey albeit with less variety (i.e., fewer taxonomic groups).Despite the significant variation in prey types, there is no corresponding diversity in the quantity of prey consumed by trout of similar sizes (Giller et al., 2015;Montori et al., 2006).Probably, the key discriminating factor characterising the dependency of diet with habitat is the suitability level of F I G U R E 2 Summary of the main items found in the stomachs of juvenile and adult brown trout from different rivers.The main food items are insects, followed by crustaceans, molluscs, and fish.[Color figure can be viewed at wileyonlinelibrary.com] the habitat itself, since trout tend to eat a higher number of prey if they are in a more suitable habitat (Greenberg et al., 1998) and this characteristic further classifies them as opportunistic feeders (De Billy et al., 2002;Grey, 2001;Khan et al., 2021;McCarter, 1986).

| Seasonality
Seasonality can have an impact on the type of insects that trout find as drift food.In order to properly define the relationships between fish diet and seasonality, it is important to combine the analysis of the stomach content with a detailed study of the composition of river macrozoobenthos.For example, Fochetti et al. (2003) determined that in the Nera River (Central Italy), the accessibility of different food categories was a primary factor for selecting diverse prey, together with other factors that can be responsible for an increase in the probability of capture by the fish, such as the dimension of the prey, colour, mobility and degree of exposure.Slack (1934) found that brown trout from the Test River (Southern England) fed mainly on crustaceans and molluscs (48.1% and 19.2% of the total diet, respectively) during winter (October to February) and on insects of the order Ephemeroptera in May (36%).Additionally, Kelly-Quinn et al. (1990) found that the food intake of brown trout was highest during the summer and early autumn, thereby overcoming also the maintenance requirements (i.e., period of high growth).During the rest of the year, food intake was not much higher than the maintenance requirements, thus causing an energy deficit and weight loss.Furthermore, observations by Bridcut et al. (1993) revealed variations in the diet of trout associated with the seasonal availability of insects and benthic invertebrates.
They emphasised the importance of considering the habitat in which trout forage for dietary studies, highlighting its impact on their diet.This leads to the conclusion that seasonality is a major factor affecting the diet of brown trout, and can be considered a deterministic force (e.g., see Section 4) affecting the type of prey available and in turn variation in trout diets.However, seasonality is not the only temporal scale at which changes in available prey types occur.There is also timing in food resources where short-term variation in the availability of some prey types (e.g., caterpillars that fall in streams or young amphibians that leave the water) can affect the diet as well (Gustafsson et al., 2014).

| Water pH
Water pH is a minor factor that can indirectly affect the diet of brown trout by altering drift patterns and the composition of the macrozoobenthos (Bernard et al., 1990;Courtney et al., 1998).The pH of river water varies based on the geological composition of the area.Specifically, when the riverbed rocks contain limestone, waters are more alkaline.Conversely, if the rocks lack limestone, the water is more acidic.Two of the first studies examining the relation between pH and trout diet were done by Southern (1934) and Frost (1938).
They found that in alkaline waters trout proliferate and weight more, while in acidic waters fish tend to remain small.Analysing the stomach contents of fish from both water types, Southern (1934) noted that the diet of the individuals was different, not only due to different sizes of the fish within the same age group, but also in the sense that trout from alkaline waters ate primarily benthic and mid-water organisms, while trout from the acidic rivers ate more terrestrial insects.
It is clear that water pH can cause differences in trout diet by altering the amount and type of prey available.However, the direct implications of the presence of acidic rather than alkaline waters on diet are difficult to define.Notwithstanding, this marginal dependency might play a non-negligible role when there is severe river regulation altering the natural flow regime and other physico-chemical water conditions.

| Habitat Suitability Index
In the literature, many studies were found that try to describe what habitat properties lead trout to inhabit one or another area based on their daily activities (Lambert & Hanson, 1989;Louhi et al., 2008;Shirvell & Dungey, 1983), although a universal rule still has not been found.In general, the spatial distribution, growth rate, and survival of fish populations are strictly related to major local ecohydraulic variables like mean flow velocity (Fornaroli et al., 2016), water depth (Bardonnet et al., 2006), type of substrate (Grost, 1991), and temperature (Edwards et al., 1979;Elliott & Elliott, 2010), and to other nonlocal (i.e., dispersed) ones like distance from cover (Ayllón et al., 2009), oxygen level (Eklov et al., 1999), and water pH (Boets et al., 2018).
