Increased population size of fish in a lowland river following restoration of structural habitat

Abstract Most assessments of the effectiveness of river restoration are done at small spatial scales (<10 km) over short time frames (less than three years), potentially failing to capture large‐scale mechanisms such as completion of life‐history processes, changes to system productivity, or time lags of ecosystem responses. To test the hypothesis that populations of two species of large‐bodied, piscivorous, native fishes would increase in response to large‐scale structural habitat restoration (reintroduction of 4,450 pieces of coarse woody habitat into a 110‐km reach of the Murray River, southeastern Australia), we collected annual catch, effort, length, and tagging data over seven years for Murray cod (Maccullochella peelii) and golden perch (Macquaria ambigua) in a restored “intervention” reach and three neighboring “control” reaches. We supplemented mark–recapture data with telemetry and angler phone‐in data to assess the potentially confounding influences of movement among sampled populations, heterogeneous detection rates, and population vital rates. We applied a Bayesian hierarchical model to estimate changes in population parameters including immigration, emigration, and mortality rates. For Murray cod, we observed a threefold increase in abundance in the population within the intervention reach, while populations declined or fluctuated within the control reaches. Golden perch densities also increased twofold in the intervention reach. Our results indicate that restoring habitat heterogeneity by adding coarse woody habitats can increase the abundance of fish at a population scale in a large, lowland river. Successful restoration of poor‐quality “sink” habitats for target species relies on connectivity with high‐quality “source” habitats. We recommend that the analysis of restoration success across appropriately large spatial and temporal scales can help identify mechanisms and success rates of other restoration strategies such as restoring fish passage or delivering water for environmental outcomes.

. Summary of the model estimates outlining probabilities of transition and 95% confidence intervals. Lower and Upper refer to the lower and upper 95% Bayesian credible intervals. Trans [1,1] refers to the probability of a fish that was in population 1 in a particular year remaining in population 1 the following year. Trans [1,2] similarly refers to the probability of a fish moving from population 1 to population 2. MC = Murray cod, GP = golden perch. 95%   and arrows indicate sampling. Lake levels for population 2 are not shown.

Monitoring design consultation
We developed our monitoring design through a consultative process with stakeholders and agency decision-makers to ensure it provided information that could be used directly by practitioners. This involved a review of currently known information on interactions between submerged wood and fish, and assessing the limitations of this information for use in management. Through stakeholder workshops, we determined which new knowledge was required, and identified the metrics that would assist decision makers to (1) determine the successes and failures of this restoration type, and (2) provide information that they could use to guide restoration and native fish management in other locations. We concluded that while there is evidence that native fish used restored woody habitats, it was unclear if this use was the result of a simple redistribution of existing individuals or a true increase in population size. We also determined that understanding the processes of survival, recruitment, immigration and emigration that can lead to changes in population size is an essential precursor to answering management questions regarding the importance of nearby source populations, hatchery stocking to supplement recruitment, and fishing mortality.

Supplementary Methods
Our modeling approach followed several of the primary assumptions of CMR analyses. First, we assumed no movement to or from the main study reaches, due to the presence of dams and weirs at several of the main entry points. However, we assumed that fish could move with varying levels of ease between the four different reaches. Next, we assumed no tag loss; as the double-tagging employed allowed us to replace single tags that had been lost. Based on previous work, we also assumed that and that tag-induced mortality was low (Bird et al 2014) and that tagging did not induce any significant avoidance behavior. We used a state-space framework (King 2012) to separate the observation and process components of our model.
Given a set of N fish that are tagged over T evenly-spaced capture-recapture occasions at times t = 1, . . . , T, we denote fi (fi ∈ 1, . . . , T) as the first instance of capture for each individual. We assume that each fish has a set of states of interest that can change over the duration of the study. In general, we use the notation si to represent the sequence of states sit (t = fi, . . . , T) for individual i over the T sampling occasions.

Process model
We initially describe ait as the 'aliveness' state and add more states as we developed the model. We defined the alive/dead state as ait = 1 if individual i is alive at time t and ait = 0 otherwise. We used the standard Cormack-Jolly-Seber model to describe transitions between alive and dead states, assuming that the states ait are Bernoulli-distributed, exchangeable random variables. The probability of fish i being alive at time t is conditional on the survival parameter μ and whether or not that fish was alive in the previous year, so that We additionally allowed μ to vary over time, between different fish ages and between stream sections using a logistic regression.
Adding states to the process model accounts for individual variation in capture probabilities over time. In our case, we have three additional states of interest. First, the study area includes four distinct sections, with varying environments and populations. Second, we are interested in how detection and survival differ across ages. Finally, for the subset of individuals carrying radio tags, we want to estimate the rate at which tags become undetectable, either through removal from the system or through tag failure. Here we introduce state vectors for each of these factors into our existing model for the observation data.
Stream section: We denote bit as the stream section where individual i was recorded at each t.
As with ait, every time an individual is observed during the study, we update bit, which remains unobserved whenever an individual is not detected or captured within a year. To model how live individuals transition between stream sections, we assume that the sequence of states bit are exchangeable random multinomial variables with 4×4 transition matrix 1 , where 1 has elements 1 jk = Pr(bit = k | bit-1 = j, ait-1 = 1).
we use the notation 1 in 1 to distinguish the matrix of transitions for live individuals versus the matrix of probabilities of dead individuals, 0 which is all 0's except for the probability of remaining dead. Because we assume that dead individuals do not move, we used the 4×4 identity matrix 1 when ait = 0.
To account for individual changes in age (and therefore, capture probabilities - Bird et al. 2014, Lyon et al. 2014), we modelled changes in individual age over time using sequential observations of how individuals grew in length (Lit) to estimate the parameters of a von Bertalanffy growth curve (separately for each reach where data were sufficient). We modelled growth based on the three-parameter von Bertalanffy growth function for asymptotic growth, where the length of individual i at time t is given by: where L∞ is the asymptotic size, L0 is the size at which individuals enter the population (defined as 0 here), and k is the unitless growth parameter. Based on this growth equation, we modelled the observed change in length between two capture occasions using the von Bertalanffy growth curve: where ( 2 − 1 ) is the expected growth of individual i between times t2 and t1, and ksi is the growth rate for state (population) si. Based on these parameters, we could back-calculate the expected age at first capture for each fish, and therefore, the influence of this age on the probability of detection. Finally, we included a state for whether each fish carried an active telemetry tag, which we modelled as a random Bernoulli variable: where records whether individual i carried an active telemetry tag at time t, and is the probability of that tag remaining active.

