B. M. Frank, Earth and Life Institute, Université catholique de Louvain, Croix du Sud 2, Box 14, B-1348 Louvain-la-Neuve, Belgium. E-mail: firstname.lastname@example.org
Abstract – Ecological models for stream fish range in scale from individual fish to entire populations. They have been used to assess habitat quality and to predict the demographic and genetic responses to management or disturbance. In this paper, we conduct the first comprehensive review and synthesis of the vast body of modelling literature on the brown trout, Salmo trutta L., with the aim of developing the framework for a demogenetic model, i.e., a model integrating both population dynamics and genetics. We use a bibliometric literature review to identify two main categories of models: population ecology (including population dynamics and population genetics) and population distribution (including habitat–hydraulic and spatial distribution). We assess how these models have previously been applied to stream fish, particularly brown trout, and how recent models have begun to integrate them to address two key management and conservation questions: (i) How can we predict fish population responses to management intervention? and (ii) How is the genetic structure of fish populations influenced by landscape characteristics? Because salmonid populations tend to show watershed scale variation in both demographic and genetic traits, we propose that models combining demographic, genetic and spatial data are promising tools for improving their management and conservation. We conclude with a framework for an individual-based, spatially explicit demogenetic model that we will apply to stream-dwelling brown trout populations in the near future.
The rapid expansion in ecological modelling parallels technological advances in field methods (i.e., individual tagging and tracking), computing, and genetic analyses. Stream ecologists are now poised to model and to better understand how the interaction of demographic and genetic factors influences the distribution and abundance of fish. This is a daunting task, however, because of the difficulty of assimilating the broad knowledge base that has developed, somewhat independently, in a number of subdisciplines (e.g., demography, genetics, physical habitat simulations, etc.). In this paper, we assemble and synthesise for the first time the vast body of ecological modelling literature on stream fish, focusing on the brown trout, Salmo trutta L. Our goal is to demonstrate how these previously independent models have begun to be integrated, and how further integration will allow ecologists to better address important questions for the management and conservation of freshwater fish.
The brown trout is a species particularly well-suited for serving as a model organism for both management and conservation. Its quantitative ecology, from individual habitat selection to population dynamics, is as well known as that of any stream fish (e.g., Elliott 1994; but see numerous others). It is also one of the vertebrate species presenting the highest degree of intraspecific biological diversity including strong genetic and phenotypic variation among populations (Laikre 1999; Bernatchez 2001). This genetic variability among brown trout populations is attributable to several factors, including the effects of recent glaciations, the physical characteristics of the hydrographic systems and local differentiation without barriers owing to territorial behaviour and strong homing instinct (i.e., individuals return to spawn in the stream in which they were born) (Laikre 1999; Antunes et al. 2006). These factors result in limited gene flow among populations, producing partially isolated random mating units both within and among watersheds (Ferguson 1989). This often leads to adaptation to local environmental conditions, changes in genetic structure and the development of unique demographic traits like morphology, feeding preferences and life history strategies (Laikre 1999; Klemetsen et al. 2003; Ferguson 2006). The importance of this intraspecific diversity for fisheries management has long been recognised (e.g., Ricker 1972; Spangler et al. 1981; Taylor 1991), and most recently Schindler et al. (2010) identified its crucial role in providing ecosystem services. Human activities, including environmental degradation (pollution, altered flow, fragmentation of habitat), fishing and fish stocking (Laikre 1999; Cowx & Gerdeaux 2004; Dudgeon et al. 2006), have resulted in a loss of intraspecific diversity of brown trout, and many remaining native stocks are now faced with a medium-term risk of extinction (e.g., Laikre 1999; Caudron et al. 2010).
In recent years, considerable attention has been paid to the ecology of brown trout. Population dynamics of a number of populations were reviewed (e.g., Roussel & Bardonnet 2002; Klemetsen et al. 2003; Lobon-Cervia 2005, 2007; Northcote & Lobon-Cervia 2008), and molecular genetic techniques have contributed to improving the basic genetic information available on population structure, both at large (Bernatchez 2001) and at small spatial scales (Hansen et al. 2001; Sonstebo et al. 2007b). Recent advances in fish marking techniques, spatial analyses and molecular genetics have allowed the establishment of long-term data sets of demography and population genetic structure based on sampling of individual fish (e.g., Hansen et al. 2002; Lobon-Cervia & Rincon 2004; Fraser et al. 2007; Haugen et al. 2008). Although advances have been achieved in both population dynamics and population genetics models, comprehensive models that integrate these two characteristics of salmonid populations are still in their infancy (Palsboll et al. 2007). Because brown trout tend to show both demographic variation and genetic diversity at the watershed scale, models that link population dynamics and genetics (i.e., demogenetics) across spatial scales hold great promise in providing insights into their management and conservation.
In this review, we show how ecological models have previously been applied to stream fish populations, particularly brown trout, and how the most advanced models might be integrated to develop a new demogenetic model. First, we conduct a bibliometric review of the literature on ecological models for brown trout, and we identify and summarise two categories and four types of models that have been developed over the past 30 years. Then, we demonstrate how some of these models have already begun to be integrated, and how they might be used to address two key questions relevant to the conservation and management of stream fish: (i) How can we predict fish population responses to management intervention? and (ii) How is the genetic structure of fish populations influenced by landscape characteristics? We conclude with a framework for a new demogenetic model for brown trout populations that will further integrate existing theory through the use of an individual-based, spatially explicit platform.
We developed a bibliometric approach to identify the main topics addressed by scientific publications of ecological models for brown trout. We followed two steps: the selection of publications, and the construction of the corresponding directed network of citations.
In the first step, we used the ISI Web of KnowledgeSM search engine to identify key publications, the references they cited and those that cited them (Table 1). We selected 68 publications (from 2003 to 2008), among which 59 articles, seven proceedings papers, one editorial material and one review, and their 2964 citations (from 1980 to 2009).