Therefore, in the following, specific attention will be paid to water depth, flow velocity, grain size distribution, and water temperature.
An important tool that scientists developed for this purpose is the HSI, a variable-related index that determines the capacity of a given area to meet habitat requirements for a specific species with respect Brown trout have specific needs in terms of habitat characteristics in that they prefer to live in rivers with cold waters and silt-free rocky substrate (Raleigh et al., 1984).Hence, sediment grain size is an important parameter to consider together with water depth, and flow velocity.These are typically the three main variables used in constructing the HSCs for brown trout.Water temperature can serve as a fourth parameter in assessing habitat suitability, but given the limited tolerance range of the species, it functions more as a limiting factor (i.e., a cutoff).HSI values not only vary based on fish activity (e.g., spawning or feeding) but also differ across the different life stages (i.e., fry, juveniles, and adults).Through a literature analysis, data from studies conducted in different parts of the world (Figure 1) and concerning the four parameters mentioned above were collated (Figures 3-6) to explore potential similarities in values across different case studies.
Furthermore, the data on habitat characteristics found in the analysed papers were divided into different categories depending on the process or age class that the author was studying (i.e., adults, juveniles, rearing, fry, spawning, nursery, eggs, alevins, and redds).For the sake of simplicity, these data were grouped into four different categories named respectively Adults, which contains data only for adults, Juveniles, which contains data for juveniles and rearing, Fry, which has data for late fry and young-of-the-year, and Spawning, which contains data for nursery, alevins, fry, eggs, spawning, and redds.Since the number of articles dealing with the alevins' life stage was limited to not more than two papers for each variable, the last category has been named Spawning.Key findings concerning the four variables are described in more detail hereafter.

| Temperature
Brown trout, being a coldwater fish species, have specific needs in terms of water temperature for the habitat they live in.According to  Elliott (2000) was able to establish that temperatures exceeding 29.7 C for more than 10 minutes or surpassing 24.7 C for up to 10 days are deemed lethal.
In winter, brown trout tend to feed less actively when water temperatures drop below 6 C (Elliott, 1975a) as appetite slowly decreases at this temperature.Conversely, in the study by French (2017), they observed that in 18 of 24 groundwater-dominated streams in Minnesota, the growth and condition over winter of both juvenile and adult brown trout were not affected.This lack of impact was attributed to increased thermal stability linked to the input of groundwater, which avoided the formation of ice and maintained higher base flows during the winter season.Simultaneously, they noted that the amount of prey consumed by each individual did not significantly impact the growth of individuals in the two age classes, suggesting that, in this particular case, temperature was the major driver for trout survival.
The presence of groundwater exfiltration input into the stream is not always an indicator of the growth and high somatic condition of trout.This is because it depends on the amount and quality of the water being exchanged.The difference in temperature linked to this input can also lead to variations in prey availability (Anderson et al., 2016) and growth rates between adults and juveniles (French et al., 2014).This difference in growth rates may be attributed to the fact that juveniles tend to live at lower water temperatures compared to adults (red and blue lines, Figure 3) and spawning seems to happen and fry seem to live in even colder temperatures (green and yellow lines, Figure 3).Given its seasonal variability, water temperature can be regarded as a periodic factor influencing the feeding behaviour of fish.

| Sediment grain size
There is a substantial difference in substrate grain size requirements between the habitat for spawning and the one where juveniles and adults live (Figure 4).This difference arises because spawning takes place in redds built by adult individuals in the gravelly substrate of rivers.Furthermore, once the eggs hatch, alevins continue to live in the same environment (i.e., the space between gravels) until the yolk sac is completely absorbed (Eklov et al., 1999;Hooper, 1973;Ottaway et al., 1981;Palm et al., 2009).For these reasons, specific requirements must be met for the successful survival and hatching of eggs and the survival of alevins.This includes a reduced presence of fines to avoid the clogging of inter-gravel spaces (Dubuis & de Cesare, 2023), high water velocity to prevent the deposit of fine particles (while avoiding erosion of the redds; Lapointe et al., 2000), and maintenance of high levels of oxygenation (Greig et al., 2005).After the complete absorption of the yolk sac, the alevins emerge from the gravels and start living in the water column close to the bottom, becoming swim-up fry.Emerged fry can be mainly found in slow-flowing waters, next to the river banks (Fetherman et al., 2021;Heggenes and Traaen, 1988).
