Redfin in Purrumbete – managing the fishery Recreational Fishing Grants Program Research Report

Redfin perch in – managing the fishery

June 2018

Recreational Fishing Grants Program Research Report

Published by the Victorian Government, Victorian Fisheries Authority (VFA), June 2018 © The State of , Victorian Fisheries Authority, , June 2018 This publication is copyright. No part may be reproduced by any process except in accordance with the provisions of the Copyright Act 1968. Authorised by the Victorian Government, 1 Spring Street, Melbourne. Preferred way to cite this publication: VFA (2017) Redfin perch in Lake Purrumbete – managing the fishery. Recreation Fishing Grants Program Research Report. ISBN 978-1-925733-43-3 (Print) ISBN 978-1-925733-44-0 (pdf/online) Copies are available by emailing [email protected] For more information contact the VFA Customer Service Centre 136 186

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Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program ii

Contents

Executive summary ______4

Introduction ______5

Methods ______7 Virtual population simulation model 7 Cost-benefit, regulatory and logistics analyses 9

Results ______11 Simulation modelling 11 Cost-benefit, regulatory and logistics analyses 13

Discussion ______17 Simulation modelling 17 Cost-benefit, regulatory and logistics analyses 18

Conclusions and recommendations ______19

Acknowledgements ______20

References ______21

Appendix I. Draft journal manuscript ______24

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program iii

Executive summary

Lake Purrumbete has long sustained and continues to support a well-known and very popular salmonid fishery with trophy Chinook salmon, brown trout and rainbow trout often caught. The most abundant species in the lake is redfin perch (Perca fluviatilis) and there are differing views amongst anglers regarding redfin perch in this mixed species fishery. While some anglers like to fish for redfin perch in the lake, and good catches of large fish have occurred recently, the species can be unpopular with other anglers due to large catches of small fish that have little sporting value and are too small to fillet. In 2016 the Lake Purrumbete Angling Club (LPAC) believe that there was an opportunity to improve the recreational fishery of the lake by investigating the active management of the redfin perch population in the lake. It was agreed at a recreational fishing stakeholder meeting that before a redfin perch management plan can be implemented for Lake Purrumbete, population simulation (modelling) and cost-benefit analyses should be undertaken to determine the effort and costs required to achieve the desired impact on the redfin perch population. The LPAC, with funding support from the Recreational Fishing Licence Working Grants Group, commissioned this study to determine the feasibility of instigating a redfin perch management plan for Lake Purrumbete by: (a) Using a population simulator (model) to estimate the effects of reducing the redfin perch population using a range of strategies. (b) Estimating the costs, logistics and resource requirements for reducing redfin perch population. Simulation modelling of the Lake Purrumbete redfin perch population suggested that a noticeable change in population abundance and structure can only be achieved by intensive harvesting (>50% of population) of small fish (<150 mm) annually. Harvesting lower proportions of the population less frequently had little effect on the population, while harvesting large fish (>150 mm) actually increased the abundance of less desirable small fish. These results were attributed to the life-history characteristics of redfin perch, such as the ability to respond rapidly to changes in environmental conditions and population structure. Modelling suggested that a noticeable change in population abundance and structure can only be achieved by intensive harvesting of small fish annually. This would require a substantial cost in the order of $30,000 per year to noticeably reduce the size of the redfin perch population in Lake Purrumbete. The number of redfin perch that can be harvested by the preferred method could not be assessed due to lack of information on the standing stock of redfin perch in Lake Purrumbete and fishing efficiency (catch per effort).

VFA Management Response Victorian Fisheries Authority (VFA) Management and Lake Purrumbete Angling Club (LPAC) Committee have met, reviewed this report and conclude that active harvest of redfin in Lake Purrumbete is not supported nor practicable based on the available information.

The report states that significant effort and costs would be required to noticeably reduce the size of the redfin population, and uncertainties exist regarding whether the actions modelled would be effective. Redfin are among the most popular freshwater fish in Victoria and a great food and sport fish, especially for kids and families to experience fishing.

The VFA and LPAC will continue to work together to improve fishing at Lake Purrumbete through monitoring and close engagement on the performance of the fishery, fish stocking trials and access improvements.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 4

Introduction

Lake Purrumbete (Figure 1) has long supported a well-known and very popular salmonid fishery with trophy fish often being taken (Tunbridge et al. 1991, Fisheries Victoria 1997, Department of Primary Industries 2008). The lake is regularly stocked with hatchery-bred rainbow trout (Oncorhynchus mykiss), brown trout (Salmo trutta) and Chinook salmon (Oncorhynchus tshawytscha) by the Victorian Government to sustain popular and productive put-grow-and-take recreational fisheries (Barnham 1997, Department of Primary Industries 2008, Hunt et al. 2014). Over the last decade between 25,000 and 50,000 salmonids have been stocked annually into the lake (Hunt et al. 2017). A recent assessment of lake’s salmonid fishery (Ingram et al. 2017) showed that: • Reintroduction of Chinook salmon has been highly successful with increasingly larger fish being taken by anglers and that catch rates are consistent with long term trends. • Trophy size brown trout (4.5 kg+) and well-conditioned rainbow trout (2 kg+) are regularly being caught. Despite this, the most abundant angling species in Lake Purrumbete is redfin perch (Perca fluviatilis) (Ingram 2016, Ingram et al. 2017), and recent social media reports suggest there have also been good catches of large fish over the last 12 months. However, there are differing views amongst anglers regarding the value of redfin perch in Lake Purrumbete. Redfin are extremely popular and targeted by recreational species in inland waters of Victoria (Australian Survey Research 2012). While some anglers like to fish for redfin perch in Lake Purrumbete, frequent catches of small fish from the lake that have little sporting value and are too small to fillet, has made the species less popular with other anglers. Further, the large numbers of redfin perch may also be negatively impacting on salmonid populations by both competing for food and preying on juveniles (Ingram 2016, Ingram et al. 2017). In Victoria, anglers are encouraged not to return redfin back to the water as they are a voracious predator that prey on native fish species and other aquatic organisms (https://vfa.vic.gov.au/recreational-fishing/). The Lake Purrumbete Angling Club (LPAC), established in 1928, has had a long history of advocating for improving the lake and its fishery, and has been a strong supporter of a science-based approach to management having either commissioned or supported a number of studies (e.g. Hunt et al. 2012, Hunt et al. 2014, Ingram 2016, Ingram et al. 2017). Since the proliferation of redfin perch in the lake in the early 1980s, the club has regularly expressed concerns about the impact this spread has had on the salmonid fishery. Consequently, there have several attempts by fisheries authorities to control their numbers. Two mitigation efforts have been attempted. 1) 1985 - using the floating Merwin Trap-net which proved unsuccessful, and 2) 1993 – when consistent annual stockings of brown trout were commenced. While it is confirmed that brown trout and Chinook salmon will prey on small redfin perch, it has also become known they do not control their population (Ingram 2016). In 2016, the LPAC considered that it is important to further explore options for actively managing the redfin perch population in Lake Purrumbete. This was on the belief that it may improve the quality of both the redfin perch and salmonid fishery. A recent review (Ingram 2016) commissioned by the LPAC, with funding from the Government of Victoria through revenue from Recreational Fishing Licence (RFL) Trust, to identify potential options for managing redfin perch numbers in the lake, concluded that: • implementation of a redfin perch management plan may improve the value and long-term sustainability of the trophy fishery for both salmonids and redfin perch • physical removal may have a more rapid and pronounced impact on numbers than other options • redfin perch management was technically feasible based on international experiences indicating that concerted fishing will reduce redfin perch populations. In February 2016, a meeting was held to discuss the redfin perch management in Lake Purrumbete. At the meeting, which was attended by representatives from the LPAC, the South West District Association of Angling Clubs, the Australian Trout Foundation, VRFish and Fisheries Victoria (now the Victorian Fisheries Authority), it was agreed that the before a redfin perch management plan can be considered for Lake Purrumbete, virtual population simulation (modelling) and cost-benefit analyses should be undertaken to determine the effort and costs required to achieve the desired impact on the redfin perch population. It was also recognised that fluctuations in redfin numbers have been observed over the years and there is a history of these peaks and troughs balancing out over time. The preparation of an application to the RFL Trust for funding this work followed, and consequently the LPAC commissioned this work following a successful project application. Virtual population models help to better understand of how complex and dynamic ecological interactions and processes work. Fisheries population modelling can provide a manageable and cost effective way of predicting how population size and structure will change over time in respond to management actions, such as changes to fishing pressures.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 5

The objective of this study was to determine the feasibility of a redfin perch management plan for Lake Purrumbete by: (a) Using a virtual population simulator (model) to estimate the effects of reducing redfin perch numbers on the size and structure of the population (b) Estimating the costs, logistics and resource requirements for adjusting redfin perch numbers to a level that enhances the fishery.

