**2. Modeling at different spatial scales**

We modeled occurrence and relative abundance of true minnows (hereafter minnows) in the upper Red River basin. Species occurrence (i.e., distributions) and abundance (i.e., population size) are fundamental ecological state variables used both in research studies and for conservation and management problems [63–65]. Both fish distributions and population sizes may be constrained by coarser-scale characteristics [1, 5, 44]. One analytical approach is to model variation in occurrence or abundance as a function of environmental variables at multiple scales (e.g., [66–68]). However, state variables are quantified differently (e.g., a binary response for occurrence and integers for abundance); thus, it is typically not possible to model multiple states in a single analysis. Different state variables also more naturally align with certain spatial scales. For example, abundance is often not ecologically meaningful at very coarse scales (e.g., basins) and measuring and managing population size at these scales is not realistic. Therefore, occurrence is typically examined at the basin scale, where the stream reach (i.e., a series of representative habitat complexes nested in tributary complexes) is the natural scale for studies and management of abundance [5, 44]. An alternative multiscale analytical approach (our approach here) is to model variation in occurrence and abundance separately at relevant spatial scales.

### **2.1 Study area**

Our study area was in the upper Red River basin of the Great Plains. The area comprised portions of the Central Great Plains and Southwestern Tablelands subecoregions of Oklahoma and Texas (**Figure 1**). The eastern boundary with the Cross Timbers sub-ecoregion corresponded with a transition from sand-bed to gravel-bed streams with lower salinity, increased vegetation, and fish species hybridization zones [69–71]. The western boundary corresponded with the higher-elevation, more-arid High Plains sub-ecoregion. The Central Great Plains is characterized by mixed-grass prairie vegetation, cropland, and landforms that include sand dunes, low mountains, and salt flats [70]. The Southwestern Tablelands has a more rugged terrain, with dissected plain, hill, and canyon landforms, sparse short grass prairie vegetation, and less cropland. Annual precipitation in the study area, though highly variable, increases from east to west eastward (mean rainfall 56–97 cm). In addition to minnows, the brackish plains killifish *Fundulus zebrinus* and Red River pupfish *Cyprinodon fluviatilis* are also common in the study area.

### **2.2 Small-bodied minnow occurrence among hydraulic response units**

We modeled occurrence probability of nine minnows species among hydraulic response units (HRUs) nested in the upper Red River basin (**Figure 1**). HRUs are sub-basins that represent 10-digit hydrologic units with refined boundaries for flow modeling based on local characteristics [72, 73]. The focal species included four pelagophils (emerald shiner *Notropis atherinoides*, plains minnow *Hybognathus placitus*, prairie chub *Macrhybopsis australis*, and Red River shiner *N. bairdi*, [52]), bullhead minnow *Pimephales vigilax*, fathead minnow *P. promelas,* red shiner *Cyprinella lutrensis*, sand shiner *N. stramineus*, and suckermouth minnow *Phenacobius mirabilis*. Most species occur elsewhere in North America east of the Rocky Mountains, with emerald shiner, fathead minnow, and red shiner widely distributed (www.iucnredlist.org).

*A Hierarchical Approach to Fish Conservation in Semiarid Landscapes: A Need to Understand… DOI: http://dx.doi.org/10.5772/intechopen.105602*

### **Figure 1.**

*Study area in the upper Red River basin. The shading in the upper panel denotes level-three sub-ecoregion boundaries (from west to east: High Plains, Southwestern Tablelands, Central Great Plains, and Cross Timbers). Inner borders on polygons show the delineation of hydrologic response units included in the occurrence modeling (Section 2.2). White circles are stream reaches surveyed for prairie chub in 2019 (Section 2.3). The polylines show the Red River mainstem (thicker line) and select major tributaries: A is the North Fork, B is the Pease River, C is the Wichita River, and D is Cache Creek.*

Red River shiner is endemic to most of the Red River basin and introduced to other basins of Arkansas, Oklahoma, and Texas [61]. Prairie chub, a species of conservation concern (see Section 2.3), is restricted to the upper Red River basin [69, 71]. We did not include minnows that only occur near the ecotone with the Cross Timbers.

Our study period was 2002–2015. The temporal range encompassed a relatively dry climatic period (2002–2014) and one year of heavy rainfall (**Figure 3** in [74]). We assumed static species occurrence states (i.e., no colonization or extirpations of HRUs) across the study period and at least a one-year lag time for any changes in minnow occurrence states following the end of the dry period.