Since the survival of fry is only marginally dependent on the grain size composition of the river bed, and juveniles and adults live, move, and feed in the water column, a few works on characteristic grain size composition of their habitat were found (Figure 4).

| Water depth and flow velocity
Although various environmental factors can influence the habitat selection of trout, there are also two hydraulic parameters that drives the selection, which are water depth and mean flow velocity (Heggenes, 2002).
A compilation of ranges for water depth and velocity for spawning, fry, juveniles, and adults reveals that, generally, spawning takes place in faster-flowing but shallower waters than the ones where adults and juveniles were reported to live, and the range of variability of habitat characteristics is notably narrower (Figures 5 and 6).
Lastly, network-based models, are database models similar to Bayesian networks used to represent objects and their relationships using graphs.Although less common, they can be helpful for studying basic relationships, such as ontogenetic diet shifts (ODS) of fish, providing a practical framework for defining predator-prey relationships and prey availability (Ramos-Jiliberto et al., 2011).

| HINTS FOR ADVANCED MODELLING
In their work, Borsuk et al. (2006) proposed a conceptual map of relationships that was used to build the Bayesian inference model.In light of the considerations advanced in the previous sections, it is instructive to refer to the Borsuk et al. (2006) map in order to identify possible ways of improvement (Figure 7).
The conceptual map can be grouped into distinct blocks (blue boxes, Figure 7

| Gaps and improvement of actual metapopulation models
Metapopulation models are being increasingly used in conservation biology and management to study the effects of human impacts on natural habitat connectivity and population dynamics (Bellard & Hugueny, 2020) and, for this reason, there is a constant need for their implementation to be able to predict the evolution of the metapopulations of the target species with an increasingly higher degree of precision.To improve the reliability of predictions of metapopulation models therefore, there is a need to identify what the main gaps are and the ways to possibly improve them.
Environmental variables (e.g., temperature or flow) as well as  Fausch, 2014;Piccolo et al., 2014).These models generally focus on drift-feeding but brown trout tend to feed also on macrozoobenthos, thus this food type should be considered in the models as well.As a consequence, this precludes modelling the effects that food availability could have in altering population dynamics.The diet habits of brown trout presented in Section 2.1 would suggest that food is probably not a primary driver influencing the characteristics of the habitat where trout are found.
However, the fact that Insecta, Crustacea and Mollusca are typically found in particular stream conditions compatible with the habitat characteristics described above for brown trout (see Section 2.2) indicates that the disappearance of certain habitat characteristics might undermine the existence of a substantial fraction of the food chain and in turn cause species displacement.Because of their opportunistic behaviour, food is therefore an important component leading fish to live in a certain habitat.It is suggested that this component should be implemented in the models in order to fully describe how river restoration may affect fish species dynamics.
Finally, when dealing with barrier removals on a river network there is the need to carefully consider not only the change in dynamics within populations of the same species and between ones of different species but also the possible spreading of invasive species that can affect native populations (Rodeles et al., 2021).The study of the spreading of invasive species caused by restoration actions is a recent topic in the literature (Cooper et al., 2021;Marks et al., 2010), nevertheless, these dynamics have not been fully implemented in metapopulation models used to assess restoration measures.

| Improvements on HSI
The concept of generalised habitat suitability curves was proposed by Louhi et al. (2008).By collecting data from the literature, the authors were able to define a comprehensive HSI curve for the spawning habitat of brown trout.