Figure 1. Location of Lake Purrumbete in south-western Victoria.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 6

Methods

Virtual population simulation model Virtual, computer-generated, fish population models provide a hypothetical cost-effective tool for estimating how populations are affected by for example fishing pressure. Existing published information on redfin perch populations (including reproduction, growth, and mortality data), along with fishery information from Lake Purrumbete, were used to create a computer-generated virtual redfin perch population that mimics the Lake Purrumbete population. This population simulator was then used to estimate the effects of fish reduction efforts on population size and structure in Lake Purrumbete. Modelling methods A detailed description of modelling methods is provided in Gwinn and Ingram (Accepted) (see Appendix I), and summarized below. Values for specific parameters used for modelling are described in Table 1 of Appendix I. The population model developed simulated annual numbers of fish at age for a range of fish growth rates (growth-type groups) to represent natural variation among individuals in growth and more realistically represent the cumulative effects of size-selective exploitation (intensity of removal) on the length composition and fecundity1 of the population. The model accounted for mortality due to natural causes and exploitation, density dependent survival in the juvenile life stage, and density dependent growth, mortality, and age-at-maturation in the adult life stage. The vulnerability of a given age and growth-type group to removal efforts was modeled as a Boolean variable (i.e. either true or false). The minimum length and maximum length of fish vulnerable to removal were determined by removal selectivity or specified as regulations constraining removal with minimum-length limits and maximum-length limits for legal harvest. The length-at-age was modelled with a standard von Bertalanffy (1938) growth curve modified to account for intra-annual variation in maximum size of fish and the rate at which they attain the maximum size. The model accounted for annual variation in adult growth due to density-dependent factors. The instantaneous annual natural mortality rate was modelled as inversely proportional to fish length. That is, natural mortality was higher for smaller (younger) fish and lower for larger (older) fish. Since redfin perch recruitment can be heavily regulated by inter-cohort interactions, such as cannibalism of smaller fish by larger fish (e.g. Craig 1978, Goldspink and Goodwin 1979, Bagenal 1982 Linløkken and Seeland 1996, Morgan et al. 2002), the model accounted for this form of recruitment regulation by using a Ricker stock-recruitment model.

Model parameterization Parameter input values used in the model are shown in Table 1 of Appendix I. Stock recruitment Because of a lack of empirical data on the biological parameters of redfin perch in Lake Purrumbete, most parameter values were derived from the literature. The Ricker stock-recruitment relationship used input values that were derived from Beverton-Holt stock-recruitment model parameters (Walters and Marell 2004). The carrying capacity is unknown for Lake Purrumbete. However, since this is a scaling parameter that does not influence model prediction when comparing the relative performance of exploitation (intensity of removal) scenarios, this value was set at 10,000 individuals. Although the density-dependent compensation in juvenile survival is also unknown for Lake Purrumbete, the literature overwhelmingly suggests that this is high for redfin perch (Craig and Kipling 1983, Paxton et al. 2004) and likely due to strong competition among juveniles for food (Ohlberger et al. 2014) and cannibalism of smaller fish by larger fish (Baras and Jobling 2002). Length-at-age

The minimum and maximum asymptotic lengths of redfin perch were set to 퐿̅푚푖푛 = 200 mm and 퐿̅푚푎푥 = 350 mm, based on values for similar latitudes in the northern hemisphere reported by Heibo et al. (2005), where 퐿̅푚푖푛 represents stunted populations and 퐿̅푚푎푥 represents non-stunted populations. These values are consistent with the range of values observed in Lake Purrumbete (Figure 2), and other in at similar latitudes to Lake Purrumbete (Morgan et al. 2002). The biomass where 퐿̅∞= 275 mm (훽50) was set to the predicted equilibrium biomass in the unfished condition. The “strength of density –dependent growth parameter” models growth suppression in the population due to high adult densities that can be relieved by reductions in the adult density. Specifically, this parameter results in a 35 mm increase in 퐿̅∞ (275 mm to 310 mm) when the population biomass is reduced by 25%, and a 67 mm increase (275 mm to 342

1 Number of eggs produced by an individual.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 7

mm) when the population biomass is reduced by 75%, which is observed for stunted and non-stunted populations of redfin perch (Le Cren 1958, Morgan et al. 2002). The von Bertalanffy growth curve slope and intercept values were based on reported estimates for redfin perch supplied by Fishbase (Froese and Pauly 2006) (see Figure 4a of Appendix I), which are consistent with others reported in the literature for redfin perch (Jellyman 1980, Buijse et al. 1992). The instantaneous annual mortality rate of adult redfin perch was approximated by setting the natural mortality rate to 1.5 times the value of von Bertalanffy growth coefficient for fish that have a total length of 275 mm (i.e. 퐿푟푒푓) (based on Jensen 1996). The maximum age was set at 13 years (based on Hoenig 1983). The length/weight relationship of redfin perch was determined from data for 3,182 fish collected between 1989 and 2009 in Lake Purrumbete during monitoring surveys (see Figure 4a of Appendix I). Maturation Age at maturation was set at 2 years (based on Jellyman 1980, Froese and Pauly 2006 and Heibo et al. 2005). Simulation of management scenarios The developed population model simulator was used to evaluate a range of population management scenarios, factors that can be manipulated by fishery managers, to estimate the magnitude (scale) of effort (number of fish removed and frequency of fish removal) required to have an effect on the redfin perch population, and how long that affect persisted. These included: a) Size class of fish targeted for removal. Three different size ranges were tested, which included, i. ≤ 150-mm total length, which approximates the size of fish that would be vulnerable to sampling gears such as hoop nets or electrofishing of the shallow littoral zone of the lake ii. > 150-mm total length, which approximates the size of fish that could be targeted by electrofishing and angling iii. Proportional harvest of all sizes, to represent a scenario where multiple methods were used to remove all lengths of redfin perch. b) Frequency of fish removal. Removal schedules of every year, every 3rd year, every 5th year, and every 10th year. c) Intensity of removal effort (i.e. exploitation rate), from 0 to 0.6 of population.

Figure 2. Length of redfin perch recorded from fishery surveys and creel surveys of Lake Purrumbete between 1987 and 2014 (values represent mean and range).

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 8

The response to simulation scenarios was measured as the long-term average abundance: a) “Small” fish. Fish 100-300-mm in total length to represent the size range of undesirable fish b) “Large” fish. Fish > 300-mm in total length to represent desirable fish vulnerable to angling. Because exploitation of populations that exhibit inter-cohort interactions can result in undesirable destabilization of the age structure and erratic behavior (e.g. Zipkin et al. 2009), the coefficient of variation of “small” and “large” fish abundance across years for each removal scenario was also outputted. Sensitivity analysis To account for uncertainty in life-history characteristics and current state (i.e. pre-removal) of the Lake Purrumbete redfin perch population, the robustness of general conclusions about the relative effectiveness of different removal strategies under different biological hypotheses was also evaluated. Different hypotheses about the stock-recruitment relationship, strength of density dependent recruitment compensation, strength of density-dependent growth, rate of maturation, and rate of natural mortality were considered (Table 2 of Appendix I). Although there is strong evidence that the stock recruitment relationship of redfin perch is affected by cannibalism of smaller fish by larger fish, Heibo et al. (2005) observed redfin perch populations that demonstrated stunted growth and did not appear to engage in cannibalistic behavior. Furthermore, in other studies no juvenile redfin perch were other observed in the diets of adult redfin perch of the (Pen and Potter 1992) and (Baxter et al. 1985). These studies suggest that cannibalism may not be a regulating factor in all redfin perch populations. Thus, a stock recruitment model in which there is no cannibalism (Beverton and Holt 1957) was also evaluated. Modelling assumed that the Lake Purrumbete redfin perch population experiences some level of growth suppression due to high densities (modeled by 휎 = 훽50⁄4). However, an alternative hypothesis is that the population densities are below levels that would result in growth suppression. This was also evaluated by adjusting the density dependent growth relationship (i.e. σ ~ 0) so that growth will not increase due to reductions in densities. Finally, the robustness of the results for alternative hypotheses about natural mortality and maturation were also evaluated by modeling a higher natural mortality rate of 0.8 and earlier maturation at age-1, which have been observed for many redfin perch populations (Heibo et al. 2005).

Cost-benefit, regulatory and logistics analyses A cost benefit analysis was undertaken to determine if it is economically feasible and practical to remove a sufficient number of redfin perch from the lake to achieve the desired outcome. Information was obtained on options for harvesting redfin and their disposal, costs associated with harvesting and disposal, and regulatory requirements. Following a review of options for managing redfin perch in Lake Purrumbete (Table 1), Ingram (2016) suggested that physical removal through a concentrated netting or trapping program may have a more rapid and pronounced impact on numbers than other methods. Therefore, the cost-benefit analysis conducted in this study focused on three removal options, electro-fishing, trapping using either “Windermere” traps and netting with modified eel fyke nets. Since no reliable figures are available on the standing stock (biomass) of redfin perch present in Lake Purrumbete, and the effectiveness of the difference gear types in catching redfin perch is unknown, costs of harvesting provided below are based on capital costs (for constructing traps and nets) plus a daily operating rate (labour for operating equipment, and harvesting and disposal of fish) for each method.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 9

Table 1. Options for managing redfin perch in Lake Purrumbete (modified from Ingram 2016). Method Use Life history Comments stage

Biological control

Predator introduction Population reduction Larvae, juveniles Mixed results. May affect non-target through predation. and adults. species.

Genetic manipulation Population reduction by Adults. Persistent over generations. reducing ability to Currently not developed for redfin perch. produce viable or fertile offspring.

Infectious agents Population reduction. Juveniles and Diseases may affect non-target species. adults.

Chemical control

Piscicides Population reduction by Larvae, juveniles Effective in small water bodies. poisoning. and adults. Affects non-target fish species.

Pheromones Attracting fish to nets Juveniles and Currently not developed for redfin perch. and traps. adults.

