High value of ecological information for river connectivity restoration
Supplementary materials
Suresh Andrew Sethi, Jesse R. O’Hanley, Jonathon Gerken, Joshua Ashline, Catherine Bradley
Contents:
Supplemental Text S1: Life Cycle Connectivity Index and barrier mitigation prioritization methods detail.
Supplemental Text S1: Life Cycle Connectivity Index and barrier mitigation prioritization methods detail.
A barrier prioritization model was devised to maximize the Life Cycle Connectivity Index (LCCI) by determining which barriers to mitigate (i.e., restore to 100% fish passability via repair, replacement, or removal) given a limited budget. We henceforth refer to this as the LCCI maximization model to differentiate it from the optimization model for maximizing the Dendritic Connectivity Index (DCI-maximization model; Cote et al. 2009; King and O’Hanley 2016). The two optimization approaches are similar in that they both utilize the network structure of habitat reaches and barrier passabilities in the decision modeling framework; however, the LCCI-maximization model builds on the DCI-maximization model by incorporating additional information on life stage specific habitat needs and dispersal behavior as well as age- and directional-dependent passabilities for a focal fish taxon (here Coho salmon, Oncorhynchus kisutch). In this supplemental text, we provide a full mathematical description of the LCCI-maximization model and provide further details on the life history information used to parameterize the LCCI index for Coho salmon in the Big Lake watershed, Alaska, U.S.A. study area. We also briefly describe the DCI-maximization, “scoring and ranking”, and “random project selection” stream barrier mitigation prioritization approaches and associated information needs.
LCCI maximization
To formulate the LCCI-maximization problem, let , indexed by , be the set of stream barriers (e.g., culverts). The primary decision variable is whether to mitigate a specific barrier or not. This is represented by binary variable , with equal to 1 if barrier is mitigated, 0 otherwise. The unmitigated passability of barrier is given by , where denotes the direction of travel, with for upstream and for downstream, and denotes the age or life stage of fish, where for adults (ad), age 0 juveniles (juv0), age 1 juveniles (juv1), and smolts (sm). The cost of mitigating barrier is given by and results in an increase in passability of . For the Big Lake watershed application, barrier mitigation was assumed to restore full passability, hence . Parameter (omega, for “operating budget”) represents the total budget available for mitigating barriers. Note that while it is assumed here that only one mitigation option is available per barrier, it is possible to extend the modeling framework to include multiple mitigation options (King and O’Hanley 2016).
Using the notation introduced in the main text, indices , , , , and denote spawning, age 0 summer rearing, winter rearing, age 1 summer rearing, and ocean habitats. The terms , , , , and express, respectively, the partial cumulative passability for ocean-to-spawning (adults), spawning-to-summer rearing (age 0 juveniles), summer rearing-to-winter rearing (age 0 juveniles), winter rearing-to-summer rearing (age 1 juveniles), and winter rearing-to-ocean dispersal (smolts). Cumulative passability is found by multiplying together the passabilities of all barriers encountered by fish as they travel from one habitat type to another.
Overall cumulative passability starting from and ending at the ocean (), via travel through spawning (), age 0 summer rearing (), winter rearing (), age 1 summer rearing (), and back to winter rearing, is given by . Recall that only feasible paths as defined by Eqn. 1 (main text) are considered. A path is feasible if the distance between habitats for a given dispersal step does not exceed a fish’s maximum dispersal radius. The feasible subpaths within for each dispersal step are denoted by , , , , and .
With this in place, a mathematical formulation of the LCCI based barrier optimization model is given by:
/ (Eq. S1)/ / (Eqs. S2)
/ / (Eqs. S3)
/ / (Eqs. S4)
/ / (Eqs. S5)
/ / (Eqs. S6)
/ / (Eqs. S7)
/ (Eq. S8)
/ / (Eqs. S9)
The objective function (Eq. S1) is simply the LCCI metric (main text Eq. 2). Equations S2 express overall cumulative passability for each feasible route as a function of the partial cumulative passability terms , , , , and . Equations S3-S7 determine the partial cumulative passability for each dispersal step, namely ocean-to-spawning (Eqs. S3), spawning-to-age 0 summer rearing (Eqs. S4), age 0 summer rearing-to-winter rearing (Eqs. S5), winter rearing-to-age 1 summer rearing and back (Eqs. S6), and winter rearing-to-ocean (i.e. smolt migration; Eqs. S7) dispersal. For example, in equations S3, partial cumulative passability from the ocean to a particular spawning area is derived by multiplying the passabilities of all barriers along the subpath to . The passability of any barrier is , which is simply the initial passability of the barrier plus the increase in passability given mitigation times variable . If barrier is mitigated (), then its passability is , otherwise () its passability is . Equations S4-S7 are similarly defined with representing the direction of travel for barrier when going from source to destination . Equations S6 include additional passability terms to account for fish making return trips from/to winter rearing and age 1summer rearing habitats and so will invariably involve both upstream and downstream passability values for any barrier in set . Inequality S8 is the budget constraint, which states that the total cost of barrier mitigation must be less than or equal to the budget . Lastly, constraints Eqs.S9 impose binary restrictions on the barrier mitigation decision variables . Note, in the present Big Lake watershed case study, we assume that mitigation of barrier at a cost of restores barrier passability to 1. However, this assumption is not necessary and the LCCI-maximization model could just as well be parameterized with partial passabilities given barrier mitigation if desired.
