Mechanistic fish habitat assessment models evaluate particular habitat types for particular types of fish, by representing how a specific measure of individual fitness depends on characteristics of both habitat and fish. These models have long been developed and used for drift feeders—fish, especially salmonids, that feed by maintaining a fixed position and capturing food particles carried past by the stream current. Classic drift-feeding models represent: (a) net energy intake (NEI; the difference between the rate of energy gain from food capture and the rate of energy expenditure for basal and swimming metabolism, assumed proportional to growth) as the measure of fitness provided by habitat; (b) water depth and velocity as the habitat characteristics affecting NEI; and (c) length and weight as fish characteristics affecting NEI. These models assume that, as water velocity increases the rate of food delivery to the fish increases, its ability to capture food decreases, and its metabolic costs increase. Consequently, NEI and growth peak at an intermediate velocity that increases with the size of the fish. Grossman (2014); Piccolo et al. (2014), and Rosenfeld et al. (2014) review NEI and related models. Naman et al. (2020) developed their use as a habitat evaluation approach for drift feeders, specifically as an alternative to the empirical relations between hydraulic variables and fish occupancy used in traditional habitat assessment methods such as PHABSIM (Bovee et al., 1998).

The fundamental assumption of NEI models, when used to assess habitat, is that fish select habitat to maximize their growth rate; yet a variety of observations indicate that stream fish can be highly concerned with predation risk. Therefore, when microhabitat-resolution individual-based models appeared as a way to evaluate stream habitat and management effects on trout populations, they attempted to represent habitat selection as depending on both growth and predation risk (e.g., Van Winkle et al., 1998). The methods used to represent risk and its effects on habitat selection in our InSTREAM individual-based trout model (Railsback et al., 2021a, 2023) contribute to the model reproducing a wide range of observed salmonid behaviors (Railsback and Harvey, 2002; Railsback et al., 2005, 2020).

InSTREAM simulates stream habitat and the trout that occupy it. It represents habitat as microhabitat cells with (a) depths and velocities that depend on stream flow, and (b) static variables for availability of velocity shelter that reduces swimming costs for drift feeders, and predation avoidance cover. On each time step, simulated fish select a habitat cell by considering how their growth and survival probability depend on both cell habitat and competition with any larger fish occupying a cell.

Our objectives here are to discuss why and how predation risk can be represented in mechanistic habitat assessment models, whether those models address only habitat (e.g., Naman et al., 2020) or also individuals and populations (as InSTREAM does). First, we provide evidence that risk affects fish habitat selection and survival in ways that can strongly affect conclusions drawn from management models. Second, we discuss conceptual models of how predation risk varies with characteristics of habitat and the prey fish. Third, we present ways of representing habitat effects on risk: what variables are useful, how risk is usually related to those variables, and how we can observe those relationships in the field. Next, we discuss ways that risk and growth can be combined into meaningful mathematical measures of individual fitness appropriate for evaluating habitat, and why some common approaches do not work. We then consider the potential use of such fitness measures by themselves as a habitat assessment method, e.g., as replacements for suitability criteria in PHABSIM (e.g. Naman et al., 2020). Unfortunately, including predation risk emphasizes instead of reduces many of the inherent uncertainties in habitat suitability models.

Because our models—like most NEI models intended for management applications—address stream salmonids, we refer to the modeled fish as trout. We refer to habitat as cells that have variables such as depth, velocity, and cover availability that differ among cells and change over time. “Risk” refers specifically to predation risk unless otherwise noted. When used mathematically, we express risk as probability per day of mortality, and “survival” is the daily probability of surviving (1 – risk).

Over recent decades, a great deal of ecological literature has addressed the importance of predation risk on animal behavior and population dynamics (e.g., Brown et al., 1999; Preisser et al., 2005). Is it important to consider predation risk in mechanistic models of habitat benefits to trout, or is it sufficient to only consider growth? One way to answer this question is via empirical experimentation to see if risk prevents fish from using habitat that provides high growth. Harvey and White (2017) conducted exactly such an experiment: they offered juvenile salmonids high rates of food intake in habitats that were increasingly risky due to lower depths and higher distances to escape cover. They observed that fish would use riskier habitat only if it provided more food, and fish would not use the riskiest habitat (e.g., depth <20 cm) no matter how much food was provided. This evidence aligns with a variety of previous studies that indicate stream fish consider both food acquisition and risk when selecting habitat (e.g., Gilliam and Fraser, 1987; Grand and Dill, 1997; Naman et al., 2019).