### *2.2.1 Fish surveys*

We compiled stream-fish surveys from state conservation and management agencies, data repositories, and online databases (Appendix 1, **Table A1**). For online databases, we used the terms "fish" and "fishes" to search all Oklahoma and Texas counties within the study area from 2002–2015. Data were processed to remove duplicate surveys. Each unique survey was spatially referenced to an HRU based on the latitude and longitude. We compiled capture histories for each species (i.e., one for detection and zero for nondetection) at each HRU. Repeat surveys at HRUs were treated as spatial replicates with replacement [76]. We also compiled the date,

sampling gear (reported in 92% of surveys), and collector (e.g., agency or individual, Appendix 1, **Table A2**). We assumed seining for surveys that did not report the gear type because it is the most-common stream-fish sampling method [77] and comprised the majority of reported surveys (64%). The additional gear types were backpack electrofishing (18% of surveys) and boat or barge electrofishing (9% of surveys).

### *2.2.2 Flow regime and fragmentation metrics*

We characterized the flow regime of each HRU using mean daily discharge estimates at the outlet. The discharge estimates were obtained from a precipitation-runoff modeling system [72] adapted from the National Hydrologic Model [78] for the Red River basin [79, 80]. We calculated flow regime metrics [81, 82] using EflowStats (version 5.0.1, median option, [83]). Due to the size of the dataset and inherent correlations among metrics, we limited the set to five with each metric representing one flow regime component (**Table 1**). The selected flow metrics were based on expected ecological relationships with minnow occurrence, particularly pelagophils (see Section 1.3), and maintaining the absolute value of Pearson's pairwise correlation coefficient *r* < 0.5.

We used the upstream network density of major dams (UNDR, #/100 rkm) at the outlet of each HRU obtained from an online database [85] to characterize fragmentation. We used UNDR because it was highly correlated with numerous other fragmentation metrics and upstream dams have been shown to be strongly associated with pelagophil distributions in the upper Red River basin [56]. We natural log transformed UNDR prior to modeling due to a right-skewed distribution. Correlation levels were reasonable between UNDR and flow regime metrics (|*r*|<0.30).

### *2.2.3 Occupancy modeling methods*

We modeled minnow occurrence relationships, while accounting for variable detection probability, using the hierarchical framework described by [86]. The latent occurrence state for minnow *i* at HRU *j* was treated as partially observed, with *zij* = 1 if the species was truly present and *zij* =0 if the species was truly absent. Each *zij* followed a Bernoulli distribution with occurrence probability Ψ:


$$z\_{i\circ} \sim \text{Bernoulli}\left(\Psi\_{\vec{\eta}}\right) \tag{1}$$

*The alphanumeric codes for metrics correspond to detailed descriptions in Appendix 7 of Kennen et al. [84].* Q*: stream discharge.*

*PCTL: percentile.*

### **Table 1.**

*Flow-regime metrics used in the species occurrence model.*

*A Hierarchical Approach to Fish Conservation in Semiarid Landscapes: A Need to Understand… DOI: http://dx.doi.org/10.5772/intechopen.105602*

The detection of species *i* at HRU *j* for survey *k* was conditional on both the true occurrence state and detection probability *p* (the probability of detecting a species in a single survey if present), where *yijk* followed a Bernoulli distribution:

$$\mathcal{Y}\_{ijk} \sim \text{Bernoulli}\left(z\_{ij}^{\*} \; \mathcal{Y}\_{ijk}\right) \tag{2}$$