The model formulated above is nonlinear due to the multiplication of partial cumulative passability terms in equations S2 and the multiplication of the variables in equations S3-S7. Cumulative passability terms were linearized using the probability chain method of O’Hanley et al. (2013). Linearization was first carried out on the partial cumulative passability term associated with subpath . A detailed explanation of this step is provided in King and O’Hanley (2016). The probability chain method was then iteratively applied to the successively longer subpaths , , , and , in order to derive the partial cumulative passability terms , , , and finally , following methods outlined in King et al. (2017) for representing a more general form of longitudinal connectivity in which fish make internal movements between different locations of a river network. A mixed integer linear programming (MILP) implementation of the LCCI maximization model was coded in the OPL modeling language using CPLEX Optimization Studio version 12.6 (IBM 2013) and solved using CPLEX’s branch and bound solver (IBM 2013).
Other barrier prioritization models
Multiple input information sets are required to parameterize the different barrier prioritization methods used in the Big Lake study system (Table S1.1). Information requirements vary by approach (Table S1.2). In the simplest case, the “random project selection” approach necessitates information only on the location of barriers, their mitigation costs, and a budget constraint. The “scoring and ranking” approach scores each stream barrier using the equation:
Eq. S10
where is the score for barrier , is the change in passability given mitigation of barrier , is the total stream habitat area above barrier , and is the cost of mitigating barrier (O’Hanley and Tomberlin 2005). After computing a score for each barrier, the barriers were sorted into descending order based on score. For any given budget amount, barriers were selected for mitigation starting with the highest scoring barrier and then selecting the next highest scoring barrier until the budget was exhausted. At any given step, only an affordable barrier was chosen. Once complete, the LCCI metric was computed for the final scoring and ranking solution. It is worth noting that this approach uses a generic fish passability ratings for each barrier (i.e., one value for all fish regardless of travel direction versus directional and fish life stage specific passabilities as with LCCI). Barrier passability was calculated as the upstream adult passability rating times the downstream smolt passability rating (Table S1.3). This combined generic passability rating was chosen to reflect a balance between adult and juvenile fish passage needs.
A formulation of DCI maximization approach is described in King and O’Hanley (2016). In brief, the aim of the model is to maximize the normalized amount of accessible river habitat above barriers (i.e., the DCI metric) subject to a budget constraint. Although this prioritization approach has the same information requirements as scoring and ranking, it utilizes this information in a more sophisticated way by considering the network structure of barriers (i.e., relative up/downstream positions) as well as the interactive effects of multiple barrier mitigation actions (Kemp and O’Hanley 2010). As with the scoring and ranking procedure, the same generic culvert passabilities were used (upstream adult passability times downstream smolt passability) and a LCCI metric was computed for each DCI-optimized solution. Finally, the LCCI maximization approach requires the highest information load, combining stream network information with detailed Coho salmon life history information.
Stream network and Coho salmon life history input information for the Big Lake watershed, Alaska, U.S.A.
Stream barrier (culvert) locations in the Big Lake watershed were georeferenced and field validated by U.S. Fish and Wildlife Service staff (J. Gerken and J. Ashline) using information from O’Doherty (2010). Mitigation cost estimates were generated by U.S. Fish and Wildlife Service engineers (Dekker and Rice 2016), and indicated a minimum culvert mitigation cost of 51,000 2015USD, a median cost of 107,000, and a maximum cost of 1,000,000. A GIS-based stream network layer was created using data downloaded from the National Hydrography Dataset (USGS 2014) and processed with the ArcGIS software platform (ESRI 2011). Culvert locations were snapped to the stream network using the Barrier Analysis Tool add-in for ArcGIS (Hornby 2013). Confluence and lake bounded river segments were chosen as the basic habitat unit for barrier mitigation prioritization analyses. Dispersal path distances and passage direction information were extracted using a customized routine written in C++. Culvert passability in the study system were initially assessed using a categorical green-grey-red ratings system implemented by the Alaska Department of Fish and Game, which rate passability based upon swimming capabilities of a 55mm juvenile salmonid (O’Doherty 2010). Stream barrier passability ratings from the Alaska Department of Fish and Game are based upon free-flowing water conditions; in some cases, winter ice conditions may further restrict stream project passabilities, however, overwinter ecology information on Coho salmon suggests these fish time migrations prior to ice up and remain relatively stationary through winter conditions (Ashline et al. 2017). The rating system was subsequently translated to quantitative up/downstream and life stage specific passabilities using the expert opinion of U.S. Fish and Wildlife Service biologists (J. Gerken and J. Ashline; Table S1.3).