Table 1. Search criteria for the selection of publications devoting to the brown trout.
Topic=(salmo* AND trutta AND model* AND (river* OR stream* OR basin* OR freshwater*) NOT sea* NOT lake* NOT (salmonel* OR chemi* OR tox* OR ion* OR metal*))
From 2003 to 2008
Science Citation Index Expanded (SCI-EXPANDED), from 1980 to 2009
In the second step, a directed network was built. First, an adjacency matrix was created. This latter consists of a symmetric matrix whose row and column elements reflect vertices (nodes), and each cell contains the value of an edge (interaction). In our case, the vertices are the 68 publications and their 2964 references, while the edges are constituted with ones and zeros, each ‘one’ representing a link between two vertices (here, 3567 links). Then, the 3032 × 3032 adjacency matrix was converted into an edge list matrix, using the ‘Network’ R package (Butts et al. 2008). It is a rectangular matrix with two columns. We chose a directed network and, in this case, each row element represents an edge and contains two vertices that are linked by this edge: the first one is taken to be the tail vertex of the edge and the second one is the edge’s head vertex (Butts 2008). Finally, importing the edge list matrix into the Cytoscape software (Shannon et al. 2003) allowed us to visualise the network properly by using, for instance, the ‘Organic layout’. To facilitate the analysis of this network, its size was reduced: vertices with four or less input edges were deleted. We obtained a network made of 59 vertices (44 publications plus 15 citations) and 104 directed edges (Fig. 1). This allowed us to identify the major categories of models, the types of models within them and links among these.
Results: literature review and synthesis
Two main references display the largest number of input edges in the directed network (Fig. 1): R766 and R355, with 19 and 12 inputs, respectively. The former reference, R766, is the well-known book ‘Quantitative Ecology and the Brown Trout’ (Elliott 1994). This book covers various subjects such as the global success of the brown trout species, growth and energetics, population dynamics of adults and juveniles, ecology and genetics. The latter reference, R355, is the report ‘A Guide to Stream Habitat Analysis Using the Instream Flow Incremental Methodology’ (IFIM) (Bovee 1982). This guide explains how to assess riverine habitats and impact of disturbances on these habitats and fish that live there.
From these two main references, three clusters are observed in the network. Cluster One, population ecology, is in the left of Fig. 1 (light-gray nodes), centred on Elliott (1994). It comprises 18 articles and six references, mostly addressing the ecology of brown trout populations (Table 2). Cluster Two, population distribution, is in the right of Fig. 1 (dark-gray nodes), centred on Bovee (1982). It comprises 19 articles and seven references that address either trout local habitat preferences or their distribution at the catchment scale (Table 3). Cluster Three (white nodes in Fig. 1) comprises seven articles linking Clusters One and Two. In this cluster, a number of publications represent recent attempts to link population ecology and population distribution (Table 4).
Table 2. Vertices belonging to the ‘Population ecology’ cluster.
A population dynamics model and habitat simulation as a tool to predict brown trout demography in natural and bypassed stream reaches
Clusters One and Two are linked to two broad categories of ecological models for brown trout: population ecology models and population distribution models (Table 5). Each category is further divided into two subcategories; population ecology models include population dynamics and population genetics models, and population distribution models include habitat–hydraulic and spatial distribution models. Initially, these population ecology and population distribution models were developed largely independently, but more recently there have been efforts to integrate them. Spatial dynamics models and landscape genetics models are promising approaches that link either population dynamics models or population genetics models across spatial scales; spatial dynamics models emphasise the importance of temporal changes in population size and age structure, and spatial variability in stream habitats; landscape genetics models allow for studying the effects of environmental features on the genetic processes regulating a population. Below, we first review population ecology models and population distribution models. Then, we review the two additional model types: spatial dynamics and landscape genetics models. We also introduce individual-based simulation techniques, which have become an integral component of these latter models.
Table 5. The six types of ecological models for stream fish that we identify based on our literature review. The study goals and parameters estimated are described for each of them.
Population dynamics models
Population genetics models
Short- and long-term changes in the size and age structure of a population
Population-level effects of genetic phenomena such as segregation, recombination, transposition and mutation
Abundance, population growth rate
Degree of population differentiation, population of origin, number of populations, past and current gene flow, effective population size
Spatial distribution models
Habitat characteristics and preferences of stream fish populations
Relationship between organisms occurrence and catchment characteristics
Habitat suitability index in relation with stream discharge
Habitat suitability maps
Spatial dynamics models
Landscape genetics models
Limitation of population density by demographic processes, influences of flow on demographic rates
Interactions between landscape features and micro-evolutionary processes
Abundance, population growth rate, habitat selection and suitability
Locations of genetic discontinuities, genetic distance and connectivity
Through this synthesis of the literature, we identify the study goals and estimated parameters associated with each of the six model types we describe (Table 5). We focus on models and methods that have been developed for stream-dwelling brown trout and use examples from other taxa in cases where models for brown trout are lacking. We do not consider models designed for multiple species. A comprehensive list of models and corresponding methods can be found in Table 6. For each model type, we provide one example of a research question that might be answered by using the model.
Table 6. Types of ecological models, software in which they are implemented, and examples of applications for brown trout (Salmo trutta) or other salmonid species.
We subdivide population ecology models into two types: population dynamics models and population genetics models. Population dynamics models address short- and long-term changes in the size and age structure of a population; typical outputs from these models are predictions of abundance and population growth rate (e.g., Lebreton 2006). Population genetics models aim to understand and to predict the genetic structure of populations (i.e., their allele and genotype frequency distributions) taking into account ecological and evolutionary factors such as population size, patterns of mating, gene flow, genetic drift, mutation and natural selection (e.g., Hartl & Clark 1989; Allendorf & Luikart 2007).