This work extends the idea of generalised habitat suitability curves to the habitat for spawning and the fry, juvenile and adult life stages and focuses on the emergence of a universal range of optimal conditions for brown trout livability based on data for temperature (Figure 3), mean sediment grain size of the riverbed (Figure 4), water depth (Figure 5), and average flow velocity (Figure 6).A weighted statistical analysis is here separately performed for the four categories (Spawning, Fry, Juveniles, and Adults) and for each main variable.Data proposed by the authors in the literature regarding suitable (i.e., nonoptimal) conditions (thin lines, Figures 3-6) are thus reanalysed by adopting a weighting factor k lower than 1 and in agreement with the literature.Given the important effect that the weighting coefficient plays in the aggregation, a sensitivity analysis is performed by varying its value within a reasonable range.According to the definition of 'good' (0.61 ≤ HSI ≤ 0.8) and 'moderate' (0.41 ≤ HSI ≤ 0.6) suitability (Garbe et al., 2016), two different k values are tested, specifically equal to 0.7 and 0.5 as representative of 'good' and 'moderate' habitat conditions, respectively.Variable values in the optimal range (thick lines, Figures 3-6) are taken into account with a weighting factor, k, equal to 1.By interpreting the values of the weighting coefficient k as a proxy of the HSI, the outcomes of the analysis may be directly interpreted as the HSI values related to a particular variable (e.g., flow depth) being considered.Therefore, the data previously collected from the literature are weighted and summed up among authors.In mathematical terms, the calculation can be written as: where the index k j x ð Þ is the above-specified weighting factor considered by the j-th author and N x ð Þ is the total number of authors considering the variable x.Given that the sum will be greater than one, a normalisation is performed with respect to the max value of b N x ð Þ, thus yielding to the following relationship: where the quantity d HSI x ð Þ may be interpreted as an effective aggregated HSI for the variable x (Figure 8).For the particular case of the substrate grain size for adult trout, the collected data do not show ranges for optimal conditions (Figure 4), so the involvement of different k-values is meaningless.As a result, only one curve for this life stage can be obtained by using any weighting factor (Figure 8b).Conversely, slight differences between curves created by using k = 0.5 (Figure 8a-d) and k = 0.7 (results presented in the Appendix A, Figure A1a-d) are highlighted for the variables.Independently from the k value that is used in the analysis, it is possible to notice that the peaks always occur for the same values, indicating that the use of different weighting factors does not affect the outcomes.
Additionally, the similar behaviour of the HSI with respect to water depth and mean flow velocity suggests that the idea of using the Froude number (Persinger et al., 2011;Plichard et al., 2020) to gather the joint effects of such variables might be inappropriate.The , where U is flow velocity, g is the acceleration due to gravity, and H is water depth) would indeed bind the variables too tightly and generate ambiguous results given that 'optimal' value of HSI could be obtained by combining 'bad' values of velocity and water depth (e.g., 'optimal' and 'good' zones with water depth and velocity equal to 20 cm and 20 cm/s, respectively would return the same Froude number as zones with values of such two variables equal to 5 cm and 10 cm/s, which classify as 'poor' and 'very poor', respectively).
The results of the analysis show that the habitat characteristics for Spawning and the three age classes are slightly different.Spawning happens in colder (peak HSI at 9 C, Figure 8a), shallower (peak HSI between 27 and 30 cm, Figure 8c) but faster-flowing (peak HSI between 30 and 35 cm/s, Figure 8d) areas with finer riverbed material (peak HSI at 25 cm, Figure 8b) in comparison to Juveniles and Adults reflecting the fact that it takes place in different areas within the catchment (i.e., lower order, colder streams for Spawning and higher order, warmer streams for Adults and Juveniles) and that the habitat for Spawning and alevins is different (i.e., have a smaller average grain size) than the habitat where Adults are found, reflecting different needs for different life stages.For Juveniles and Adults, it must be noted that the peak HSI-values generally occur at higher values with respect to Spawning and the peak for adults is generally at higher values with respect to juveniles.When looking at the water velocity graph, it is possible to notice that the peak for Fry is at higher values with respect to the one for Juveniles (i.e., 11-14 cm/s and 20-23 cm/ s, respectively) and that the one for Fry almost coincides with the one for Adults (i.e., 22-25 cm/s).This does not resemble the situation that is normally found in nature, where fry inhabits areas with lower flows than Juveniles and Adults.This will be remarked in the Discussion (Section 4).Wider optimal and good ranges for Adults and Juveniles support the idea that trout have high invasive capacity (Budy et al., 2017, among others).

| Improvements on the Suitable Area (SA)
The HSI indicator is valuable for assessing habitat suitability at the micro-scale (i.e., at the river element or hydraulic unit scale).However, it may fall short when analyses on habitat suitability have to be performed at a larger spatial scale (e.g., the reach scale) to assess the best renaturation measure for a given area.To better quantify the extent of areas meeting the needs of target species preservation, spatially distributed hydrodynamic models have proved to be beneficial.These models can be used to evaluate the suitable area (SA) at the reach scale based on average characteristics of flow depth and velocity along equidistant cross-sections.The SA can be computed with the formula: where A i and HSI i are the area and the HSI of the i th computational cell, respectively, and HSI min is the minimum allowed HSI value.On the contrary, the WUA does not take into account a minimum HSI value, and therefore it may be computed as By combining the definitions of SA and WUA, a third indicator can be obtained.The weighted suitable area (WSA) represents the total weighted area above a minimum HSI value.Accordingly, the WSA can be computed as Based on Equations ( 3)-( 5), simple relationships hold among the indicators (i.e., WUA ≥ WSA and SA ≥ WSA).The relationship between WUA and SA is case-specific, depending on the distribution of HSI i and cell area, A i .