To inform the LCCI optimization model for the Coho salmon life cycle in the Big Lake watershed (Figure S1.1), we utilized information from a suite of in situ field studies led by the U.S. Fish and Wildlife Service. Timing of life stage transitions in the Big Lake system were informed by primary ecological studies conducted in the study system, as detailed below. Coho salmon life stage specific habitat needs were characterized through a combination of adult fish stream surveys, mobile minnow trapping, fixed weir and fyke net sampling, and Passive Integrated Transponder (PIT) tag deployments (citations follow). Adult spawning habitat was identified from in-stream surveys and radio telemetry tracking conducted by the U.S. Fish and Wildlife Service (Foley et al. forthcoming). Field records of discrete spawning enclaves were mapped onto the Big Lake stream network (Figure S1.2). Age specific juvenile Coho salmon summer rearing habitat needs were characterized by assessing relative habitat use using minnow trapping data from throughout the Big Lake watershed as detailed in Bradley et al. (In press; also see Sethi et al. 2017). Henceforth, ages of salmon follow the “European” system (Quist el al. 2012; Mosher 1968), where age corresponds to winters after emergence. Thus, “age 0” juvenile Coho salmon refer to fish that have spent 0 winters in freshwater as free-swimming fish, whereas “age 1” indicates individuals have spent one winter in freshwater after emergence. Smolts, which migrate to the sea in the Spring following their second winter in freshwater after emergence, are thus technically age 2 fish. Age 0 juvenile Coho salmon were found to prefer wider shallower mainstem habitats for summer rearing, whereas age 1 juveniles preferred deeper mainstem reaches (Figure S1.2).
Both age 0 and age 1 juvenile Coho salmon exhibited strong preference for lakes as overwinter habitat in the Big Lake drainage (Figure S1.2; Ashline 2017; Sethi and Benolkin 2013). After two winters in freshwater, juvenile Coho salmon migrate from overwinter areas downstream to the sea as smolts. Individuals face different outward migration distances, depending on which lakes they selected for overwintering. We estimated apparent survival of PIT tagged out-migrating smolts (n = 1, 463) in the Big Lake watershed for 2012-2014 using a suite of fixed tag detection arrays deployed throughout the drainage and hand-wand tag detection at a smolt trap (modified fyke net) above the confluence with saltwater at the estuary (cf. Ashline 2017). Smolting mortality was strongly linearly related to migration distance over the range of distances observed in the Big Lake drainage, indicating high mortality during this discrete migration event (Figure S1.3). To reflect the relative values of different smolt migration origination habitats (i.e., age 1 overwinter habitat locations) in avoiding mortality along the outward migration, we imposed a discount factor on age 1 overwinter habitat equal to the apparent survival for smolts emigrating from different subbasins in the Big Lake watershed (Table S1.4). In this manner, age 1 overwinter lakes closer to saltwater represent higher quality habitat (lower smolting migration origination habitat discount) because a relatively larger fraction of smolting individuals would survive the transition to the ocean rearing life stage, and vice versa for lakes further up in the drainage at greater distance from the ocean. Smolt migration discount factors, denoted , were incorporated into the LCCI metric by simply defining adjusted overwintering habitat amounts and and then substituting these in place of and in equation 2 (main text).
Maximum fish dispersal distances achievable by different life stages were established based on a combination of expert opinion from U.S. Fish and Wildlife Service fisheries biologists (J. Gerken and J. Ashline) and analysis of recorded movements of PIT-tagged juvenile Coho salmon in the Big Lake watershed (Ashline 2017; Gerken and Sethi 2013). Adult Coho salmon and smolts were assumed to have unrestricted maximum dispersal distances (i.e., ).Based upon recorded movement of Big Lake tagged fish, age 0 juveniles are estimated to travel up to 500m from spawning/emergence areas to summer rearing grounds (i.e., . Similarly, tagged fish movements indicated a 16km maximum dispersal distance for the age 1 summer rearing to overwinter out-and-back redistribution migration (i.e., ).
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