Population ecology models are thus a means to explain changes occurring in the demographic or genetic structure of a population, caused either by dynamic processes (i.e., births, deaths and dispersal) or by micro-evolutionary processes (i.e., natural selection, genetic drift, gene flow and mutation). Population dynamics and population genetics models can be integrated with two other types of models, habitat–hydraulic and spatial distribution models, to obtain spatial dynamics models and landscape genetics models, respectively. These latter model types are both reviewed in the second section of this literature synthesis, and in the last section, we demonstrate how they can address two questions relevant to the management and conservation of freshwater fish.
Linking evolutionary and demographic processes in ecological models (i.e., demogenetic models) and applying these to understand the patterns of genetic variation in freshwater fish populations should provide new insights to address questions about their management and conservation. For instance, levels of fecundity, mortality, immigration and emigration may alter the degrees of genetic exchange among populations, and these are capable of feeding back into one another (Kool 2009). As suggested at the end of this literature review and synthesis, the use of individual-based simulation techniques should greatly facilitate the development of the demogenetics field and its associated demogenetic models.
Population dynamics models
Population dynamics models can be subclassified into either mathematical or statistical models. Mathematical population models are dynamic and deterministic, because they describe how a population changes over time, and they have no random component (Ellner & Guckenheimer 2006). Exponential (Malthus 1798) and logistic (Verhulst 1838) models of population growth are the simplest mathematical population models describing changes in a population’s size. They differ on their assumptions about the availability of resources and are rarely used today. Another class of mathematical population models are the stock-recruitment models (e.g., Ricker 1954; Beverton & Holt 1957), which give the number of fish expected to survive (the recruits) at a later time, as a function of the number of spawners (the stock) at a previous time. For instance, Elliott (1994) used a Ricker model to describe the number of recruits at the different stages of the life cycle of brown trout, given the number of eggs at the beginning of each year. The last class of mathematical population models we describe here is the matrix projection models (see Caswell 2001). Age-structured models developed by Leslie (1945) are the deterministic matrix models most commonly used in the literature, and several were developed for brown trout populations (e.g., MODYPOP: Sabaton et al. 1997; Gouraud et al. 2001; see also Table 6). The approach of Leslie was upgraded by classifying individuals into stages of development (Lefkovitch 1965) or size classes (Usher 1966) and was eventually generalised to consider any structuring factor (Caswell 2001). Recently, integral projection models, or IPMs, have been developed as a practical alternative to deterministic matrix models for structured populations with continuous trait variation. The IPM theory (Easterling et al. 2000; Ellner & Rees 2006) is used to understand how complex demographic processes, and the associated individual variation, affect population growth and the evolution of life history strategies (Jongejans et al. 2008). Until now, such models have been mostly applied to plant and mammalian populations (e.g., Ramula et al. 2009; Ozgul et al. 2010).
Most statistical population models are static and stochastic (Sanz & Bravo de la Parra 2007). They are divided into two classes: birth–death models and population growth models. On the one hand, birth–death models are a special case of continuous time Markov models and describe changes in a population through births and deaths, assuming that only one event happens at a time (Otto & Day 2007). On the other hand, population growth models consider two sources of stochasticity simultaneously: demographic and environmental (Sanz et al. 2003; Otto & Day 2007). In small populations, the effects of demographic stochasticity may be crucial, sometimes even causing total population extinction (Sanz et al. 2003; Sanz & Bravo de la Parra 2007).
A link between mathematical and statistical population models has been made recently using a state-space framework. Two processes are considered in state-space population models: one for state and one for observation (Fig. 2). The first process describes the state of a population at successive time steps, through demographic processes such as birth, survival and movement. The observation process links the unknown states to data on the population, recorded during surveys or experiments, and gives the probability of obtaining a particular observation depending on the population’s state (Thomas et al. 2005; Buckland et al. 2007; Patterson et al. 2008) (for a mathematical description of state-space models, see Buckland et al. 2004). To our knowledge, no state-space models have been applied to brown trout, although they have been successfully applied to Atlantic salmon (Salmo salar) by Rivot et al. (2004).
Population genetics models
Classical population genetics models rely on the Wright–Fisher assumption of an idealised population, in which the entire population reproduces simultaneously and no selection occurs (Otto & Day 2007) (e.g., the infinite alleles and the stepwise mutation models of Kimura & Crow 1964 and Ohta & Kimura 1973, respectively; the island and the stepping-stone dispersal models of Wright 1943 and Kimura & Weiss 1964, respectively). The coalescent model (Kingman 1982; reviewed by Hudson 1990; Nordborg 2001) is a natural extension of classical (forward-time) population genetics models, and it investigates the shared genealogical history of genes (Rosenberg & Nordborg 2002; DeSalle & Amato 2004). Forward-time simulation programs (e.g., EasyPOP: Balloux 2001; SFS-CODE: Hernandez 2008) and coalescent, or backward-time, simulation programs (e.g., SEQ-GEN: Rambaut & Grassly 1997; MS: Hudson 2002) provide a means to explore the effects of micro-evolutionary processes on populations of constant size. The forward-time approach is more appropriate for studying how the long-term behaviour of evolutionary systems depends on initial conditions (Rosenberg & Nordborg 2002). The coalescent approach can be used as a simulation tool for (i) studying the effects of past evolutionary forces on current genetic variation, and thus to estimate parameters like migration rates and effective population sizes, and (ii) hypothesis testing and exploratory data analyses (Rosenberg & Nordborg 2002; Kuhner 2009).