Physical removal (targeted fishing)

Netting and trapping Population reduction by Juveniles and Results affected by method and fishing removal of fish. adults. intensity (time and effort). May capture non-target species and is not consistent with fisheries management policy

Electro-fishing Population reduction by Juveniles and Non-target species may be released. removal of fish. adults. Limited by water depth.

Recreational fishing Population reduction by Juveniles and Already occurring, limited impact in Lake removal of fish. adults. Purrumbete, noting fluctuations over time.

Removal of egg Population reduction by Eggs. Limited application to date. Requires strands reducing recruitment. knowledge of spawning season and habitats in Lake Purrumbete.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 10

Results

Simulation modelling Simulation modelling results for a range of harvest lengths ( 150 mm,  150 mm and all lengths), intensity of removal effort (exploitation rates) (0 to 0.6 of population) and harvest frequency (yearly, every 3 years, every 5 years and every 10 years) are summarised in Figure 3. Modelling suggested that the magnitude of reductions in “small” (undesirable) redfin perch depends on the lengths of fish targeted for harvesting, the intensity of exploitation and frequency of harvesting (Figure 3). Results indicated that a noticeable reduction in the redfin perch population, particularly small (undesirable) fish was achieved only when both the exploitation rate ( 0.5 of population) and frequency of harvest (i.e. annually) were high. Harvesting small redfin perch ( 150 mm) only (Figure 3b) resulted in marginally better reductions in abundance than harvesting all size lengths (Figure 3a). Under all scenarios tested harvesting small redfin perch reduced the abundance of small (undesirable) fish and increased the abundance of large (desirable) fish. Harvesting all size lengths increased the abundance large (desirable) fish for most scenarios, except at the highest intensity of removal effort and harvest frequency rates, which reduced their abundance. In contrast, however, harvesting large redfin perch ( 150 mm) only resulted in increases in the abundance of small (undesirable fish) under all intensity of removal (exploitation rate) and harvest frequency scenarios and either no change or a net loss in large fish abundance regardless of the intensity of removal (exploitation rate) and harvest frequency (Figure 3c). Modelling indicated that harvesting fish annually resulted in nearly zero annual variation in small and large fish abundances, while harvesting less frequently resulted in higher annual variation (See Appendix I). Sensitivity analysis demonstrated that the resulting abundances of small and large fish were highly dependent on the biological assumptions of the model. However, the relative performance of management scenarios was fairly stable with two general patterns emerging. Firstly, the lowest abundance of small fish may be achieved by either targeting fish proportional to abundance or fish  150mm in length, depending on the assumed stock-recruitment relationship (See Appendix I). Secondly, targeting fish  150mm in length never resulted in the best outcome for either small (undesirable) fish or large (desirable) fish regardless of biological assumptions, intensity of removal (exploitation rate) and harvest frequency (see Appendix I).

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 11

Figure 3. Predicted abundance of small (undesirable) and large (desirable) redfin perch in Lake Purrumbete following harvesting at different levels of intensity (0.05, 0.1, 0.3 to 0.6 of population) and frequency (every 10 years, every 5 years, every 3 years and yearly) for harvesting that targeted all size lengths (a), fish . 150 mm

(b) and fish  150 mm (c).

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 12

Cost-benefit, regulatory and logistics analyses Three harvest options for removing redfin perch from Lake Purrumbete were assessed, electro-fishing, trapping with “Windermere“ traps and fyke netting. Harvest options Electro-fishing Electro-fishing may be effective at targeting schools of juveniles in the shallower parts of lake. Commercial electro-fishing operations, cost in the order of $1,500 to $2,000 per day, which includes labour and use of specialised electro-fishing equipment (Table 2). Five days of fishing is expected to cost up to $14,000, which equates to around $52,000 to $168,000 for 4-12 weeks of operation per year (Table 3). “Windermere” traps The “Windermere” trap, as described by Worthington (1950) and Bagenal (1972) (Figure 4), was adopted as the primary method of catching redfin perch in the Lake Windermere (England) as less labour was required compared to seine and gill netting (Le Cren 2001). The traps are laid unbaited on the lake bed in 4.5-6 m of water and their positions marked with floats. Trapping was concentrated around the spawning season (Le Cren 2001), and caught fish between 90 and 300 mm in length (Le Cren 1987). Information on intensive trap fishing in Lake Windermere, which reduced the redfin perch population to about 13% of its original density within a few years (Worthington 1950, Le Cren 1958, Le Cren 2001), was used to estimate the number of traps required in Lake Purrumbete. In Lake Windermere (1475 ha, 36 km coastline), around 600 traps were Figure 4. “Windermere” trap (Image monitored weekly by 30 operators, which represents about 17 traps per source: Bagenal 1972). km of coastline. In Lake Purrumbete (528 ha, 10 km coastline), this equates to around 167 traps and nine operators. Construction of the traps was estimated to be approximately $200 and twice weekly monitoring (labour) was nominally $1,800 ($25/hr x 9 operators x 4 hrs/operator twice per week) (Table 2). A trapping exercise over 4-12 weeks during the warmers months of the year would cost in the order of $7,200 to $21,600 per year (Table 3). Operators will require a vessel large enough to manage the deployment and monitoring of the traps. Modified fyke nets Redfin perch are often caught as bycatch in commercial eel nets (Figure 5) in Lake Purrumbete (Figure 6, Figure 7). Catches are typically highest in spring and summer, but catch is highly variable (as indicated by error bars) (Figure 7). For example, for the month of October from 2001 to 2014 the catch per unit effort was 0 – 0.6 kg/net/day, which may reflect the high annual variability in abundance of redfin perch in the lake (Figure 8). Using modified fyke nets, specifically designed to target small redfin may be more efficient at catching redfin perch than standard eel fyke nets. Having one to three extended wings, fyke nets may be able fish a larger area than the “Windermere” traps and so fewer nets may be required. Construction of the modified fyke nets, including changes to design, mesh size and grills for targeting juvenile redfin and limiting catch on non-target species, was estimated to be around $400 per net. Weekly monitoring (labour) of the 50 fyke nets was nominally $2,625 ($25/hr x 3 operators x 5 hrs/operator for 7 days per week) (Table 2). Annual cost for operating a netting exercise over 4 -12 weeks during the warmers months of the year would cost in the order of $7,500 to $22,500, per year (Table 3).

Fishing season and location Bycatch data from commercial eel fishing data (Figure 7), suggests that concentrating fishing effort during the warmer months in shallower water around the margins of the lake may improve the catch of small (juvenile) redfin perch, which tend to congregate in these areas. Fishing in warmer months may also limit catch of non-target salmonid species, which are more likely to be in the deeper, cooler, water of the lake at this time. However, there is a risk that small native species, such as common galaxias () (Galaxias maculatus), flathead gudgeon (Philypnodon grandiceps) and (Nannoperca australis), may be caught in traps and nets. Galaxias are an important prey item for salmonids in Lake Purrumbete (e.g. Cadwallader and Eden 1981), and changes in their abundance have been suggested to affect the quality of the salmonid fishery in the lake (e.g. Eddy and Smith 1995). Please refer to the sections below titled ‘Other Regulatory Matters’ regarding commercial net fishing management in inland waters.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 13

Table 2. Indicative costs of redfin harvesting in Lake Purrumbete.

Method Description Capital Labour per week

Cost inclusive of equipment use Electro-fishing Nil $14,000 and labour

167 traps ($200/trap). “Windermere” Monitored twice weekly by 9 $33,333 $1,800 trapping operators (4 hrs twice per week at $25/hr)

50 nets ($400/net). Fyke-netting Monitored daily by 3 operators (5 $20,000 $2,625 hrs per day for 7 days at $25/hr)

Table 3. Capital and accumulative annual operating cost for harvesting redfin perch from Lake Purrumbete (costs based on figures in Table 2).

Number Accumulative operating cost Method Capital of weeks per year* Year 1 Year 2 Year 3 Year 4 Year 5

Electro- Nil 4 $52,000 $112,000 $168,000 $224,000 $280,000 fishing 8 $112,000 $224,000 $336,000 $448,000 $560,000

12 $168,000 $336,000 $504,000 $672,000 $840,000

“Windermere” $33,333 4 $7,200 $14,400 $21,600 $28,800 $36,000 trapping 8 $14,400 $28,800 $43,200 $57,600 $72,000

12 $21,600 $43,200 $64,800 $86,400 $108,000

Modified $20,000 4 $10,500 $21,000 $31,500 $42,000 $52,500 fyke-netting 8 $21,000 $42,000 $63,000 $84,000 $105,000

12 $31,500 $63,000 $94,500 $126,000 $157,500 * 7 days per week

Figure 5. Fyke net (http://delwp.vic.gov.au/fishing-and-hunting/recreational-fishing/recreational-fishing-guide).

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 14

Figure 6. Eel fyke nets (left) set in Lake Purrumbete in January, and juvenile redfin perch removed from the nets (right) (Photo source: Richard Allan)

Figure 7. Catch and catch per unit effort of redfin perch (as bycatch) in commercial eel fyke nets in Lake Purrumbete between 2011 and 2014 (values = mean ± standard error) (Date source: Victorian Fisheries Authority, used with permission of the licence holder).