Data models
We treated all capture data as independent, exchangeable Bernoulli variables with probability of success conditional on a capture parameter p that can itself depend on the states sit. We additionally assumed that observations are conditional both on fish having a recognizable tag and being within the study area for sampling in each of the T observation periods. Because the Murray River has many side branches, we assumed that fish can migrate out of the sampling area, thus rendering them unavailable for sampling.
However, we assumed that this movement is random and therefore confounded with p.

Electrofishing
We electrofished within discrete sampling areas and did not cover the entire fishable area.
However, because fish migrate (Koehn and Harrington 2006), we assumed that movement in

Anglers
We use the notation ri to denote the vector of angler resightings for individual i. As with electrofishing, we assumed that a fish must be alive to be captured, so Pr(ri = 1| ait-1, μt) = ait.
However, unlike the electrofishing data, we assumed that anglers were distributed throughout the sampling area. As well, anglers provided data on the fates of their catches. Thus, we were able to update ait = 0 for fish that were killed on capture or released.

Telemetry
The vectors xi and yi provide the series of observations by telemetry survey and logger-tower records for each fish. We denote the time of implantation for each telemetry-tagged fish as Fi, and zi as the tag-activity state for each fish, with zit = 1 if a tag is implanted and active and 0 otherwise. We initially set the activity state for tags to be 0 for all times beyond their guaranteed failure dates, and ignored any detections following this date. For both telemetry and logger-tower observations, we assumed that the detections are exchangeable Bernoulli random variables with probability of detection and , respectively.
However, for telemetry observations, we assumed that detections were not conditional on whether or not the fish was alive. This is based on the observation that much of the river is shallower than the maximum depth of 3 m at which radio telemetry is thought to attenuate in fresh water, and presupposes that live and dead fish have similar detection rates. We also ignored temporary and permanent movement of radio-tagged fish. Because the telemetry tags emit a unique signal for fish that have remained motionless for > 1 week, we were also able to update the aliveness history ai whenever a tag was detected, whether the fish was alive or dead.

Logger towers
By contrast, we assumed that logger towers could only detect fish if they were alive, because fish needed to swim within the vicinity of a radio tower to be recorded. As a consequence, is less of a detection probability than a probability that a radio-tagged fish will swim past a tower and be detected. In our initial models, we made no distinction between detections by any of the towers in the study area. However, we did use the sequence of transitions between towers for each fish to infer which stream section a fish was in during the electrofishing sampling period.

Incorporating latent states in the observation models
We use an individually-based logistic regression to model the dependence of capture probabilities on stream section, age and tag status. We here define the fully parameterised models which include all combinations of latent state data, which were then simplified by removing various combinations of latent states. Given the large number of possible parameter combinations, we take a pragmatic approach to modelling combinations of parameters and note that when we removed parameters from one capture model we also removed it from the others. For electrofishing and angler recaptures, we include terms for the p in each stream section and year. Next, we assumed a linear relationship between age and capture probabilities that is consistent between all 4 streamsections. This gives logit( ) = e 0 + e y + e b + age ageit where e 0 is the intercept parameter, e y is vector of year-specific parameters, e b is a length 4 vector of stream section-specific parameters, and age is a coefficient describing the linear relationship between capture and age. We defined a similar model for p e . For telemetry and logger observations, we kept the dependence on stream section and year, removed the age parameter, and included a parameter for whether or not the fish was alive. We also conditioned telemetry detections on whether or not the tag borne by a fish was active, such that

Inference and model evaluation
We used Markov chain Monte Carlo to sample from the posterior distribution of each model.
We gave all parameters in the logistic regression model diffuse Normal (0, 0.0001) priors, and gave dirichlet priors to the rows of the transition matrix 1 . For each model, we ran three chains of 120,000 samples in parallel, disregarding the first 80,000 chains and keeping every 40 th sample for the remaining 40,000 chains in each, for a total of 3,000 samples from each posterior distribution. Instead, we used Bayesian p values and root mean-squared error, both of which provide measures of how distant model-predicted values are from observed data (goodness-of-fit). We calculated both of these goodness-of-fit indices for each of the data sources when present in a model, and report how these values vary among models.
Because we accounted for major sources of variation in capture probabilities (i.e., movement, variation in size, and mortality), we estimated population size Ny for each year of the study by modelling the observed number of captures ny within each age class as a binomial random variable with probability of capture defined by py and a vague Gamma (0.01, 0.01) prior distribution for the true population size Ny. We used Markov chain Monte Carlo sampling software JAGS in the R package R2jags.