When a more detailed quantification is required (i.e., mesohabitat or microhabitat scale), additional variables and processes must be taken into account, such as the occurrence of steep-channel bedforms (e.g., riffles and pools), the shading effects of riparian plants, and the presence of boulders or cobbles or other generic obstacles in the river that may interact with the stream within a range of flow discharges.
Generally, these obstacles possess a characteristic size of the order of the mean water depth of the river up to a range of discharges beyond which they are then submerged.In the following, such obstacles are referred to as macro-roughness.Macro-roughness can emerge from the water surface and create downstream wake zones (Negretti et al., 2006;Niayifar et al., 2018).This happens as long as the water depth is in the same order of magnitude of the characteristic size of such obstacles (e.g., the diameter of significant boulders and cobbles).
As a result, downstream regions affected by wakes display a reduced flow velocity, making them favourable locations for fish to use as shelters and feeding purposes.High-resolution numerical models have been used (Farò et al., 2023;Waddle, 2010) to correct the WUA and account for the role of such small-scale features.This requires to run the numerical model either for different flow rates or in unsteady conditions and does not allow to easily separate the two scale effects.To overcome this issue and to calculate the contribution of small-scale features to the WUA some analytical procedure was proposed by Niayifar et al. (2018).
By following the findings of Negretti et al. (2006) The addition of the wake zones as suitable areas for brown trout could modify the shape of the suitability curve generating an additional peak at either higher-or lower-flow regime discharges, thus increasing the SA of the river reach (Figure 9).This recently developed approach is a mathematical model that allows modellers to evaluate the effect of large obstacles on flow characteristics.Unlike classical approaches used in the literature for 2D hydraulic-habitat suitability models, which incorporate the effect of macro-roughness by creating a more refined mesh, thus increasing the computational time of the model (Farò et al., 2023;Waddle, 2010), the method from Niayifar et al. ( 2018) has a simpler application.This model allows scientists to directly extract the SA curve given by the macro-roughness without the need for high-definition hydraulic models but just by knowing some parameters of the river (e.g., width, steepness, manning coefficient).Additionally, this method can be coupled with flow modelling at any scale, from the micro-to the macro-scale.
From the perspective of water management plans, considering the presence of macro-roughness will increase the suitable area and allow for more accurate design of habitat conservation measures.

| DISCUSSION, RECOMMENDATIONS AND CONCLUSIONS
This work provides an up-to-date discussion about life habits, habitat characteristics and population modelling of brown trout (Salmo trutta L.), and an outlook for possible improvements.
In the data collection carried out regarding the characteristics of trout habitat no distinction was made regarding the different methodologies used (e.g., electrofishing, snorkelling) to measure habitat use and the stream size of the study river.In the latter case, the focus was on finding the most common physical conditions selected by brown trout for feeding and reproductive purposes, regardless of the river size.It is possible to notice that the curve of water velocities for Fry presents a peak for values higher than the ones for Juveniles and almost coincident with the ones for Adults (Figure 8c).This bias could be related to an overestimation of the water velocities made during the collection of data in the referred studies.In particular, the data retrieved from the literature were mean water velocity measurements, meaning that the measures were taken at a depth of around 0.4 from the river bed.Since Fry usually live closer to the river bed to hide from predators and to be protected from high flow velocities, the actual values experienced by the young fish can be very different from the ones reported in the studies, leading to an overestimation of the whole habitat suitability curve.
Additional uncertainties can be also related to the limited number of data available for the four categories.Overall, this study analysed 91 peer-reviewed articles, but generally, each of them reported values on the habitat characteristics for only one category.Only a limited number of studies provided values for all four variables.Specifically, there were 25 studies reporting data on water temperature, 44 on sediment grain size, 62 on water depth, and 61 on water velocity.
Even though the number of analysed studies is low, it is still possible to have an idea of the values of depth, velocity, grain size, and temperature that allow the survival of brown trout.Specifically, the general habitat suitability curves (HSC) proposed in this work can be employed as a starting point for defining the habitat characteristics that may or may not support the presence of brown trout at different life stages in terms of water flow and depth, sediment grain size, and temperature.This will assist scientists and experts from all over the world in creating a habitat model for this species, facilitating a quick assessment of the key measures necessary to preserve trout habitat in a specific river.Additionally, these curves can be further refined with field data for a more precise evaluation of habitat characteristics when a more detailed estimation is required.