Figure 8. Catch per unit effort Redfin perch caught in Lake Purrumbete using fishery independent methods (Data source: Baxter 1987, Baxter et al. 1988, Baxter et al. 1989, Baxter et al. 1990, Baxter et

al. 1991, Baxter et al. 1992, Baxter and Vallis 1993, Baxter and Vallis 1994, Baxter and Vallis 1995, Pomorin 2004, Hall and Douglas 2010, and Snobs Creek Fisheries Database). (Catch per unit effort based on catch from standardised fleet of gill nets (50-250 mm mesh size) fished for 15-40 hrs).

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 15

Other regulatory matters Commercial net fishing in inland waters raises a number of policy and regulatory matters. Commercial net fishing in inland waters was phased out in 2002. Redfin perch cannot be commercially fished in Victoria. Currently licenced commercial fishing in Victoria is restricted to eel fishing, yabby fishing, removal of noxious species and collection of bait species. For example, eel fishery access licence holders must return to the water immediately all fish, other than eel, carp, goldfish, roach, tench or any noxious fish; and any other (Fisheries Regulations 2009, Regulation 144 – (Division 7—Conditions of Eel Fishery Access Licence).

Fish disposal options If commercial redfin fishing was allowed, options for disposal of harvested fish may include: a) Sale for human consumption. Allowing sale of harvested fish may offset costs of removal activities. Although there are existing markets for redfin perch, such as in NSW where the species is listed as a Class 1 noxious fish (http://www.dpi.nsw.gov.au/fishing/pests-diseases/freshwater-pests/species/redfin-perch), this option is not likely to occur for fish harvested from Lake Purrumbete particularly if small fish ( 150 mm) are being targeted. b) Composting. The fee for disposal of organic waste for composing through the Corangamite Shire Council is $84.60/t, which is more cost effective than disposal to land fill, which costs $178 /t (https://www.corangamite.vic.gov.au/Property/Rubbish-and-Recycling).

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 16

Discussion

Simulation modelling Hypothetical modelling results suggest the removal scenario that will result in the greatest reduction in small fish and the greatest increase in large fish in the Lake Purrumbete redfin perch population is one that directs harvest at small fish( ≤ 150 mm) with high levels of harvest, annually. This result was consistent across most assumptions about life-history characteristics, density dependent processes, and population dynamics rates, suggesting that this management strategy is robust to most relevant biological uncertainties. Modelling also suggested that harvesting redfin perch annually will reduce annual variation in the population size and structure, which is common for fish populations that exhibit cannibalism of smaller fish by larger fish, such as redfin perch. Responses of redfin perch to harvesting in the present modelling study were consistent with other observations of redfin perch and species with similar life histories in the literature. For example, modelling in the current study suggested that management scenarios that turn on and off harvest pressure (intensity and frequency of harvest) will result in annual variation in the redfin perch population. This variation is partially due to the periodicity of harvest exploitation, but is also expected for fishes that exhibit inter-cohort interactions, such as redfin perch. This is because larger older fish regulate the survival of smaller younger fish through predation. Thus, any disruption to this regulation can result in exaggerated boom and bust cycles of recruitment. This phenomenon has been observed for redfin perch in Lake Windermere, England, after disease resulted in an extreme decline in large fish in 1977 (Ohlberger et al. 2014). This result was also observed for smallmouth bass (Micropterus dolomieu), a species with similar life-history characteristics, in a temperate lake in New York, USA (Zipkin et al. 2008). For this population, an intensive removal effort resulted in increases in overall abundance and annual variation in abundance of fish primarily due to increases in recruitment. Although modelling in the current study suggests that population stability can be achieved if intensive removal efforts are applied annually, other studies have highlighted the risk of applying removal efforts to populations that can demonstrate increased recruitment due to less cannibalism and potential for boom and bust cycling of the population (e.g. Zipkin et al. 2008, Ohlberger et al. 2014). The current modelling study suggests that strategies that target small fish for removal can result in less smaller fish and more larger fish. This result is consistent with the predictions of Zipkin et al. (2009) for a range of animal species. Zipkin et al. (2009) demonstrated that adult harvest strategies and equal proportions harvest strategies can generate increased recruitment compared to harvest strategies that target juveniles only. However, they also demonstrated that all harvest strategies may result in increased recruitment when the strength of density-dependent compensation in juvenile survival was high and strongly related to cannibalistic behavior. Cannibalism contributed greatly to the cyclic fluctuations in redfin perch abundance in Lake Geneva (Dubois et al. 2008). For redfin perch in Lake Purrumbete, however, the strength of density dependent juvenile survival is unknown and its link to cannibalism is also unknown. Alternatively, studies from other systems suggest that density-dependent compensation in juvenile survival has the potential to be high (Craig and Kipling 1983, Heibo et al. 2005) and a cannibalistic diet can exist for fish larger than 120 to 200 mm in length (Popova and Sytina 1977, Goldspink and Goodwin 1979, Pen and Potter 1992, Ohlberger et al. 2014). Information on the diet of redfin perch in Lake Purrumbete is limited. Pomorin (2004) examined the stomach contents of 56 redfin perch (255-374 mm in length) collected from two restricted sampling events in Lake Purrumbete in November 1999 and October 2000, 70% had empty stomachs while others had galaxiids, gudgeon, unidentified fish, snails, insects, shrimp, freshwater crabs, amphipods and detritus in the stomachs. Conducting a more detailed diet study, particularly at times of the year when juveniles are abundant, may reveal whether cannibalism is a strong regulating factor for Lake Purrumbete redfin perch and which sizes of fish engage in cannibalism. This information may help managers understand the potential risks of removal efforts on this population and help refine removal strategies. For example, size classes of fish that engage in cannibalistic behavior will have some regulating effects on recruitment, thus, management strategies to remove fish smaller than these sizes would be preferred. This modelling study has, however, several key limitations. Firstly, the model did not explicitly separate density- dependent juvenile survival due to intra-cohort competition from density-dependent juvenile survival due to cannibalism of smaller fish by larger fish, which were both aggregated in the Ricker stock-recruitment model. The implication of this simplification is to overestimate the recruitment response due to the exploitation of smaller sizes of fish. Thus, the model predictions of the relative reduction in small fish due to the harvest of fish ≤ 150 mm are likely conservative relative to harvesting fish > 150 mm. Secondly, the study did not evaluate the harvesting of redfin perch egg masses as a management action as this is unlikely to have a strong population-level effect unless harvest rate is very high (e.g. Gwinn and Allen 2010). This is because density dependent survival of fish typically occurs during the larval/juvenile life stage (Walters and Marell 2004). Thus, reducing densities of eggs may improve larval survival due less density dependent pressures. Lastly, modelling did not consider inter-species interactions in the analysis. For example, in Lake Windermere, England, removal of redfin perch resulted in a reduced population that persisted for decades, which was

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 17

attributed to regulation by pike predation and cannibalism of smaller fish by larger fish (Bagenal 1982). However, the management strategy to maintain recruitment regulation by protecting larger redfin perch from removal applies to recruitment regulation by other fish species as well. For example, maintaining predators of larval and juvenile redfin perch in Lake Purrumbete, such as brown trout and Chinook salmon, should have a desirable influence on the age and size composition of the redfin perch stock. Modelling populations where larger older individuals cannibalize younger juveniles can be difficult to control because older cohorts regulate the survival of younger cohorts. When this regulation is removed through reductions in the abundance of older cohorts, increases in juvenile survival can lead to recruitment spikes and destabilization of the population age structure (Zipkin et al. 2009). This phenomenon of increased recruitment resulting from reductions in adults is often termed overcompensation and has been observed for many animal species including redfin perch (Ohlberger et al. 2014) and other fish species with similar life-history characteristics (Zipkin et al. 2008).

Cost-benefit, regulatory and logistics analyses Three fishing methods for harvesting redfin perch from Lake Purrumbete were assessed, electro-fishing, trapping with “Windermere “ traps and fyke netting. Electro-fishing is a common and well-established sampling method in freshwaters and is reported to be capable of detecting more fish species and wider range of sizes within species than traditional sampling techniques, such as fyke and mesh netting sand seining (Reynolds and Koltz 1983, Cowx and Lamarque 1990). Electro-fishing is most effective in complex habitats (above weeds, near banks and around woody and rocky habitats) and in shallow waters (<3m). Electro-fishing is less effective in open waters and large mobile pelagic species that can avoid approaching vessels are especially difficult to catch. Other factors affecting capture efficiency relate to visibility of fish to operators including high currents, high turbidity and increased wave action. Since 85% of Lake Purrumbete is over 5 m deep and 80% over 10 m deep (based on bathymetric information provided by Timms 1976), electro-fishing would be limited to the margins of the lake only. Electro-fishing was considered cost prohibit, costing around $52,000 to $168,000 for 4-12 weeks of operation per year. Estimating costs of harvesting redfin perch from Lake Purrumbete to achieve a meaningful change in the population, as identified from modelling outputs (i.e. intensive harvesting of small fish annually), was severely hampered by the lack of information on the standing stock (biomass) of redfin perch present in the lake. The fisheries of Lake Purrumbete are one of the most intensively monitored in Victoria, yet all previous studies have relied on gill net surveys and angler creel surveys only, neither method of which can be used to reliably estimate standing stock. Being a passive type of fishing equipment it is very difficult to assess the area that gill nets sample and are therefore not suitable for estimating of absolute stock size (numbers or biomass/area) (Ligtvoet et al. 1995). Fishing efficiency (catch per effort) of each of the redfin perch harvest methods assessed is scant, being limited to some published information (trapping in Lake Windermere, England), bycatch records (fyke-netting) and anecdotal information. Intensive fishing of redfin perch using un-baited traps in Lake Windermere over several years reduced the population to about 13% of its original density (Le Cren 1958). The traps predominantly caught redfin perch, small numbers of pike, eels (Anguilla anguilla) and brown trout, are also caught (Bagenal 1972). Catch in “Windermere” traps can be highly variable (Worthington 1950, Bagenal 1972), and during the spawning season the behaviour of mature male redfin perch results in more males than females being caught by the traps (Le Cren 2001). Modelling has suggested that this selection against males may have caused the population collapse in Windermere Lake (Langangen et al. 2011). After an initial outlay for construction of traps, annual cost for operating a trapping exercise over 4 -12 weeks during the warmers months of the year would cost in the order of $7,200 to $21,600, per year. Operating costs include labour, however, this may be reduced by using volunteer labour. However, this method was not preferred because it does not target small fish, as recommended by modelling, but instead targets larger (adult) fish.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 18

Table 4. Estimated level of harvest from modified fyke netting.