Second, FST can also be used as a basis for estimating past gene flow, i.e., the number of migrants exchanged among populations per generation (Holderegger et al. 2006), because gene flow is naturally related to population subdivision. Indeed, a lack of genetic exchange among populations is expected to result in genetic differentiation (Allendorf & Luikart 2007). Classification methods (also called assignment tests) address the following question: ‘Which population does a particular individual originate from?’ (see the review of Manel et al. 2005), while clustering methods allow to determine how many distinct genetic populations are present in a system (Pearse & Crandall 2004). Methods that permit both classification and clustering of individuals are the most frequently used (e.g., STRUCTURE: Pritchard et al. 2000; see Sonstebo et al. 2007a for an example of application to brown trout populations). Less sophisticated methods like multilocus contingency tests (as implemented in GENEPOP: Raymond & Rousset 1995; Rousset 2008) are a good alternative to clustering methods (Waples & Gaggiotti 2006). In addition to assigning individuals to their population of origin, classification methods can also be used to infer first-generation migrants (e.g., BAYESASS: Wilson & Rannala 2003). An alternative approach for studying current gene flow is the parentage analysis (reviewed by Wilson & Ferguson 2002; Jones et al. 2010; Jones & Wang 2010a). Using sibship and parentage analysis software (e.g., COLONY: Jones & Wang 2010b; Wang 2004), Hudy et al. (2010) were able to describe the spatial distribution of brook trout (Salvelinus fontinalis) spawning sites, and the dispersal from these sites after fry emergence (see Serbezov et al. 2010a for an example of application to brown trout). Broquet & Petit (2009) have recently reviewed the use of molecular genetic markers to estimate dispersal parameters.
Third, changes in genetic diversity and thus in population size can be inferred via the estimation of the effective population size, or Ne (Fisher 1930; Wright 1931). This is the size of an ‘ideal population’ that would have the same rate of genetic change owing to drift as does the population under consideration (Schwartz et al. 2007; Luikart et al. 2010). More roughly, Ne is an approximation of the number of breeding individuals producing offspring that live to reproductive age, and it enables direct tests for changes in population size by quantifying it (Schwartz et al. 2007). We focus on genetic methods that can be used to estimate contemporary or current Ne. Methods to estimate historical Ne have recently been reviewed in Charlesworth (2009). Recent coalescent programs are presented in Kuhner (2009); they estimate the product of effective population size times mutation rate (i.e., the effective number of migrants per generation) (e.g., MIGRATE: Beerli & Felsenstein 2001; Beerli 2006; LAMARC: Kuhner 2006). Quantification methods of contemporary Ne can be divided according to the number of samples they require; the lower the intensity of sampling, the higher the number of assumptions (Broquet & Petit 2009; Luikart et al. 2010). Examples of methods requiring a single sample from the same population are the heterozygote excess in progeny method (e.g., Pudovkin et al. 1996; Luikart & England 1999), and the linkage disequilibrium method (e.g., LDNe: Waples & Do 2008; ONeSAMP: Tallmon et al. 2008). They are less reliable compared to the temporal method, which is based on samples from the same population from at least two time periods (Schwartz et al. 2007). Several approaches of the temporal method have been proposed, based on moment (e.g., TempoFs: Jorde & Ryman 2007), likelihood (e.g., MLNE: Wang 2001; Wang & Whitlock 2003) or coalescent Bayesian (e.g., TM3: Berthier et al. 2002) estimators (Leberg 2005; Luikart et al. 2010). For instance, Ostergaard et al. (2003) as well as Jensen et al. (2005a) used a likelihood-based implementation of the temporal method on brown trout populations in Denmark (see also Table 6). All Ne quantification methods presented so far assume that samples come from a single isolated population, and thus concern related individuals, except for the MLNE program that was designed to jointly estimate Ne and migration rate using multiple samples from multiple generations of two or more populations (Vitalis & Couvet 2001; Skalski 2007).
Many fitness-related phenotypic characters (growth rate, age and size at maturity, etc.) are complex and quantitative in nature. They vary continuously and are coded by many interacting genes, which are in turn influenced in their expression by the environment (Naish & Hard 2008). Population genetics methods presented earlier are no longer suitable for this kind of traits, so complementary genetic methods have been developed. In quantitative genetics, the aim is to understand distributions of quantitative characters, and the temporal change of the means and variances of these distributions (Coulson et al. 2010). The infinitesimal model (Falconer & Mackay 1996; Lynch & Walsh 1998) describes the genetic basis variation of quantitative traits within populations and assumes that phenotypic differences observed among individuals are related to differences in a large number of genes, each of them having a minor effect (Wilson et al. 2010). Application of the infinitesimal model in natural populations is addressed by linear mixed effect models, and more specifically by the so-called animal model. This model is used to decompose the phenotypic variance of a trait into genetic and environmental sources of variance, to estimate parameters such as the heritability of this trait and genetic correlation with other traits (Wilson et al. 2010). We refer the reader to Kruuk (2004) and Wilson et al. (2010) for a general introduction to the animal model, and to Serbezov et al. (2010b) for an example of application of this model to brown trout populations. In the field of management and conservation of fish populations, the role of quantitative genetic methods has been discussed by Naish & Hard (2008), considering evolutionary effects of both fishing and adaptation to climate change issues. Quantitative genetics has also allowed the integration of ecology and genetics. For instance, the approach described in Coulson et al. (2010) is based on integral projection models (IPMs, see the previous section on Population dynamics models) and is aimed to explain within and between species patterns in quantitative characters, life history and population dynamics.
Population distribution models
The second modelling category corresponds to population distribution models. Most of them are descriptive (or phenomenological); they concentrate on observed patterns in the data and give a quantitative summary of the observed relationship among a set of measured variables (Ellner & Guckenheimer 2006; Bolker 2008). At the stream scale, habitat characteristics (e.g., water depth and velocity, substrate size) and preferences of stream fish are evaluated using habitat–hydraulic models (e.g., Ahmadi Nedushan et al. 2006; Anderson et al. 2006). At a larger scale, the relationship between fish occurrence and catchment characteristics (e.g., rainfall, elevation, vegetative cover) is addressed by spatial distribution models (e.g., Olden & Jackson 2002; Ahmadi Nedushan et al. 2006).