Data analysis on the brown trout diet confirms the opportunistic behaviour of such a species, which can adapt and feed on varying food sources, including cannibalism.However, the major component of the brown trout diet is Insecta.This result may encourage scientists to exploit such dietary habits in order to influence fish behaviour in a beneficial way.For example, the design of fish mobility structures could address connectivity as a functional goal while supporting trout dietary needs (e.g., to help trout move from a habitat with limited food resources to one with high food availability; Wysujack et al., 2009).As a result, effective strategies can be developed to steer fish through preferential paths to facilitate their journey across barriers to new habitats.This perspective offers numerous ideas for future applied research directions, particularly towards investigating optimal habitat characteristics for fish, both in terms of physical and dietary variables.
Based on the context above, the food chain plays a key role.The fact that this aspect is rarely explicitly (Hauer et al., 2012)  This work progressed in this direction in two ways.First, it suggests that there is a certain degree of universality in brown trout habitat characteristics for both environmental and hydraulic variables and such characteristics are distinct for different life stages.Second, improvements to SA estimation are proposed by showing how the interaction between small-scale obstacles and the stream can be used to generate additional SA and demonstrating the effect that an additional SA can have on the total suitable area at different discharges.A more precise prediction of the amount of SA and its related suitability for the study reach scale (namely WUA) would be helpful for the assessment of the effectiveness of restoration measures at both the patch and reach scales.
Significant advancements can be made by incorporating the mentioned dynamics and stochastic forcing in metapopulation modelling.
Metapopulation models, based on the dispersal kernel matrix, are particularly suitable to introduce flow dependency in WUA and new features such as simplified food chain dynamics, perhaps at the expense of slightly higher computational costs.Stochastic forcing does not necessarily generate pure randomness in the system, particularly if over-influenced by weak deterministic periodic forcing that modifies system characteristics (e.g., seasonal dynamics activating biological components).Noise-induced phenomena such as stochastic resonance and coherent resonance may appear, which would shed light on how the transitions between spatial and temporal states may be standardised through the interaction between random and deterministic effects (Ridolfi et al., 2011).Because the hydrological network is characterised by temporal scales imposed by flow conditions and fish mobility, similar coherent effects could also appear spatially in migration patterns, and thus further support the importance of natural (i.e., temporally stochastic) flow variability.
In conclusion, this work analyses brown trout ecology and related modelling approaches and provides an outlook for future improvements in the biomorphological description of their habitats.These improvements involve incorporating life history, improved descriptions of habitat suitability, and suggestions regarding where and how to include these elements into metapopulation models.Such models are useful tools in supporting river scientists and practitioners who work on projects involving restoration planning and management, which are currently part of national and international political agendas.

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I G U R E 1 Distribution of studies analysed in this paper about the ecology and habitat characteristics of brown trout.[Color figure can be viewed at wileyonlinelibrary.com]T A B L E 1 Percentage composition of the stomach contents of juvenile and adult brown trout (Salmo trutta L.) according to several references from the literature.