Number of fish Kg of fish harvested Methods Assumptions harvested per per week week 0.048-0.213 (0.154) kg/net/day1 Modified fyke- 3,325 – 14,875 16.6 – 74.4 50 nets fishing 7 days/week netting Mean fish size 5 g2 (mean 10,763) (mean 53.8) 1. Based on catch per unit effort of redfin perch (as bycatch) in commercial eel fyke nets in Lake Purrumbete for October-December (Figure 7), plus 25% improvement in catch following modification of nets. 2. Nominal size of juveniles in October – December period.

Conclusions and recommendations

Modelling and cost analysis undertaken as part of this study suggest that a substantial amount of effort (intensive harvesting of small fish annually) and cost are required to noticeably reduce the size of the redfin perch population in Lake Purrumbete. However, there is still uncertainty about whether the resourcing options proposed in this study are sufficient to harvest the necessary amount of small fish to substantially reduce the abundance of redfin stocks. Future decisions regarding the management of recreational fisheries in Lake Purrumbete will need to consider the value of redfin perch fishery in the lake, especially seeing they are a popular angling species and good catches of large redfin are occasionally reported from Lake Purrumbete. Simulation modelling of the Lake Purrumbete redfin perch population suggested that a noticeable change in population abundance and structure can be achieved only by intensive harvesting (>0.5 of population) of small fish (<150 mm) annually. Harvesting lower proportions of the population less frequently had little effect on the population, while harvesting large fish (> 150 mm) actually increased the abundance of less desirable small fish. These results were attributed to the life-history characteristics of redfin perch, such as the ability to respond rapidly to changes in environmental conditions and population structure (e.g. increased recruitment resulting from reductions in adults). Three fishing methods for harvesting redfin perch from were assessed, electro-fishing, trapping with “Windermere “ traps and fyke-netting. The number of redfin perch that can be harvested by these methods could not be assessed due to lack of information on the standing stock (i.e. biomass) of redfin perch in Lake Purrumbete and fishing efficiency (catch per effort) of the harvest methods. Since the early 1960s there have been multiple fishery independent surveys and creel surveys of Lake Purrumbete (e.g Hume 1991b, Hume 1991a, Eddy 1998, Pomorin 2004, Hall and Douglas 2010, Hunt et al. 2013, Ingram et al. 2017). These surveys have provided valuable information on the size and catch rates of chinook salmon, brown trout, rainbow trout and redfin perch. Galaxias (minnow) are an important part of the diet of predatory fish in Lake Purrumbete (e.g. Cadwallader and Eden 1981), yet little is known about their population dynamics. Managing the recreational fishery in Lake Purrumbete will be greatly improved by better understanding lake ecology and productivity of key species (such as galaxias), and how these affect the fishery.

VFA Management Response Victorian Fisheries Authority (VFA) Management and Lake Purrumbete Angling Club (LPAC) Committee have met, reviewed this report and conclude that active harvest of redfin in Lake Purrumbete is not supported nor practicable based on the available information.

The report states that significant effort and costs would be required to noticeably reduce the size of the redfin population, and uncertainties exist regarding whether the actions modelled would be effective. Redfin are among the most popular freshwater fish in Victoria and a great food and sport fish, especially for kids and families to experience fishing.

The VFA and LPAC will continue to work together to improve fishing at Lake Purrumbete through monitoring and close engagement on the performance of the fishery, fish stocking trials and access improvements.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 19

Acknowledgements

This project was instigated by Lake Purrumbete Angling Club with funds from the Victorian Government to improve recreational fishing in Victoria through revenue from Recreational Fishing Licenses. The efforts of Rob Hems of the Lake Purrumbete Angling Club are especially acknowledged for establishing and commissioning the project. Taylor Hunt and John Douglas provided constructive comments throughout the project. Rob Hems and Steve Eddy (Victorian Fisheries Authority) provided comments on the report. Bill and Richard Allan are thanked for advice on fyke netting in Lake Purrumbete and for providing permission to use fyke net bycatch information.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 20

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Appendix I. Draft journal manuscript

Optimizing fishery characteristics through control of an invasive species: strategies for redfin perch control in Lake Purrumbete, Australia.

1* 2 Daniel C. Gwinn and Brett A. Ingram

1 Biometric Research, Albany 6330, WA, Australia. 2 Victorian Fisheries Authority, Alexandra, Vic., Australia.

* Corresponding author, [email protected]

Abstract: Controlling invasive fish species can be tricky perch are considered an invasive pest species in Australia.

Keywords: European perch, overcompensation, exotic species, recreational fisheries management

Introduction The spread of species beyond their natural range is one of the greatest threats that natural ecosystems experience today (Didham et al. 2005). The number of invasive species continues to grow on a global scale with impressive numbers, such as more than 50,000 invasive species in the United States alone (Pimental et al. 2005) and more than 11,000 in Europe (Hulme et al. 2009). These invasive species can alter how ecosystems function, driving changes in nutrient pathways (Ehrenfeld 2010) and causing extinction of native species (Clavero and Garcia-Berthou 2005). Furthermore, these invasions can result in losses of ecosystem services (Charles and Dukes 2008; Vila et al. 2010) and generate high societal costs (Pimentel et al. 2005). In freshwater systems fish invasions are strongly linked to fisheries activity (Cambray 2003; Davis and Darling 2017) and the costs and benefits of introduced fish species are actively debated (Gozlan 2008; Vitule et al. 2009). Some non-native fish introductions have been clearly catastrophic from a biodiversity perspective with little if any benefit to society. One such example is the mass introduction and continued invasion of freshwaters by common carp (Cyprinus carpio) in North America and Australia (Weber and Brown 2009; Koen 2004). Common carp were introduced into both countries in the mid-1800s and now represent the majority of fish biomass in many freshwater systems of the U.S. and south-east Australia (Lubinski et al. 1986; Harris and Gehrke 1997). Other introduced fish species can create management conflicts because they offer some positive benefit to society. For example, in the Colorado River, Grand Canyon, threats to the federally endangered humpback chub (Gila cypha) include predation by invasive salmonids (Coggins et al. 2011; Yard et al. 2011); however, these salmonids were purposely introduced for recreational fishing and support a world class fishery and associated guide businesses that exist today. In Australia, redfin perch (i.e. European perch, Perca fluviatilis) represents an exotic invasive species with both negative and positive aspects. Redfin perch was introduced into Australia in the late-1860s to develop a recreational fishery (Weatherley 1977). Today, redfin perch are considered an invasive pest in Australia because they prey upon native fish species causing a conservation concern (Barrett et al. 2014; Lintermans et al. 2014; Beatty and Morgan 2016). Population control methods have been considered (Barrett et al. 2014; Becker et al. 2016; Ingram 2016), however, the species has life-history characteristics that make it a poor candidate for eradication or control through removal. Firstly, the species is highly productive (Heibo et al. 2005) with potential for rapid population growth, making it an ideal invader (Olden et al. 2006). Secondly, adult redfin perch are known to cannibalize juveniles (Morgan et al. 2002) creating the potential for explosive recruitment and erratic population changes when this predation pressure is released by reducing the adult population (referred to as overcompensation, Zipkin et al. 2008, 2009). Lastly, the species remains a desirable recreational fish species for some fishers, particularly when fish sizes are large, creating a difficult management problem. Lake Purrumbete, Victoria, supports a well-known and popular salmonid fishery with trophy fish often being caught. The lake is regularly stocked with rainbow trout (Oncorhynchus mykiss), brown trout (Salmo trutta) and Chinook salmon (Oncorhynchus tshawytscha) by the Victorian Fisheries Agency. Since introduction to the lake in the 1960s, redfin perch have become abundant and although the occasional large redfin perch is harvested, anglers are often overwhelmed by numerous small undesirable fish. While some anglers target redfin perch in the lake, most loath the species and regularly lobby for control measures. Although, mitigation has been attempted in 1985 and 1993, these measures failed to substantially influence the redfin perch population (Ingram 2016). Here we evaluate removal strategies of redfin perch in Lake Purrumbete with the primary aim to improve the quality of Lake Purrumbete multi-species recreational fishery. We acknowledge that eradication is highly unlikely for this species and thus focus on removal efforts that will reduce the nuisance catch of small redfin perch, minimize the reduction of (or enhance) large desirable fish, and minimize the risk of explosive recruitment and population destabilization. We perform our evaluation in two main steps. First, we evaluate the effects of various removal scenarios on redfin perch with a population model parameterized to represent Lake Purrumbete. The population model was structured and parameterized to represent our a priori belief about the life-history characteristics, population dynamics rates, and density-dependent factors governing redfin perch of Lake Purrumbete. Secondly, we conducted a sensitivity analysis (e.g. Allen and Gwinn 2013) to determine the robustness of our general results under alternative hypotheses about the biology of the Purrumbete redfin perch population. This second evaluation can offer insight into the robustness

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 24 of management strategies across a range of conditions and identify key uncertainties about the biology of the population that may influence the performance of management strategies.