Population distribution models are thus a means to explain fish habitat preferences and distribution. But they can also be used to address questions relevant to the management and conservation, when integrated with population dynamics or population genetics models. That is the subject of the last section of this literature synthesis, which addresses spatial dynamics models and landscape genetics models and demonstrates how these can be used to predict the effects of anthropogenic impacts such as habitat alteration or barriers to gene flow on stream fish populations.
Habitat–hydraulic models are a combination of hydraulic models and habitat suitability models (Harby et al. 2004; Mouton et al. 2007b). Hydraulic models are intended to calculate water levels from characteristics such as water velocity, channel depth and channel width and can be one-, two- or three-dimensional (Harby et al. 2004; Clark et al. 2008). Habitat suitability models are used to evaluate the potential availability of fish habitat (Mouton et al. 2007b).
The evaluation of fish habitat suitability comprises three steps. First, the frequencies with which animals use various habitat types and the availability of these habitat types are observed (Railsback et al. 2003). Then, the ratio of habitat use to habitat availability is transformed into a measurement of habitat selection, the habitat suitability index. This index is based on curves representing the degree of preference displayed by fish over the complete range of different habitat variables found in a river, such as velocity, water depth and substrate size (Guay et al. 2000). Preference indices range from 0 (poor habitat) to 1 (best habitat), for each of the considered physical parameters. The fish preference curves of Bovee (1982) are the most used, but modified versions can be developed to adapt them to the stream under study. Finally, the aquatic space available to a fish species for a river at a given flow is quantified by the weighted usable area or WUA, an aggregate measurement expressed in square metres of habitat per 1000 m of river. The WUA is simply the sum of the products of the habitat suitability index by the wet section areas (Booker & Dunbar 2004; Clark et al. 2008). For instance, Ovidio et al. (2008) calculated the WUA for adult brown trout living in a Belgian tributary. Other examples are listed in Table 6.
Hydraulic and habitat suitability models were linked by Bovee (1982), through his IFIM. This concept is a means to describe habitat by including discharge variability, i.e., the change of stream flow in magnitude, frequency or duration at some point in time and space (Petts & Kennedy 2005). The methodology was first implemented in a suite of numerical models, called Physical HABitat SIMulation or PHABSIM (Waddle 2001). For example, such models were used by Nehring & Anderson (1993) to investigate the effect of flow related to habitat changes on wild rainbow trout (Oncorhynchus mykiss) and brown trout populations. Several other models based on PHABSIM were developed later, such as EVHA (Ginot 1995; Pouilly et al. 1995), and a new approach based on fuzzy set theory appeared recently (Ahmadi Nedushan et al. 2006) (see Table 6 for examples of application of these methods). The IFIM approach linking instream hydraulics to fish distribution is now being applied worldwide by environmental managers as part of environmental assessments and decision-making (Tharme 2003; Mouton et al. 2007b; Clark et al. 2008).
Spatial distribution models
The development of models aimed to predict the spatial distribution of organisms had two historic steps (Olden & Jackson 2002; Joy & Death 2004). Initially, only comparative studies were made describing linear and nonlinear relationships between environmental variables and the occurrence of populations or species. The next step was to predict their spatial distribution from these environmental factors by incorporating geographic information systems (GIS).
At the start, linear relationships between environmental variables (e.g., water depth) and fish occurrence (e.g., presence/absence data) were assumed. Traditional linear approaches include linear regression, multiple regression and discriminant analysis (see Table 6 for application examples). Because patterns of fish occurrence often exhibit complex (i.e., nonlinear) relationships to habitat heterogeneity and biotic interactions, alternative approaches were developed in the late 1990s. In such nonlinear models, occurrence is recorded for all sites or a random subset of sites in the study area (Buckland & Elston 1993). Classification and regression trees and artificial neural networks are typical examples of nonlinear techniques. The capacity of predictive models using GIS to fill in the gaps between sample sites permits to enhance the accuracy of spatial maps of the probability of fish occurrence (Joy & Death 2004; Dauwalter & Rahel 2008).
Spatial distribution models are widely used in the field of management and conservation of fish populations (Guisan & Zimmermann 2000; Olden & Jackson 2002). For instance, a general linear model was used by Schager et al. (2007) to analyse the influence of selected abiotic and biotic parameters on the density of brown trout populations (see Table 6 for other examples). A large number of competing approaches are available today. Therefore, comprehensive studies that compare the performance of these approaches (e.g., Manel et al. 1999; Olden & Jackson 2002) should be taken into consideration when using this kind of model.
Integration of population ecology and population distribution models – Addressing key questions for stream fish management and conservation
Here, we review two recently developed types of ecological models: spatial dynamics models and landscape genetics models. These models are attempts to integrate either population dynamics models or population genetics models across spatial scales; indeed, they combine population dynamics with stream scale habitat characteristics, and population genetics with landscape ecology, respectively. These two spatially explicit approaches make intensive use of individual-based simulation methods, for instance to incorporate demographic stochasticity (Marjoram & Tavaré 2006; Epperson et al. 2010; Segelbacher et al. 2010), so we first introduce individual-based simulation models. We review spatial dynamics models and landscape genetics models in the two next sections, with the intent to show how these models can address two key questions relevant to the management and conservation of freshwater fish, with a focus on the brown trout (Fig. 3). For each question, we give examples of individual-based simulation models that have been or could be applied to brown trout, and we present the data they require. In the final section, we address the developing field of demogenetics that employs individual-based simulation models.