However, evidence that risk affects fish habitat selection does not necessarily mean we need to consider risk in management analyses such as the evaluation of alternative instream flow regimes. Do models that only address growth produce results similar to those of models that also consider predation risk, such that the two kinds of models might lead to the same management conclusions? We addressed this question in two ways, using the InSTREAM version (7.0) and application sites of Railsback et al. (2021b). The two sites are a habitat restoration site with complex and diverse habitat, and a degraded site with a simple, U-shaped channel (Figure 1). First, we contrasted two measures of habitat availability: the percentage of stream area providing positive growth for a 15-cm trout at 15°C and negligible turbidity, and the percentage of stream area that provides positive growth and daily survival probability > 0.99 (Figure 2). Second, we examined the importance of considering risk by simulating how long-term populations varied across a range of flow regimes (the same range examined by Railsback et al., 2021b), using (a) InSTREAM’s standard formulation in which risk varies with characteristics of both habitat and individual fish, and (b) uniform risk, with all fish subject to the same daily predation survival probability of 0.995 (Figure 3).

Both of these approaches show that including how risk varies with habitat and among fish strongly alters the relation between instream flow and predicted habitat benefits, particularly by predicting greater benefits of higher flows. The effects are especially clear at the degraded site, where the simple channel provides, at low flows, ample habitat for growth but little protection from predation. Consequently, the population simulations considering NEI only predict highest abundance at a lower range of flows than do the simulations with non-uniform risk. This simple experiment indicates that evaluating habitat via NEI only and ignoring risk is likely to result in instream flow analyses that—for at least some channels—favor conditions that real trout would be afraid to use.

We begin our discussion of predation risk in habitat evaluation models by identifying conceptual models of how risk varies that we have found useful and well-supported. These conceptual models are generalizations about how risk varies with characteristics of habitat, predators, and trout prey; they of course have many exceptions.

For spatially explicit modeling, the challenge of including predation risk requires estimates of predation risk for individuals within the habitat units included in the model, with risk depending on multiple characteristics of both habitat and fish. In the InSTREAM model, we use “survival increase functions” to represent how separate characteristics of habitat cells and individual prey fish affect risk (Figure 4). These are functions (often, logistic curves) that describe how one habitat or prey variable affects survival probability; they range from 0 (no reduction in risk) to 1 (complete protection). These functions are treated as general relations that are each based on a variety of evidence, and that need little or no adjustment among model application sites.

The first step in our process of modeling risk is to determine what habitat and prey characteristics to include in the model and how to quantify them in ways most directly related to predation risk. Traditional measures of salmonid habitat such as substrate size or the amount of wood within habitat units may not best describe variation in predation risk. In InSTREAM, we use a representative distance to escape cover as the variable to describe the availability of cover relevant to immediate avoidance of predation, without regard for the material providing the cover (e.g. stone substrate, undercut banks, or vegetation). The availability of cover useful for long-term concealment behavior is treated separately. InSTREAM includes habitat depth as a factor affecting risk, although it is assumed to have opposing effects on predation risk from aquatic versus terrestrial predators. InSTREAM also includes water velocity as a potential reducer of risk from terrestrial predators. Both water velocity per se and the surface turbulence commonly associated with water velocity in streams may reduce visibility from overhead and therefore risk from terrestrial predators. We believe meaningful relations between risk and factors such as cover, depth and velocity can be established at the scale of habitat units typically used in InSTREAM (2–20 m² area), but these are unlikely to be directly usable in models that represent habitat on larger spatial scales. In contrast, other risk-affecting factors such as temperature and turbidity may be readily represented on larger spatial scales.