We modeled variation in Ψ and *p* as a function of covariates [86]. Detection covariates comprised HRU surface area (km<sup>2</sup> , hereafter area) and drainage area. Spatially replicated surveys can result in a violation of the closed-system assumption for occupancy modeling because a species may occur at a site, but not be locally present at the time of the survey [76]. Thus, we used area to account for variation in *p* associated with patchier species distributions in larger HRUs. Drainage area characterized the stream order of the mainstem for each HRU to account for variation in *p* associated with species abundance. We natural-log transformed both detection covariates due to right-skewed distributions. Detection relationships with covariates were allowed to vary by species as deflections around the group mean hyperparameter governed by a probability distribution [64, 87, 88]. More common minnows may have inherently higher detection probability. Thus, we modeled the correlation (ρ) between species occurrence probability intercepts α*<sup>i</sup>* and species detection probability intercepts υ*i*. The intercepts were jointly distributed as [α*<sup>i</sup>* , υ*<sup>i</sup>* | Σ] � *N*(0, Σ), where Σ is a 2 x 2 matrix comprising variance components **σ<sup>2</sup>** *<sup>α</sup>* and **σ<sup>2</sup>** *<sup>v</sup>* and covariance σασ [88, 89]. We also allowed each species detection intercept to vary by both sampling gear type *g* (1, seining, 2,backpack electrofishing, 3, boat and barge electrofishing) and collector *c* (1–6, Appendix 1, **Table A2**) using a grouping factor [90, 91]. The detection component of the occupancy model can be written as:

$$\begin{aligned} \text{logit}\left(p\_{ij\text{kpc}}\right) &= \mathbf{u}\_i + \boldsymbol{\beta}\_{1i}\mathbf{X}\_{1jk} + \boldsymbol{\beta}\_{2i}\mathbf{X}\_{2jk} + \boldsymbol{\gamma}\_{ij} + \boldsymbol{\tau}\_{ic}, \text{for } i = \text{9, for } j = \text{97, for } k = \text{1, 2...K}, \quad \text{(3)}\\ \boldsymbol{\beta}\_{mi} &\sim \text{Gaussian}\left(\boldsymbol{\mu}\_{\text{flux}}, \sigma\_{\text{\tilde{\mu}m}}^2\right), \text{ for } n = 2\\ \boldsymbol{\gamma}\_{\text{ig}} &\sim \text{Gaussian}\left(\mathbf{0}, \sigma\_{\text{\gamma}}^2\right), \text{ for } \mathbf{g} = \text{3}\\ \boldsymbol{\tau}\_{ic} &\sim \text{Gaussian}\left(\mathbf{0}, \sigma\_{\text{\tilde{\mu}}}^2\right), \text{ for } \mathbf{c} = \text{6} \end{aligned}$$

where υ is the detection probability intercept, β<sup>1</sup> and β<sup>2</sup> are slopes for associated detection covariates area *X*<sup>1</sup> and drainage area *X*2, γ is the gear type grouping factor, τ is the collector grouping factor, and μ is species group mean. Occurrence covariates comprised UNDR and five flow regime metrics (see Section 2.2.3). We allowed each occurrence covariate to vary by species using the same model structure described for the detection component of the model. The occurrence component of the occupancy model can be written as:

$$\text{logit}(\Psi\_{\vec{\eta}}) = \mathfrak{a}\_{i} + \mathfrak{f}\_{\text{ni}} X\_{\eta\_{i}} \text{ for } i = 9, \text{for} \, j = 97, \text{for} \, n = 6, \mathfrak{b}\_{\text{ni}} \sim \text{Gaussian}\left(\mathfrak{u}\_{\text{f\#}}, \mathfrak{o}\_{\text{f\#}}^{2}\right), \tag{4}$$

where α is the detection probability intercept and β1–β<sup>6</sup> are slopes for associated occurrence covariates *X*1–*X*6. All detection and occurrence covariates were standardized to a mean of zero and standard deviation (SD) of one. Model coefficients are reported as the mode (most likely value) with a 90% highest density interval (HDI, [92]). Model specifications, diagnostics, and fit tests are provided as supplemental information (Appendix 2).

### *2.2.4 Occupancy modeling results*

There were varying detection relationships among minnows. Detection probability across all minnows (i.e., the group mean) at mean levels of covariates was 0.47 (90% HDI: 0.31, 0.64). Detection probability was lower in larger HRUs for all minnows, with the strength of the relationship similar to the group mean (Appendix 1, **Table A3**). The strength of the detection relationship with drainage area was higher than the group mean for emerald shiner, plains minnow, prairie chub, and Red River shiner and lower for the remaining five minnows. There was more unexplained variation in detection probability attributed to collector (SD = 0.84) than gear type (SD = 0.25). Detection probability and occurrence probability intercepts were moderately positively correlated (ρ = 0.63).

The direction of occurrence relationships with flow-regime characteristics and fragmentation varied both among all minnows and within pelagophils (emerald shiner, plains minnow, prairie chub, and Red River shiner). Occurrence probability across all minnows at mean levels of covariates was 0.76 (90% HDI: 0.60, 0.89).