to indicate a 'population of populations', meaning a population of a particular species as a collection of interconnected subpopulations occupying different habitat patches within a larger landscape, which are separated by some degree of habitat fragmentation or isolation.At the same time,Levins (1969) developed the first metapopulation model that was used to describe the occupancy of connected habitat patches in a homogeneous landscape, where the species moved F I G U R E 5 Suitable (thin lines) and optimal (thick lines) ranges of water depth for spawning (green), fry (yellow), juvenile (red), and adult (blue) trout.An 'r' next to the author's name refers to data from different rivers retrieved from the same article.[Color figure can be viewed at wileyonlinelibrary.com] between identical patches at random.However, in nature, landscapes are never truly homogeneous.Subsequent advancements were made byHanski (1982) andGotelli (1991), who introduced the rescue effect concept, which is a reduction in the extinction rate caused by an increase in the immigration rate from individuals of surrounding patches.Over time, various models have been developed to study different aspects of population dynamics and the individuals with them, considering habitats that are anisotropic and dynamic.An example of the implementation of theLevins (1969) model is provided byNakazawa (2015).Nakazawa improved the original model by introducing stagespecific spatial distributions to address the assumption of a homogeneous landscape and random movement between identical patches.This improvement is important because species often exhibit stagespecific habitat preferences, and dispersal primarily occurs for reproduction and maturation (i.e., ontogenetic habitat shifts).Nakazawa's work offers new insight into the Levins model, allowing the study of how the persistence of stage-structured metapopulations is affected by intraspecific competition and the rescue effect.Conversely, when modelling the dynamics and interactions of populations belonging to different species (i.e., interspecific competition), the models developed are referred to as metacommunity models (e.g.,Convertino et al., 2009;Muneepeerakul et al., 2008;Muneepeerakul et al., 2011).Individual-based models (IBMs) simulate the fate of each individual within a population, incorporating factors such as demographic and environmental stochasticity, habitat quality, and density dependence(Akçakaya & Brook, 2009).A review by Judson (1994) delves into the origins of IBMs, discussing their advantages, disadvantages, and most suitable applications.IBMs fall within the broader category of spatially explicit models, which combine a population simulator with a landscape map depicting the spatial distribution of landscape features(Dunning et al., 1995).In this framework, local populations are represented as cells on a grid, and population size can be treated as a discrete or a continuous variable.A fundamental assumption of these models is that populations can only interact with neighbouring populations.The migration across non-neighbouring cells can be modelled by considering a dispersal kernel matrix, which accounts for the probability of an individual moving from one cell of the grid to another.An example of the application of the spatially explicit models coupled with a dispersal kernel matrix has been developed byGonzález-Ferreras et al. (2019).They assessed the impact of reduced river connectivity due to barriers along river paths on the distribution of brown trout in a Spanish river network.Models capable of predicting the spatial distribution of species are often referred to as Habitat Suitability models, which are statisti-F I G U R E 6 Suitable (thin lines) and optimal thick lines ranges of mean flow velocity for spawning (green), fry (yellow), juvenile (red), and adult (blue) trout.[Color figure can be viewed at wileyonlinelibrary.com] cal models relating field observations to environmental variables, reflecting key niche factors such as climate, topography, geology, or land cover(Hirzel et al., 2006).An example is the work of Rodeles et al. (2021) where they developed the Population Connectivity Index (PCI) based on the Dendritic Connectivity Index byCote et al. (2009).The PCI calculates the degree of connectivity in a metapopulation, allowing the identification of naturally isolated metapopulations and the assessment of dam impacts on fish metapopulation fragmentation.The index considers factors such as the number of populations, total river length occupied by each population, distance between populations, dispersal capability of fish, and presence of barriers in the river.Two additional tools for metapopulation studies are hierarchical models and Bayesian probability networks.Hierarchical models, a family of statistical models, analyse the impacts of biotic and abiotic factors on fish populations(Buisson et al., 2008).They encompass multiple levels of ecological organisation, providing a more comprehensive understanding of their interactions and facilitating the identification of key drivers of metapopulation dynamics.Moreover, hierarchical models have proven to be effective in assessing the consequences of climate change on freshwater organisms as well(Zhang et al., 2019).On the other hand, Bayesian probability networks (BNs) are employed for analysing metapopulation dynamics, and they have gained increasing popularity in various environmental science fields over the past two decades due to their utility in probabilistic and causal modelling.BNs are directed acyclic graphs where the causal relationships and associated uncertainty between the different nodes of the graph are quantified using conditional probability.These models are particularly valuable because they enable the integration of field-collected data with expert judgements, providing a more robust and transparent framework for model inference and decision-making (Jannicke Moe et al., 2021).For example, Borsuk et al. (2006) used a Bayesian probability Network to assess the decline of brown trout in Switzerland.They analysed together various factors contributing to the decline of brown trout, using a network based on a dynamic, age-structured population model.The study highlighted the importance of considering factors such as competition, bird predation, angler catch removal, and immigration/ emigration to model the quality of a brown trout€™s life.Other examples of models that use Bayesian statistics are the recently developed integrated population models (IPMs).These complex statistical models, usually hierarchical (i.e., with multiple linked sources of variability and uncertainty), aid in identifying and exploring knowledge gaps within life histories, allowing the estimation of biologically meaningful parameters like immigration or reproduction (Riecke ), representing abiotic habitat conditions and biotic characteristics of brown trout biology.External factors such as temperature conditions and flow effects causing scouring and clogging represent either internal or external forcing actions impacting either directly or indirectly on the habitat and biological dynamics.A nonexplicit link between two such dynamics, which is regularly disregarded in both habitat and population models, is the role of the food chain.An important element of distinction characterising the dynamics of the processes within the boxes is the different temporal scales with which they manifest, which in turn conditions the mathematical technique reasonably adoptable in developing coupled models.