While neglected in InSTREAM, effects of prey fish density on risk could be represented in models. Within some specific spatial resolution, higher prey density could be assumed to reduce per-individual risk (especially for schooling fish) due to prey dilution and enhanced prey detection, or to increase risk by attracting predators.

The second step in our risk modeling process is to develop quantitative survival increase functions such as those in Figure 4. Formulation of functions relating predation risk to habitat and prey fish characteristics will almost always involve substantial speculation: few available observations can serve directly as data points. Modelers can overcome this limitation in several ways. First, functions relating risk to habitat or fish characteristics can be based on the kinds of conceptual models discussed above. For example, a relation between prey fish length and the risk of predation by other fish can be based on the “gape limitation” concept: as a fish grows, fewer other fish are large enough to consume it. Likewise, it makes conceptual sense that a fish’s risk of capture increases with its distance from escape cover. Relations based on conceptual models can often be supported and quantified by empirical evidence from the literature. Where piscivorous warmwater fish are a significant risk, for example, the conceptual model that risk increases with temperature as their metabolic rates increase can be supported with laboratory data on how piscivore respiration and digestion rates vary with temperature.

A second way to address uncertainty in risk relations is via empirical evidence. Traditional ecological field experiments can provide direct measures of relative predation risk, with the caveats that enclosure effects may vary among treatments and many experimental units will be needed to provide the range of treatments necessary to achieve the goal of describing complete gradients in risk. Tethering experiments can also provide direct measures of risk, but these also must be interpreted with caution, in part because of the potential for unequal tethering artefacts across treatments (Baker and Waltham, 2020). Combining tethering with camera trapping (Harvey and Nakamoto, 2013) mitigates the problem of prey losses not due to predation and adds information on predator identity.

A variety of indirect measures of risk may inform the effort to quantify habitat – risk relations. While fundamental risk and the perception of risk cannot be strictly equated (Gaynor et al., 2019), the latter may provide useful information for the purpose of quantifying habitat – risk relations. Harvey and White (2017) measured giving-up harvest rate with a purpose-built feeding device to quantify the perception of risk in stream salmonids along gradients of water depth and distance to cover. This approach seems likely to have limited application due to a variety of constraints, including the need to train individual fish to use a feeding device and the likely confounding influence of a variety of nuisance variable such as fish condition and the availability of alternative food resources in natural settings. Giving up food density, successfully used to measure the perception of risk in a variety of prey taxa (Gaynor et al., 2019), is likely to be difficult to apply in efforts to measure the perception of risk on relatively small spatial scales for many stream fishes, because of their ability to capture static food resources in brief forays to risky areas. Observations of where predation occurs have been widely used to assess predation risk in other systems (e.g. ungulate-carnivore, [Miller, 2015]), but such observations are more difficult in aquatic systems, in part because evidence of kill sites does not persist. However, camera trapping has been used to quantify predation rates on unconfined stream salmonids (Sullivan et al., 2023). Importantly, passive observations measure realized predation rather than fundamental predation risk: predation events are affected by antecedent habitat selection of prey and predators. Also, prey density affects per capita risk. Passive observation of predator presence alone, although an additional step away from fundamental predation risk, might also provide useful information for the purpose of estimating habitat – risk relations.

A third way to address uncertainty is via model analysis: once a model has been applied to a site, it can be analyzed to determine (e.g.) how sensitive model results are to parameters controlling each risk relationship and how sensitive management decisions based on model results (often, the rank of management alternatives such as instream flow regimes) are to uncertainty in parameter values. Such analyses are especially valuable if they guide field studies to better understand especially important relations; the study by Harvey and White (2017) was inspired by a parameter sensitivity analysis of an early version of InSTREAM that showed the relation between water depth and risk from terrestrial predators to be especially important.