Methods Modelling methods Our population model simulates annual numbers of fish at age for a range of fish growth rates referred to as growth-type groups (e.g. Coggins et al. 2007; Gwinn et al. 2015). The model incorporated multiple growth-type groups to represent natural variation among individuals in growth expected in exploited fish stocks and more realistically represent the cumulative effects of size-selective exploitation on the length composition and fecundity of the population. Two of the main population characteristics that govern how fish populations respond to exploitation are the productivity of the stock in terms of natural mortality and growth rates, and the level of density dependence of population dynamics rates (Beverton and Holt 1957; Lorenzen 2016). To capture these important features, our model accounted for mortality due to natural causes and exploitation, density dependent survival in the juvenile life stage, and density dependent growth, mortality, and age-at-maturation in the adult life stage. Abundance of fish at time t, age a, and growth-type group g was modeled as:

푁푡,푎,푔 = 푁푡−1,푎−1,푔푆푡−1,푎−1,푔(1 − 푈푡−1푉푡−1,푎−1,푔) (1)

−푀푡,푎,푔 where 푆푡,푎,푔 is the finite annual survival rate (i.e. 푒 ) that models the proportion of fish surviving from deaths due to natural causes for each age, growth-type group, and year. The parameter 푈푡 is the finite annual exploitation rate, describing the proportion of vulnerable fish removed annually from the population. The term 푉푡,푎,푔 is the length-based vulnerability of fish to exploitation, which models the potential for removal efforts to target different sizes of fish. The term (1 − 푈푡푉푡,푎,푔) models the proportion of the population that survive removal (i.e. not captured) at time t. The vulnerability of a given age and growth-type group to removal efforts (i.e. 푉푡,푎,푔) was modeled as a Boolean variable where 푉푡,푎,푔 = 1 indicates that fish of age a in growth-type group g are of size vulnerable to removal and 푉푡,푎,푔 = 0 indicates that fish of age a in growth-type group g are of a size invulnerable to removal. The values of 푉푡,푎,푔 were determined by a logical test as:

푉 = 1, when 퐿 < 퐿 < 퐿 푡,푎,푔 푚푖푛 푡,푎,푔 푚푎푥 (2) 푉푡,푎,푔 = 0, when 퐿푚푖푛 > 퐿푡,푎,푔 or 퐿푚푎푥 < 퐿푡,푎,푔 where 퐿푡,푎,푔 is the length of fish during year t at age a of growth-type group g, Lmin is the minimum length of fish vulnerable to removal and Lmax is the maximum length of fish vulnerable to removal. The values of Lmin and Lmax can be determined by removal selectivity or specified as regulations constraining exploitation with minimum-length limits and maximum-length limits for legal harvest. The length-at-age a (퐿푡,푎,푔) was modelled with a standard von Bertalanffy (1938) growth curve modified to account for variation in length-at-age due to intra-annual variation in maximum size of fish (i.e. growth-type group) and inter-annual variation in the maximum size of fish and the rate at which they attain the maximum size. We modeled length-at-age as:

−푘푡(푎−푡0) 퐿푡,푎,푔 = 퐿∞,푡,푔(1 − 푒 ) (3) where L∞,t,g is the asymptotic size of growth-type group g at time t, kt is the time varying metabolic parameter that determines the rate that L∞,t,g is attained for each year, and t0 is the theoretical age at length equal to zero. We simulated variability in growth by assigning each growth-type group a unique 퐿∞,푡,푔 for each year based on a range between ± 20% of an average annual asymptotic length 퐿̅∞,푡 (Coggins et al. 2007; Gwinn et al. 2015). We accounted for annual variation in adult growth due to density-dependent factors by modeling kt as a linear function of 퐿̅∞,푡 (i.e. 푘푡 = 휂0 + 휂1퐿̅∞,푡, 휂0 = intercept, 휂1 = slope) and modeling 퐿̅∞,푡 as a sigmoidal function of adult biomass (ages 2+) similar to Lorenzen and Enberg (2002). The average annual asymptotic length was specified as:

(퐿̅ − 퐿̅ ) (4) ̅ ̅ 푚푎푥 푚푖푛 퐿∞,푡 = 퐿푚푎푥 − (퐵 −퐵 ) − 푡−1 50 (1 + 푒 휎 ) where 퐿̅푚푎푥 and 퐿̅푚푖푛 are the maximum and minimum possible values for 퐿̅∞,푡. The parameter Bt is the adult biomass at time t and B50 is the adult biomass when 퐿̅∞,푡 is a value half way between 퐿̅푚푎푥 and 퐿̅푚푖푛. The parameter 휎 determines the rate at which 퐿̅∞,푡 transitions from 퐿̅푚푖푛 to 퐿̅푚푎푥 as the adult biomass is reduced, and thus, effectively models the strength of density-dependent growth. For example, infinitely high vales of 휎 result in a constant value of 퐿̅∞,푡 across a gradient of Bt, whereas, small values of 휎 result in a sharp transition of 퐿̅∞,푡 = 퐿̅푚푖푛 to 퐿̅∞,푡 = 퐿̅푚푎푥 as Bt declines past B50. We modeled the instantaneous annual natural mortality rate 푀푡,푎,푔 (i.e. −푙표푔(푆푡,푎,푔)) as inversely proportional to fish length according to Lorezen (2000) as.

퐿푟푒푓 (5) 푀푡,푎,푔 = 푀푟푒푓 ( ) 퐿푡,푎,푔 where 퐿푟푒푓 is a reference length where the natural mortality rate is known to be a given value (i.e. 푀푟푒푓). This formulation describes natural mortality as higher for smaller, younger fish and lower for larger, older fish and makes an explicit link

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 25 between adult survival and density through equation 3 and 4, thus accounting for density-dependent survival in adult fish as suggested for redfin perch by Heibo et al. (2005). There is overwhelming evidence that redfin perch recruitment can be heavily regulated by inter-cohort interactions such as cannibalism (e.g. Popova and Sytina 1977; Craig 1978; Goldspink and Goodwin 1979; Bagenal 1982; Linlokken and Seeland 1996; Morgan et al. 2002), resulting in a dome-shape stock-recruit relationship (Craig and Kipling 1983; Ohlberger 2014). Thus, we chose to account for this form of recruitment regulation with a Ricker stock- recruitment model specified as:

−훽휑푡 푅푡+1,푔 = 푃푔(훼휑푡푒 ) (6) where 훼 describes the productivity of the stock and 훽 describes regulation due to density dependence. The parameter φt is the total fecundity of the population at time t. The parameter Pg is a vector of fixed proportions that apportion the number of recruits each year to the different growth-type groups. Specifying Pg as a fixed vector makes explicit the assumption that variation in growth is similar among years and is not a heritable trait. The total fecundity at time t (φt) was calculated as:

(7) 휑푡 = ∑ 푁푡,푎,푔 푓푡,푎,푔 푎,푔 where fa,g is the fecundity of fish at age a in growth-type group g and was calculated as the difference between the weight of fish at age a in growth-type group g (i.e. wa,g) and the age-at-maturation (negative values set to zero). The total fecundity of the unexploited stock 휑0 was set equal to 휑푡 at t = 1 before exploitation. The weight of fish was calculated with a standard weight/length relationship as:

푏 푤푡,푎,푔 = 푎퐿푡,푎,푔 (8) where 푎 is the scaling parameter and 푏 is the allometric parameter that modifies the relationship between length and weight.