Individual-based simulation models
Occasionally used in ecology since the 1960s, individual-based models (IBM) made a breakthrough in the late 1980s when object-oriented programming (OOP) became available (Grimm 1999; DeAngelis & Mooij 2005; Breckling et al. 2006). Since then, a number of applications have arisen in ecology: reproduction, dispersal, formation of patterns among individuals, foraging and bioenergetics, species interactions, local competition and community dynamics, population management strategies (Breckling et al. 2005; DeAngelis & Mooij 2005). Individual-based modelling techniques can be viewed as complex computer simulations, which the goal is to mimic a real-world empirical system by creating a ‘computer-world’ to represent the system’s biological processes (Peck 2004). The approach lends itself directly to the use of OOP methods: elements of the program are ‘objects’ which pass, receive and respond to ‘messages’ (Kimmerer et al. 2001). Thus, OOP is a natural way for implementing IBMs and is designed to be independent of software platforms.
Individual-based simulation techniques treat individuals as unique and autonomous discrete entities, and these models can be used to explore how the properties of higher level ecological entities, like populations, emerge from interactions of individuals with each other and their environment (Grimm & Railsback 2005). The great potential of IBMs comes at a cost. First, demographic stochasticity is an intrinsic property of any IBM (DeAngelis & Mooij 2005), and it is thus not possible to study the effects of its absence on a population. Second, data requirements can be a serious limitation. Indeed, IBMs require much data to be calibrated and validated (Jorgensen 2008), with more complex models requiring more parameters to specify the processes (Grimm & Railsback 2005; Breckling et al. 2006). This structural complexity can make IBMs harder to implement, analyse and communicate than are equation-based models such as population dynamics models and F-statistics. Furthermore, the high number of parameters requires detailed biological knowledge (Breckling et al. 2006), e.g., behavioural data that can be difficult to obtain for some species. Thus, limits in biological knowledge might restrict the application of this model type (Breckling 2002).
The respective limitations and strengths of both equation-based and individual-based models should be considered when choosing the appropriate approach for an investigation (Breckling et al. 2006). Individual-based models should be used when a modeller wants to consider one or more of the following individual-level characteristics to explain system-level behaviour: heterogeneity among individuals, local interactions and adaptive behaviour which is based on decision-making (Thiele & Grimm 2010).
Individual-based simulation models should not be confused with ecological models dealing in some way with individuals. For instance, in population genetics, classification and clustering methods are implemented in individual-centred programs, i.e., for which the main focus of the analysis is on individuals (Excoffier & Heckel 2006).
Spatial dynamics models – How can we predict fish population responses to management intervention?
Stream fish populations are subject to natural control processes that continually affect their structure and abundance, as well as their life cycles, in response to a wide range of factors (Milner et al. 2003). The knowledge of how fish populations are naturally regulated is thus necessary to determine how they might respond to a management intervention, for instance a modification of the stream flow resulting in an alteration of their habitat. The first step is to model the dynamics of the studied population. Then, we need to add habitat heterogeneity in the model and, therefore, consider small spatial scales. By modifying variables in the model, we can finally predict the outcome of the management intervention. The use of population dynamics models in a spatially explicit framework (i.e., spatial dynamics models) is one of the possible answers to address the first key question: ‘How can we predict fish population responses to management intervention?’ This question is management-oriented and focuses on a single population at a small spatial scale (i.e., the stream reach).
Our review of habitat–hydraulic models demonstrates that understanding the spatial variability of stream habitat and the complex interactions between habitat and fish is a major issue in stream ecology. Brown trout show strong preferences for habitat features such as spawning substratum, temperature, flow and water quality (see Elliott 1994). The inclusion of stream scale habitat characteristics into population dynamics models has lead to the development of spatial dynamics models, which can theoretically be linked to the ecohydraulics field. Ecohydraulics is an interdisciplinary approach that tends to understand the demographic processes that limit population density, to determine which life stages are important and to determine whether, and how, demographic rates are affected by flow (Lancaster & Downes 2010).
Another way to include biological characteristics into habitat–hydraulic models is to combine models dedicated to the evaluation of the physical habitat of fish, such as habitat suitability models and habitat–hydraulic models, with population dynamics models. First, matrix projection models were enhanced to include environmental stochasticity (Tuljapurkar 1990). For instance, the fish survival rates in a Leslie matrix (see the section on Population dynamics models) can be reduced according to fluctuation in the habitat using WUA time series (see Capra et al. 2003 for an example with brown trout). Most recently, Letcher et al. (2007) studied the importance of dispersal and fragmentation on the dynamics of a brook trout population, using a spatially explicit stage-based matrix model. Second, the development of integral projection model formulations for stochastic environments is another promising approach (see Rees & Ellner 2009). Two examples applied to aquatic insects that illustrate the integration between ecology and hydraulics are described in Lancaster & Downes (2010). Third, spatial dynamics models implemented with individual-based simulation techniques permit the integration of not only habitat heterogeneity but also the complex interactions between individuals and their habitat (DeAngelis & Mooij 2005). For instance, the software HexSim (Schumaker 2011) enables the simulation of terrestrial populations’ complex life history under multiple spatial themes representing habitat, disturbance regimes or even landscape barriers.
As a result of the merging of population dynamics and habitat–hydraulic models, spatial dynamics models need three types of data: demographic, hydraulic and habitat suitability. First, demographic and reproductive data on stream fish are gathered by observations, trapping and electrofishing. When fish are marked in some way (e.g., fin clipping), statistical methods known as ‘capture–recapture methods’ can be used for estimating the size of the studied population as well as fish survival rates. Reproductive observations such as number of eggs, number of nests and nest success are estimated by monitoring gravid females and nests counting. Second, hydraulic data are based on transect sampling of water depths and flow velocities and on visual estimation of substrate classes (Mouton et al. 2007b). Third, preference curves needed to evaluate habitat suitability of fish (see the section on Habitat–hydraulic models) are produced from observational studies of habitat utilisation, literature surveys and expert opinion (Heggenes et al. 2002).
Landscape genetics models — How is the genetic structure of fish populations influenced by landscape characteristics?