Occurrence probability for all pelagophils increased sharply with increasing daily streamflow magnitude (MA2, **Table 2** and **Figure 2a**). There was a weak positive occurrence relationship with MA2 for bullhead minnow and suckermouth minnow, a weak negative relationship for sand shiner, and no relationship for fathead minnow


*BUM, bullhead minnow; EMS, emerald shiner; FAM, fathead minnow; PLM, plains minnow; PRC, prairie chub; RRS, Red River shiner; RES, red shiner; SAS, sand shiner; SUM, Suckermouth minnow; UNDR, upstream network dam density; DL17, low flow duration variability; FH3, flood pulse count; MA2, median daily flow; RA9, variability of reversals; and TH2, annual maxima variability.*

### **Table 2.**

*Minnow occurrence model coefficients reported on the logit scale as the mode with associated 90% highest density interval (HDI) from the posterior distribution. The intercept is interpreted as estimated occurrence probability at mean levels of covariates. Each covariate coefficient is interpreted with others held constant.*

*A Hierarchical Approach to Fish Conservation in Semiarid Landscapes: A Need to Understand… DOI: http://dx.doi.org/10.5772/intechopen.105602*

### **Figure 2.**

*Line graphs showing relationships between occurrence probability and daily streamflow magnitude (MA2, panel a), variability in reversals of flow (RA9, panel b), variability in timing of annual maximum streamflow (TH2, panel c), and upstream dam density (UNDR, panel d) for four small-bodied minnows in hydraulic response units of the upper Red River basin. The yellow lines represent emerald shiner, the bluelines represent prairie chub, the orange lines represent red shiner, and the black lines represent suckermouth minnow. Mean daily discharge was measured as m<sup>3</sup> /s.*

and red shiner. Occurrence probability decreased with increasing variability of reversals (RA9) for all minnows, including the cosmopolitan red shiner (**Table 2** and **Figure 2b**). Emerald shiner occurrence probability also increased sharply with increasing variability in annual maxima (TH2, **Table 2** and **Figure 2c**). The positive occurrence relationship with TH2 was weaker for bullhead minnow, fathead minnow, red shiner, sand shiner, and suckermouth minnow. Prairie chub and Red River shiner had a weak negative occurrence relationship with TH2, while plains minnow had no relationship. The group mean and all minnow occurrence relationships were similar with low flow duration variability (DL17) and flood pulse count (FH3). Occurrence probability increased with both increasing DL17 and FH3 (**Table 2**). Plains minnow, prairie chub, and Red River shiner occurrence probability decreased sharply with increasing upstream dam density (UNDR, **Table 2**, **Figure 2d**). However, there was no occurrence relationship with UNDR for emerald shiner. Sand shiner occurrence was also negatively associated with UNDR, but the strength of the relationship was weaker than that for the three pelagophils. Suckermouth minnow and bullhead

minnow occurrence probability increased sharply with increasing UNDR (**Figure 2d**). Fathead minnow occurrence was also positively associated with UNDR, but the strength of the relationship was weaker. There was no occurrence relationship with UNDR for red shiner.

### *2.2.5 Projected minnow distributions*

We projected distributions adjusted for detection probability across the study area for emerald shiner, prairie chub, red shiner, and suckermouth minnow. These minnows represented varying occurrence relationships with flow regimes and fragmentation among focal species (see Section 2.2.4). A species was considered present at all HRUs with a detection. We calculated occurrence probabilities for each species at HRUs where either there were no surveys, or they were not detected using occurrence model coefficients and covariate values (**Table 2**). We emphasize that a high occurrence probability more appropriately represents suitable conditions for occurrence, not an assurance the species is present, and a species might be present at an HRU with a low occurrence probability. Opportunity (i.e., biogeography) and other spatial and environmental factors (i.e., biogeography) not considered here also play a role in aquatic species distributions [1, 5, 93] and, like any modeled relationship, there is inherent error. This is particularly true for HRUs closer to western ecotone with the desert-like High Plains (**Figure 1**). Nevertheless, the projected distributions reflect underlying ecological relationships based on where species were either detected during sampling or likely present but not detected. Further, these modeled relationships can provide an initial step to guide species reintroduction or translocation efforts, which do not depend on present occurrence state (also see Section 3.1).