Model parameterization Parameter input values used in the model are shown in Table 1. Because of a lack of empirical data on the biological parameters of redfin perch in Lake Purrumbete, most parameter values were derived from the literature. The Ricker stock-recruitment relationship required input values for 훼 and 훽. We derived these parameters from the Beverton- Holt stock-recruitment model parameters 푅0 and 퐶푅 per Walters and Martell (2004, box 3.1 p56) because their biological meaning is more easily interpreted and they are more easily informed from the scientific literature. The Ricker parameters were calculated as, 훼 = 퐶푅⁄휑0 and 훽 = 푙표푔(훼휑0)⁄(푅0휑0). The average number of age-1 recruits in the unexploited condition (i.e. 푅0, carrying capacity) is unknown for Lake Purrumbete; however, because 푅0 functions as a scaling parameter in the model, its value does not influence model prediction when comparing the relative performance of exploitation scenarios. Thus, we arbitrarily set 푅0 to 10,000 individuals. The density-dependent compensation in juvenile survival 퐶푅 is also unknown for Lake Purrumbete, however the literature overwhelmingly suggests that it is high for redfin perch (Craig and Kipling 1983; Paxton et al. 2004) likely due to strong competition among juveniles for food (Ohlberger 2014) and intra-cohort cannibalism (Baras et al. 2002). Thus, we set 퐶푅 to a value of 10 to approximate the strength of density dependence reported in Craig and Kipling (1983) (Fig. 1). The minimum and maximum asymptotic lengths were set to 퐿̅푚푖푛 = 200 mm and 퐿̅푚푎푥 = 350 mm based on values for similar latitudes in the northern hemisphere reported by Heibo et al. (2005), where 퐿̅푚푖푛 represents stunted populations and 퐿̅푚푎푥 represents non-stunted populations. These values are consistent with the range of values reported in other lakes in Australia at similar latitudes to Lake Purrumbete (Morgan et al. 2002), New Zealand (Jellyman 1980; Sebetian et al. 2015), and are consistent with the range of lengths observed in Lake Purrumbete (Hall and Douglas 2010). The parameter 훽50 was set to the predicted equilibrium biomass in the unfished condition. The parameter σ was set to 훽50⁄4, which models growth suppression in the population due to high adult densities that can be relieved by reductions in the adult density. Specifically, this parameterization resulted in a 35-mm increase in 퐿̅∞ (275 mm to 310 mm) when the population biomass was reduced by 25% and a 67-mm increase (275 mm to 342 mm) when the population biomass was reduced by 75% (Fig. 2). This value of 휎 generates similar density dependent growth as observed by Linlokken and Seeland (1996) and ranges in growth observed for stunted and non-stunted populations by Le Cren (1958) and Morgan et al. (2002). Values of the slope and intercept of the model defining the relationship between the von Bertalanffy metabolic parameter 푘 and the average asymptotic length 퐿̅∞ were based on a linear regression of the log values of 96 reported estimates of 퐿∞ and 푘 for redfin perch supplied by Fishbase (Froese and Pauly 2006) (Fig. 3). This analysis resulted in a range of predicted 푘 values from 0.20 for high biomass conditions (i.e. 퐿̅∞ = 350) to 0.34 for low biomass conditions (i.e. 퐿̅∞ = 200), which are in the range of Jellyman (1980) and Morgan et al. (2002). These specified growth parameters produce growth curves depicted in Fig. 4a for high and low biomass conditions and are consistent with others reported in the literature (Jellyman 1980; Buijse et al. 1992). We approximated the instantaneous annual mortality rate of adult redfin perch by setting 푀푟푒푓 to 1.5 times the value of 푘 for fish that have a total length of 275 mm (i.e. 퐿푟푒푓) based on Jensen (1996). This length approximates the length of a fish greater than six years old and is consistent with the natural mortality rates of adult redfin perch in southern Australia (Pen and Potter 1992; Morgan et al. 2002) and internationally (Linlokken and Seeland 1996). We set the maximum age to 13 years based on Hoenig (1983). The length/weight relationship of redfin perch was determined from data collected between 1989 and 2009 in Lake Purrumbete as part of a long-term monitoring program. Sampling methods are detailed in Hall and Douglas (2010). To predict weight from length, we estimated 푎 and 푏 parameters from length and weight measurements of 3,182

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 26

fish. Using maximum likelihood of the normal distribution, values of 2E-06 and 3.37 were estimated for the 푎 and 푏 growth parameters (Fig. 4b), which are consistent with values reported for southern Australia (Morgan et al. 2002) and New Zealand (Sebetian et al. 2015). Age at maturation was set at 2 years based on Jellyman (1980), Froese and Pauly (2006), and Heibo et al. (2005).

Simulation protocol We evaluated the effects of the target size class of removals, the periodicity of removals, and the intensity of removal effort (i.e. exploitation rate) as these are the three factors that can be manipulated by managers. We chose to evaluate three different size ranges to target with removals, which included, (i) ≤ 150-mm total length, (ii) > 150-mm total length, and (iii) proportional harvest of all sizes. We chose to evaluate the removal of ≤ 150-mm total length fish because this approximates the size of fish that would be vulnerable to sampling gears such as hoop nets or electrofishing of the shallow littoral zone of the lake. The size range of > 150-mm total length was chosen because it approximates the size of fish that could be targeted by electrofishing and angling. Harvest of all sizes proportional to their abundance was chosen to represent a scenario where multiple methods were used to remove all lengths of redfin perch. We simulated the removal for a range of exploitation rates from 0 to 0.6 and for removal schedules of every year, every 3rd year, every 5th year, and every 10th year. We measured the response of the simulated system to removals with the long-term average abundance (100- year average) of fish 100-300-mm total length and > 300-mm total length to represent the size range of undesirable fish and desirable fish vulnerable to angling, respectively (hereafter referred to as “small” and “large” fish, respectively). Because exploitation of populations that exhibit inter-cohort interactions can result in undesirable destabilization of the age structure and erratic behavior (e.g. Zipkin et al. 2008), we also outputted the coefficient of variation of small and large fish abundance across years for each removal scenario as a measure of annual variation in redfin perch abundance.

Sensitivity analysis To account for uncertainty in the life-history characteristics and current state (i.e. pre-removal) of the Lake Purrumbete redfin perch population, we evaluated the robustness of our general conclusions about the relative effectiveness of different removal strategies under different biological hypotheses. We considered different hypotheses about the stock-recruitment relationship, strength of density dependent recruitment compensation, strength of density- dependent growth, rate of maturation, and rate of natural mortality (Table 2). Although there is strong evidence that the stock recruitment relationship of redfin perch is dome shape due to inter-cohort cannibalism, Heibo et al. (2005) observed redfin perch populations that demonstrated stunted growth and did not appear to engage in cannibalistic behavior. Furthermore, Pen and Potter (1992) observed no juvenile redfin perch in the diets of adult redfin perch of the Murray River, Australia and Baxter et al. (1985) observed no juvenile redfin perch in the diets of adult redfin perch in Lake Burrumbeet, Victoria. These studies suggest that cannibalism may not be a regulating factor in all refin perch populations. Thus, we evaluated an asymptotic Beverton-Holt stock-recruit model (Beverton and Holt 1957) that is consistent with recruitment dynamics under the hypothesis of no inter-cohort cannibalism. The asymptotic Beverton-Holt stock-recruitment function was specified as:

(9) (퐶푅⁄휑0)휑푡 푅 = 푃 ( ) 푡+1,푔 푔 퐶푅 − 1 1 + 휑푡 ( ) 푅0휑푡 where 푅0 is the average number of juvenile fish surviving to age-1 in the unexploited condition (i.e. carrying capacity) and 퐶푅 is the recruitment compensation ratio. We also evaluated a lower compensation ratio 퐶푅 of 10 to approximate the values reported for Percids in Meyers et al. (1999). Our base assumption was that the Lake Purrumbete redfin perch population currently experiences some level of growth suppression due to high densities, which is modeled by 휎 = 훽50⁄4. However, an alternative hypothesis is that the population densities are below levels that would result in growth suppression. We evaluated the impacts of removal under this hypothesis by setting the standard deviation (σ) of the density dependent growth relationship to 106. Under this parameterization, growth will not increase due to reductions in densities. Lastly, we evaluated the robustness of our results for alternative hypotheses about natural mortality and maturation by modeling a higher natural mortality rate of 0.8 and earlier maturation at age-1 observed for many redfin perch populations by Heibo et al. (2005). All simulations and analyses were performed with program R (R Core Team 2015).

Results Our results suggest that the magnitude of reductions in small undesirable fish would depend on the lengths targeted, the intensity of exploitation and the temporal periodicity of exploitation. For example, the lowest abundance of small undesirable fish always resulted from exploitation directed at fish ≤ 150-mm total length across exploitation rates and temporal periodicities with the exception of one condition (Fig. 5a, black line). This condition was met when the rate of exploitation was > 0.5, occurred annually and targeted exploitation proportional to size, which resulted in the lowest abundances of small undesirable fish (Fig. 5c, black line). Alternatively, management scenarios that targeted exploitation at fish > 150-mm total length only resulted in increases in the abundance of small undesirable fish under all exploitation and temporal scenarios (Fig. 5b). Thus, management strategies that target fish ≤ 150 mm will likely have the greatest potential to conspicuously reduce the abundance of small, undesirable redfin perch in Lake Purrumbete unless exploitation is high (U > 0.5) and constant (annual). Our results suggest that targeting exploitation on fish ≤ 150-mm total length will also result in the best outcome for the abundance of large desirable fish when higher exploitation rates are applied more frequently. For example, for exploitation rates > 0.10 applied at annual periodicities, our model predicts a 30 to 26,000% greater abundance of large

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 27 desirable fish than targeting all sizes proportionally at the same periodicity (Fig. 5d,f, black line). For exploitation rates > 0.35 implemented every 3rd year, our model predicts a 30 to 250% greater abundance of large desirable fish than targeting all sizes proportionally at the same periodicity (Fig. 5d,f, red line). Alternatively, scenarios that result in low removal effort such as longer periodicities and lower exploitation rates, the resulting abundance of large fish is nearly equivalent (e.g. Fig. 5d,f, blue and green lines for U < 0.4). Furthermore, targeting large fish was predicted to result in either no change in large fish abundance or a net loss regardless of the exploitation rate or removal cycle (Fig. 5e). We found that the annual variation in both small and large fish abundance was dependent on the specific removal scenario. For example, implementing removals on an annual timescale resulted in nearly zero annual variation in small and large fish abundances, while the other periodicities resulted in higher annual variation (Fig. 6). Additionally, the highest levels of annual variation in both small and large fish abundance resulted from targeting all sizes of fish (Fig 6c,f). Our sensitivity analysis demonstrated that the abundances of small and large fish resulting from our removal scenarios was highly dependent on the biological assumptions of our model. However, the relative performance of management scenarios was fairly stable with two general patterns emerging. Firstly, the lowest abundance of small fish could be achieved by either targeting fish proportional to abundance or ≤ 150 mm depending on the assumed stock- recruitment relationship (Fig. 7a,b,d). Specifically, specifying the assumption of no inter-cohort cannibalism by applying a Beverton-Holt stock-recruitment model resulted in proportional exploitation as the best management strategy as opposed to targeting ≤ 150-mm fish (Fig. 7a,b,d; “BH SR” compared to “Base”). Secondly, targeting fish > 150 mm never resulted in the best outcome for either small undesirable fish or large desirable fish regardless of biological assumptions, exploitation rates and temporal periodicity of removal effort (Fig. 7).