To manage natural fish populations living in a river basin, it is vital to identify both the number of populations to manage and the interactions that exist among them. These two points allow information to be gathered on the genetic structure of populations, which is a prerequisite to study the effects of landscape features on the genetic processes regulating those populations. The first step is to infer the current and historical genetic structure of a population to determine the number of genetically distinct fish populations present in a system and the interactions between them. Then, we need to integrate the riverscape (i.e., the riverine landscape, see Wiens 2002) in the model. The use of population genetics models in a spatially explicit framework (i.e., landscape genetics models) is one answer to address the second key question: ‘How is the genetic structure of fish populations influenced by landscape characteristics?’ This question is conservation-oriented and considers several fish populations at a larger spatial scale.
In the field of population genetics, coalescent simulation programs have been extended to incorporate the influence of environmental parameters on migration (e.g., SPLATCHE: Currat et al. 2004). On the side of quantitative genetics, quantiNEMO (Neuenschwander et al. 2008a) is an individual-based program that investigates the effects of mutation, selection, recombination and drift on quantitative traits in populations connected by migration and located in a heterogeneous habitat. The inclusion of spatial details into genetics models allowed the development of landscape genetics models, theoretically linked to the discipline of the same name. Landscape genetics aims to study the interactions between landscape features and micro-evolutionary processes (i.e., within species) that generate genetic structure across space (Manel et al. 2003), and it has been identified as a field that integrates population genetics, landscape ecology and spatial statistics (Storfer et al. 2007).
The key steps of landscape genetics are twofold (Manel et al. 2003; Pearse & Crandall 2004). First, the spatial detection and location of genetic discontinuities among populations allow the determination of spatial genetic patterns (Manel et al. 2003). Common patterns described in the salmonid literature are isolation by distance (i.e., genetic differentiation among populations that increases with their geographical distance, see Poissant et al. 2005; Dionne et al. 2008), barriers to gene flow (e.g., impassable waterfalls or dams, see Dillane et al. 2008), mosaic structure of evolutionary lineages (see Sanz et al. 2002; McKeown et al. 2010) and coexistence of anadromous and resident migration morphs (i.e., sympatric populations, see Ferguson 2004; Narum et al. 2008). The second key step is the correlation of spatial genetic patterns with environmental features, such as elevation, rainfall and upstream distance, using statistical methods similar to those presented in the section on Spatial distribution models. Geographic information systems are then used to produce statistical and visual materials on landscape characteristics and patterns (Johnson & Gage 1997).
The flexibility of individual-based simulation models has progressively increased the incorporation of spatial and ecological details and processes into landscape genetics models (Balkenhol et al. 2009a; Epperson et al. 2010). For instance, an individual-based spatially explicit landscape genetics model, CDPOP, has recently been developed by Landguth & Cushman (2010) to simulate dispersal, mating and genetic exchange as probabilistic functions of cost distance among individuals (Segelbacher et al. 2010). An alternative approach proposed by Epperson et al. (2010) is to combine individual-based programs from ecology and genetics like HexSim and simuPOP (Peng & Kimmel 2005; Peng & Amos 2008), but this has not been tested yet. The scope of the landscape genetics field is expanding and will tend to be more interdisciplinary as it merges with geography, ecology, evolution and phylogeography (Epperson et al. 2010; Sork & Waits 2010).
In landscape genetics models, genetic data are combined with spatial data. First, genetic data, i.e., individual multi-locus genotypes and allele frequencies of fish samples, are provided by DNA markers (e.g., micro-satellites, see Carvalho & Hauser 1998). DNA is extracted from fin or muscle biopsies, which are collected from fish captured either by trapping or by electrofishing. Second, spatial data are generally presented in the form of digital maps from GIS (Jager et al. 2005). For stream fish, such data usually provide information about watershed characteristics. Guidance on sampling and analysis of landscape genetics data can be found in Anderson et al. (2010).
The developing field of individual-based demogenetics
The population dynamics and population genetics models reviewed earlier show that considerable advances have been achieved in both fields, mostly in separate ways. However, ecological and life history characteristics such as population size, dispersal pattern and mating system have been shown to influence fish population genetic divergence through their effects on genetic drift and gene flow (Turner & Trexler 1998; Dawson et al. 2002; Whiteley et al. 2004). Individual-based simulation techniques enable the joint generation and analysis of demographic and genetic data (Palsboll et al. 2007) and have thus allowed the development of attempts including either more genetic realism into population dynamics models or more biological realism into population genetics models. Table 7 lists the software associated with these attempts, which are described below, and the software mentioned earlier in the section on Population ecology models. This table shows (i) the great flexibility of coalescent simulation techniques, which is somewhat limited by their difficulties in integrating natural selection in the simulations, and (ii) the progressive use of individual-based simulation techniques.
Table 7. List of software from population dynamics and population genetics relevant to individual-based demogenetic models. Features implemented in each program are specified.
*In the new version of the MS program (released October 14, 2007), the user can specify if the population has been growing or shrinking exponentially.
IBM, individual-based model; VarPop, variable population size; Sel, natural selection; Rec, recombination; Migr, migration or dispersal; Mut, mutation; PD, population dynamics; PG, population genetics, with forward-time (F) or coalescent (C) simulation programs; QG, quantitative genetics.
In the field of population dynamics, the individual-based model METASIM (Strand 2002) provides a flexible environment, based on matrix projection theory, to simulate population genetics of complex population dynamics. Population dynamics models are also frequently used for population viability analysis or PVA, which aims to predict the likelihood of the persistence of an endangered species for a given time in the future (DeSalle & Amato 2004). PVA programs such as VORTEX (Lacy 2000) aim to study the effects of deterministic forces and stochastic events on the dynamics of populations, including changes in genetic variation.