demographic and environmental stochasticity (e.g., flow variability) are generally not explicitly considered in models.The model by González-Ferreras et al. (2019) might be particularly suitable to incorporate such variables and reconsider how artificial barriers affect populations.In the model developed by Nakazawa (2015), local population dynamics affecting density and patch occupancy and how these relate to the food web model would allow one to better explain stage structure evolution.In the literature, few models exist that try to model the food web and related links ( Conceptual map as modified from Borsuk et al. (2006).Minor processes have been removed from the graph (e.g., % Agriculture, Early and Late Stocking, Angler catch).The blue boxes highlight the influence of food dynamics in relationships.[Color figure can be viewed at wileyonlinelibrary.com] b

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I G U R E 8 The aggregated Habitat Suitable Indices corresponding to the four variables built by using the weighting factor k = 0.5 are shown for spawning (green lines), fry (yellow lines), juveniles (red lines), and adults (blue lines) life stages.(a) d HSI curve for water temperature, T; (b) d HSI curve for average riverbed diameter, D 50 ; (c) d HSI curve for water depth, H; (d) d HSI curve for mean flow velocity, U. [Color figure can be viewed at wileyonlinelibrary.com] considered in defining the HSI (and the WUA) or in models should motivate the development or the inclusion of new concepts of habitat suitability, especially for specific functions.Process timescales are critical for better understanding how perturbations propagate from lower to higher levels of the riverine ecosystem (and vice versa) and for addressing the appropriate level of model complexity for use in a target problem.
| SENSITIVITY ANALYSIS ON PARAMETER K In this section, the sensitivity analysis on parameter k is shown.F I G U R E A 1 The aggregated habitat suitable indices corresponding to the four main variables considered in the analysis built by using the weighting factor k = 0.7 are shown for spawning (green lines), juvenile (yellow lines), and adult (blue lines) life stages.(a) d HSI curve for water temperature, T; (b) d HSI curve for average riverbed diameter, D 50 ; (c) d HSI curve for water depth, H; (d) d HSI curve for mean flow velocity, U. [Color figure can be viewed at wileyonlinelibrary.com] T A B L E 2 Ranges of HSI found in the literature.
to a Hung et al., 2022)s index takes values from 0, which indicates a habitat that is completely unsuitable, to 1, which means that the habitat is optimal.More specifically, the HSI sometimes can be divided into ranges defining different levels of suitability (Table2).Once the HSIs for each variable are obtained, they can be used separately or combined to build the habitat suitability curves (HSC) for the entire river reach.The combination of the HSIs of different variables is called compound HSI, also found in the literature as the combined suitability factor(CSF;Hung et al., 2022)and it represents the overall likelihood of an individual inhabiting a specific area based on various factors.
Suitable (thin lines) and optimal (thick lines) ranges of temperature for spawning (green), fry (yellow), juvenile (red), and adult (blue) trout.[Color figure can be viewed at wileyonlinelibrary.com] Forseth et al. (2009)optimal temperature range for brown trout growth and survival spans from 3.8 C to 18.4 C.However,Forseth et al. (2009)suggest a slightly broader range of 5-23 C, noting a rapid decline in trout appetite beyond the maximum and a gradual decrease below the minimum.Furthermore, through laboratory experiments, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/rra.4349by Schweizerische Akademie Der, Wiley Online Library on [30/07/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License F I G U R E 9 A qualitative graph of the suitable area as a function of the flow discharge without accounting for the presence of macroroughness (solid black line).The effects induced by the presence of macroroughness are shown with two examples based on their different relative influence: when the area of macroroughness is relatively high (solid magenta line) the additional peak in the total SA curve at low flow discharges may not be neglected (dotted pink vs. solid black lines).Conversely, for very low relative influence (solid blue line) the effects are negligible (dashed-dotted cyan vs. solid black lines).The asymptote on the right-hand side represents the areas near banks where fish shelter during high-flow events.[Color figure can be viewed at wileyonlinelibrary.com] semi-spherical obstacle, and modelled the flow-dependent statistical distribution of the wakes by means of a derived distribution approach.