All four minnows had similar distributions based on naïve occurrence (i.e., where the species was detected) and high occurrence probability along the downstream portion of the Wichita River; however, pelagophils were less likely to occur in HRUs elsewhere (**Figure 3**). As expected, red shiner had a high occurrence probability throughout the study area (**Figure 3a**). The lower red shiner occurrence probability in the southwest portion of the study area reflects the negative relationship with higher variability in flow reversals shared with all upper Red River minnows. Suckermouth minnow had a high occurrence probability along the upstream portion Red River mainstem and in the northern portion of the study area (**Figure 3b**). The higher suckermouth minnow occurrence probability corresponds to HRUs with more dams upstream. Suckermouth minnow occurrence probability was low in the southern portion of the study area with fewer upstream dams. Conversely, prairie chub had a low occurrence probability in the northern portion of the study area and along the upstream mainstem (**Figure 3c**). Prairie chub occurrence probability was higher than both emerald shiner and suckermouth minnow in the southern portion of the study area, particularly along the upper Wichita River. Although emerald shiner is more widespread overall than prairie chub, its projected distribution was narrower in the upper Red River (**Figure 3d**). The higher emerald shiner occurrence probability in the northern portion of the study area and along the upper mainstem is reflective of not sharing the negative upstream dam relationship with other pelagophils.

### **2.3 Prairie chub relative abundance at the stream reach scale**

Historically, the endemic prairie chub was abundant in the upper Red River mainstem and its higher-order tributaries [52]. Suspected population declines and

*A Hierarchical Approach to Fish Conservation in Semiarid Landscapes: A Need to Understand… DOI: http://dx.doi.org/10.5772/intechopen.105602*

### **Figure 3.**

*Predicted species distribution maps for hydraulic response units (HRUs) in the Cross Timbers and Southwestern Tablelands level-three sub-ecoregions in the upper Red River basin (Section 2.1, Figure 1). Occurrence probabilities were estimated using modeled relationships with flow regime metrics and upstream dam density (Section 2.3). Panel a is red shiner, panel b is suckermouth minnow, panel c is prairie chub, and panel d is emerald shiner. Species were assumed to not occur at HRUs filled with black, which are completely under reservoirs.*

poorly understood ecology has resulted in conservation concerns for prairie chub in multiple states [94, 95]. At the federal level, prairie chub is currently threatened and included as a potential endangered species on the 2021–2025 National Domestic Listing Workplan [96].

We show relationships between reach-scale adult prairie chub counts and the predictor variables longitude, stream discharge, and salinity. Prairie chub populations were surveyed at 44 stream reaches of the upper Red River basin in early autumn 2019 (**Figure 1**). A reach was defined as a longitudinal distance of twenty times mean wetted width constrained by a minimum of 100 m and a maximum of 500 m. Adult prairie chub counts were obtained using multi-pass removal sampling with a seine. Sampling occurred west of the overlap and hybridization zone with the morphologically similar shoal chub *Macrhybopsis hyostoma* [71] to minimize misidentified prairie chub (see [97] for a detailed description of sampling methods). Capture probability was fairly constant, which allowed for relative abundance comparisons among reaches. We present relationships as descriptive scatterplots of adult prairie chub counts versus each predictor variable; thus, relationships are independent and not additive. Eastern longitude and stream discharge were more highly correlated (*r* = 0.40) than salinity and longitude (*r* = 0.08) and salinity and discharge (*r* = 0.02).

Adult prairie chub counts of zero were most common (*n* = 32 reaches), with a count of only one at two reaches (**Figure 4**). All counts >1 were in the eastern half of

### **Figure 4.**

*Scatterplots depicting relationships between reach-scale adult prairie chub counts and longitude (panel a), stream discharge (panel b), and salinity (panel c). A constant of one was added to each count prior to natural-log transforming. Reach discharge was measured as m<sup>3</sup> /s and salinity was measured as PPT.*

*A Hierarchical Approach to Fish Conservation in Semiarid Landscapes: A Need to Understand… DOI: http://dx.doi.org/10.5772/intechopen.105602*

the study area, with the highest counts furthest east (**Figure 4a**). There was a general positive linear trend in relative abundance with increasing reach discharge for counts >1 (**Figure 4b**). Counts >1 also increased with increasing salinity (**Figure 4c**). However, the highest counts were associated with intermediate salinity (�2–6 PPT), which suggested a quadratic relationship.