In population genetics, earlier coalescent simulation programs assumed a constant population size, because the original formulation of the coalescent approach was made under the assumption of a Wright–Fisher model. More realistic versions of this approach have been developed to take into account factors such as genetic recombination, gene conversion, population subdivision, population growth and demography (Marjoram & Tavaré 2006; Kuhner 2009). A method named approximate Bayesian computation (Beaumont et al. 2002; reviewed by Bertorelle et al. 2010 and Csilléry et al. 2010) proposed a more flexible framework to address complex scenarios (Segelbacher et al. 2010). In addition, forward-time simulation programs such as simuPOP and NEMO (Guillaume & Rougemont 2006) explicitly model the properties of individuals and specify arbitrary patterns of population size changes. In the field of quantitative genetics, the recent development of individual-based eco-genetic models allowed evaluating the relative importance of genetic and ecological effects on fish life-history traits and stock productivity by taking into account quantitative genetic traits inheritance (e.g., Dunlop et al. 2009; Wang & Hook 2009).
In all of these attempts to develop models that integrate demography and population genetic structure, the expected level of population genetic divergence is still estimated under specific population size change and dispersal rate patterns (Palsboll et al. 2007). A further understanding of how demography influences the genetic structure of stream fish populations is an important next step in developing comprehensive individual-based demogenetic models.
Discussion and summary: towards a spatially explicit demogenetic model for brown trout
Our review demonstrates the historic development of ecological models for brown trout over the past 30 years, and the extent to which modelling currently plays a role in the management and conservation of freshwater fish. To our knowledge, this is the most comprehensive effort to date to review and synthesise this broad topic. We found that initially the development of ecological models followed four separate trajectories: population dynamics, population genetics, habitat preferences and spatial distribution. Our review highlights efforts that have been made to integrate ecological models across spatial scales and shows the increasing use of individual-based simulation techniques. First, we addressed models integrating stream scale habitat characteristics into population dynamics (i.e., spatial dynamics models), or landscape ecology into population genetics (i.e., landscape genetics models). Table 8 lists the programs associated with these models and mentioned earlier. Second, there have been efforts to integrate population dynamics and population genetics models, and we reviewed individual-based demogenetic models that have appeared recently (second half of Table 7). Comprehensive and flexible individual-based demogenetic models however are in the early stages of development. Furthermore, we believe there is a need to integrate spatially explicit methodology into demogenetic models, to better address the important issue of ecological scale (e.g., Wiens 1989; Peterson & Parker 1998; Schneider 2001; Lischke et al. 2007).
Table 8. List of software from spatial dynamics and landscape genetics relevant to individual-based, spatially explicit demogenetic models. Features implemented in each program are specified.
*In the new version of the program, SPLATCHE 2 (Ray et al. 2010), a recombination model has been implemented.
IBM, individual-based model; VarPop, variable population size; Sel, natural selection; Rec, recombination; Migr, migration or dispersal; Mut, mutation; PG, population genetics, with forward-time (F) or coalescent (C) simulation programs; QG, quantitative genetics; SD, spatial dynamics; LG, landscape genetics.
Future model development efforts should include spatially explicit demogenetic models that integrate demographic, genetic and spatial data. The interplay between environmental processes and demogenetic characteristics is crucial. For instance, at the stream scale, an environmental perturbation can represent a radical and rapid change in the demographic and genetic structure of a population, producing local catastrophes and reductions in suitable areas where fish can thrive (Pertoldi & Topping 2004). At a larger scale, the structure and complexity of the riverscape can affect the demogenetics of fish populations by influencing the occurrence of their dispersal strategies, and by interacting with the micro-evolutionary processes. Individual-based, spatially explicit demogenetic models may be particularly useful for fish and wildlife management and conservation questions. They can serve as a tool for understanding specific questions like the influence of barriers on the dispersal of a species, or as a simulation tool for testing hypotheses concerning the response of a population to future changes in the environment, either natural or anthropogenic.
To our knowledge, only one spatially explicit individual-based demogenetic model has been developed. KERNELPOP (Strand & Niehaus 2007) provides a population genetics simulation environment with both demographic and spatial realism. According to the authors, this model allows the implementation of almost any arbitrary population demographic and genetic model in a spatially explicit context (Table 8). Although R (R Development Core Team 2010) was used as an interface for this model, the simulation engine was implemented in C++. Therefore, the ease with which new features can be added to the model may be limited, because the user has to learn the complex details of a standard programming language (i.e., C++ in this case). A flexible yet simple method to realistically link demography and population genetics at various spatial scales is needed.
NetLogo (Wilenski 1999) provides a simplified programming language, a graphical interface and an automated simulation experiment manager that allows the user to build, observe and run IBMs. Furthermore, it is now possible to call R from NetLogo (Thiele & Grimm 2010). We believe that the combination of these powerful tools may provide a simple and flexible framework to implement individual-based, spatially explicit demogenetic models, which can in turn become a major tool in management and conservation of freshwater fish populations.
In summary, the ecological models applied to brown trout have become increasingly complex, and they have been used to predict an expanding range of responses at various spatial and temporal scales. Most recently, efforts have focused on linking the models across these scales and disciplines, but much remains to be done. Although a few models combining both demographic and genetic characteristics of populations have appeared recently, no comprehensive, spatially explicit, demogenetic model has been proposed. We have described the framework for such a model, advocating the use of individual-based simulation techniques to include individuals’ variability and different levels of spatial details. This framework, which involves both NetLogo (for model programming) and R (for model development, testing and understanding), will be tested and applied to stream-dwelling brown trout populations to describe the variations in their demogenetic structure at both stream and watershed scales. We anticipate that the application of such spatially explicit, individual-based demogenetic models to fish and wildlife populations will further improve their management and conservation, by generating testable hypotheses as to how populations might respond to natural or anthropogenic disturbances.
The first author is a recipient of a Ph.D. grant financed by the ‘Fonds pour la formation à la Recherche dans l’Industrie et dans l’Agriculture’ (F.R.I.A.). We thank Volker Grimm, Emmanuel Hanert, Filip Volckaert, Michael Morrissey and one anonymous reviewer for useful comments on earlier versions of the manuscript.