The survival increase functions for terrestrial predators in Figure 4 were developed using all these methods (Railsback et al., 2023 provide full details). The function for trout length is based on the conceptual model that very small prey fish are difficult to see, can readily hide in most substrate, and are of little value to predators. The function for cell depth is based on the conceptual model that increasing depth reduces visibility to overhead predators, supported by the field observations by Harvey and White (2017) of trout willingness to feed vs. depth. The function for cell velocity is based on the concept that surface turbulence, which often increases with velocity, reduces visibility from overhead. The irradiance (light intensity) function is based on knowledge of irradiance values at different times of day, and on the assumption that most terrestrial predators are less effective at low light levels but night predation is still common. The escape cover function is based on the conceptual model that the time it takes a prey fish to reach nearby escape cover is approximately inversely proportional to its distance from cover, while distant cover offers little protection.

Once we have determined how to represent the separate effects on predation risk of several different characteristics of habitat and a fish, how do we combine those effects into one estimate of survival probability? And then how do we consider that probability in a meaningful measure of habitat value? We consider these questions here.

It is tempting to directly apply a fitness measure such as InSTREAM’s as a measure of habitat value. We could assume a typical fish size and condition, and a particular set of habitat conditions—river flow, temperature, turbidity—and then calculate, for example, the area of stream that provides >50% expected probability of the fish surviving predation and starvation for 60 days. Such a habitat measure would certainly have clearer ecological meaning than the habitat “suitability” measure of PHABSIM. (PHABSIM, a widely used management model, evaluates habitat using “suitability” functions that are typically developed from empirical habitat selection data; Bovee et al., 1998. One criticism of PHABSIM is that its suitability functions lack clear biological meaning; Railsback, 2016).

Unfortunately, that approach would still ignore major factors and uncertainties that undermine its meaningfulness. First, the physical and water quality variables that drive growth and survival—flow, temperature, turbidity—inevitably change over time and fish respond to those changes by adapting where and when they feed. Second, the daily light cycle affects growth and survival, and fish adaptively select different habitat and activities at different times of day (discussed by Railsback et al., 2021b). Third, the approach does not address competition: the growth and survival provided to individuals by a habitat cell decreases as the number of fish occupying it increases. Finally, this approach does not eliminate a fundamental limitation of habitat models: even habitat measures with clear meaning for particular individuals (e.g., 4-cm fry, 10-cm juveniles, and 20-cm adults) do not have clear meaning for populations. Meaningful evaluation of alternative instream flow regimes or habitat restoration projects at the population level requires evaluating their cumulative effects across all life stages. Including both growth and predation risk in a measure of habitat value makes these basic limitations of habitat modeling even harder to ignore.

Individual-based models (IBMs) are the only approach we know of that has been used to overcome these limitations. IBMs let us represent how habitat and animals change over time, how animals adapt to those changes and compete, and therefore how life stages are linked over time to produce meaningful and testable predictions of population response to management alternatives. IBMs have the cost of additional assumptions and parameters, but also the advantage of providing a way to estimate particularly important and uncertain parameters. For example, estimating the value of S_min in Equation 2 via field studies is very challenging, but we can readily estimate it (along with food availability) via calibration of an IBM: we can adjust these parameters until the model produces realistic fish abundance and size results. For stream salmonids, InSTREAM and InSALMO (a version of InSTREAM for freshwater lifestages of salmon) are ready-to-use IBMs that have been validated in a number of ways (Railsback et al., 2021a, 2023).

Mechanistic habitat assessment models for stream fish have important advantages over traditional observation-based habitat selection approaches (Rosenfeld et al., 2014; Naman et al., 2020). They provide conceptual clarity by representing specific elements of individual fitness, and are more reliable under novel conditions (new sites, different flows, different species mixes) than models based only on observed habitat selection. However, mechanistic approaches that consider growth (or NEI) as the only element of fitness neglect the potentially strong and important effects of predation risk on the value of habitat. Ignoring risk in habitat assessment is likely to over-value habitat that provides high growth but low survival probability because it lacks features such as depth and escape cover that reduce risk (Figure 6). The consequence, as we illustrate in Figures 2 and 3, can be underestimation of the flow needed to provide safe as well as productive habitat.

Here we introduced our methods for incorporating risk into mechanistic representation of stream habitat value, representing fitness as a tradeoff between growth and risk. Our approaches (explored more generally by Railsback and Harvey, 2020, 2025) are relatively simple but still useful, and they provide a framework for future development.