Discussion Our results suggest that removal scenarios that will result in the greatest reduction in small fish and the greatest increase in large fish in the Lake Purrumbete redfin perch population is one that directs exploitation at fish ≤ 150-mm total length with high levels of exploitation, annually. This result was consistent across most assumptions about life- history characteristics, density dependent processes, and population dynamics rates, suggesting that this management strategy is robust to most relevant biological uncertainties. Furthermore, we found that exploiting redfin perch on an annual time scale will result in the lowest annual variation in the population due to disruption of the age and size structure of the population, which is common for fish populations that exhibit inter-cohort cannibalism such as redfin perch. We believe that these results can help managers choose strategies to manipulate the redfin perch population of Lake Purrumbete and achieve more desirable fishery characteristics. Our predicted responses of redfin perch to exploitation is consistent with other observations of redfin perch and species with similar life histories in the literature. For example, our model indicated that management scenarios that turn on and off exploitation will result in increased annual variation in the redfin perch population. This variation is partially due to the periodicity of exploitation, but is also expected for fishes that exhibit inter-cohort interactions. This is because larger older fish regulate the survival of smaller younger fish through predation. Thus, any disruption to this regulation can result in exaggerated boom and bust cycles of recruitment. This phenomenon has been observed for redfin perch in Lake Windermere, England, after disease resulted in an extreme decline in large fish in 1977 (Ohlberger et al. 2014). This result was also observed for smallmouth bass (Micropterus dolomieu), a species with similar life-history characteristics, in a temperate lake in New York, USA (Zipkin et al. 2008). For this population, an intensive removal effort resulted in increases in overall abundance and annual variation in abundance of fish primarily due to increases in recruitment. Although our study suggests that population stability can be achieved if removal efforts are applied on an annual time scale, we may have underestimated the risk of increased variation, particularly if we underestimated the strength of density dependence in Lake Purrumbete (Zipkin et al. 2009). Our study suggests that strategies that target small fish for removal can result in less smaller fish. This result is consistent with the predictions of Zipkin et al. (2009) for a range of animal species. Zipkin et al. (2009) demonstrated that adult harvest strategies and equal proportions harvest strategies can generate increased recruitment compared to harvest strategies that target juveniles only. However, they also demonstrated that all harvest strategies could result in increased recruitment when the strength of density-dependent compensation in juvenile survival was high and strongly related to cannibalistic behavior. For redfin perch in Lake Purrumbete however, the strength of density dependent juvenile survival is unknown and its link to inter-cohort cannibalism is unknown. However, studies from other systems suggest that density-dependent compensation in juvenile survival has the potential to be high (Craig and Kipling 1983; Heibo et al. 2005) and a cannibalistic diet can exist for fish larger than 120 to 200-mm total length (Popova and Sytina 1977; Goldspink and Goodwin 1979; Pen and Potter 1992; Ohlberger et al. 2014). Pomorin (2004) examined the stomach contents of 56 redfin perch (255-374-mm in length) collected during two restricted sampling events in Lake Purrumbete in November 1999 and October 2000. 70% of fish sampled had empty stomachs while others had native fish, unidentified fish, snails, insects, shrimp, freshwater crabs, amphipods and detritus in the stomachs. Conducting a more detailed diet study, particularly at times of the year when juvenile redfin perch are abundant, could reveal whether cannibalism is a strong regulating factor for Lake Purrumbete redfin perch and which sizes of fish engage in cannibalism. This information could help managers understand the potential risks of removal efforts on this population and help refine removal strategies. For example, size classes of fish that engage in cannibalistic behavior will have some regulating effects on recruitment, thus, management strategies to remove fish smaller than these sizes would be optimal. Our study has several key limitations. Firstly, our model did not explicitly separate density-dependent juvenile survival due to intra-cohort competition from density-dependent juvenile survival due to inter-cohort cannibalism. Both of these density-dependent processes were aggregated in the Ricker stock-recruitment model. The consequence of this simplification is to overestimate the recruitment response due to the exploitation of smaller sizes of fish. Thus, our predictions of the relative reduction in small fish due to the exploitation of fish ≤ 150-mm total length are likely conservative relative to targeting fish > 150-mm total length. Secondly, we did not evaluate the harvesting of redfin perch egg masses as a management action. However, we believe that harvesting eggs is unlikely to have a strong population- level effect unless you are able to exploit them at very high rates (e.g. Gwinn et al. 2010). This is because density

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 28 dependent survival of teleosts typically occurs during the larval/juvenile life stage (Walters and Martell 2004). Thus, reducing densities of eggs would only serve to release this density dependent pressure, increasing larval survival. To create a population-level impact, removal strategies would need to exploit at a magnitude beyond the capacity of larval survival to compensate (often termed recruitment overfishing). For the levels of recruitment compensation modeled in our study (i.e. CR = 20), this would require an exploitation rate of ≥ 0.8, which would be logistically difficult to achieve. Lastly, we did not consider inter-species interactions in our analysis. For example, in Lake Windermere, England, removal of redfin perch resulted in reduced populations that persisted for decades, which was attributed to regulation by pike predation and adult cannibalism (Bagenal 1982). However, the management strategy to maintain recruitment regulation by protecting larger redfin perch from removal applies to recruitment regulation by other fish species as well. For example, maintaining and enhancing predators of larval and juvenile redfin perch in Lake Purrumbete, such as by stocking brown trout and Chinook salmon, should have a desirable influence on the age and size composition of the redfin perch stock.

Conclusion Controlling invasive fish species can be difficult with little guarantee of success (Britton et al. 2011). Redfin perch represent a particularly risky species to control because they demonstrate the capacity for overcompensation which can lead to increases in small fish when removal efforts are employed. This presents a trade-off that is mainly dependent on two key population processes, i.e., recruitment regulation through inter-cohort cannibalism and density- dependent growth. However, measures can be taken to reduce the negative impacts of this species through strategic removal strategies. For the Lake Purrumbete redfin perch population, management seeks to reduce the abundance of small individuals and enhance or hold constant the abundance of large individuals. The ideal management strategy to achieve this objective will be one that exploits fish in such a way as to reduce competition for resources to increase growth without removing the regulatory effects of cannibalistic adult fish on recruitment. Our results indicate that the selective harvest of small fish may meet this requirement.

Conflict of interest The authors declare no conflict of interest.

Acknowledgements We acknowledge the funding that supported this work granted by the Lake Purrumbete Angling Club (LPAC) Incorporated using funds from the Victorian Government to improve recreational fishing in Victoria through revenue from Recreational Fishing Licenses. We would like to thank Rob Hems (LPAC) for his support of the work and Simon Conron (Victorian Fisheries Authority) for comments that improved this paper. We extend thanks to three anonymous reviewers whose comments and suggestions greatly improved this work.

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Tables

Table 1. Life history and biological parameter input values and information sources used for simulations of Lake Purrumbete redfin perch (Perca fluviatilis, Percidae).

Parameter Description Value Beverton-Holt SR 푅0 Average annual unfished recruitment 10,000 퐶푅 Recruitment compensation ratio 20 Ricker SR 훼 Ricker productivity parameter 퐶푅⁄휑0 훽 Ricker carrying capacity parameter 푙표푔(훼휑0)⁄(푅0휑0) Length-at-age

퐿푚푎푥 Maximum asymptotic length (mm) 350 퐿푚푖푛 Minimum asymptotic length (mm) 200 퐵50 Biomass where 퐿̅∞= 275mm virgin biomass prediction 휎 Strength of density-dependent growth 퐵50⁄4 -1 ̅ 푘푡 von Bertalanffy growth coefficient (yr ) 푒휂0+휂1log(퐿∞,푡) 휂0 푘푡 model intercept 1.7123 휂1 푘푡 model slope -0.9328 푡0 von Bertalanffy theoretical age at length = 0 0 Mortality 퐴 Maximum age (years) 13 -1 푀푟푒푓 Natural mortality rate at 푇퐿푟푒푓 (yr ) 0.38 푇퐿푟푒푓 Reference length where 푀 = 푀푟푒푓 (mm) 275 Length-weight 푎 Length-weight scaling parameter 2E-06 푏 Length-weight allometric parameter 3.37 Maturation 퐴푚푎푡 Age at maturation (years) 2

Table 2. Alternative hypotheses about Lake Purrumbete redfin perch (Perca fluviatilis, Percidae) life-history, population dynamics, and density-dependent factors evaluated to determine robustness of management outcomes.

Base Alternative Parameter Description hypothesis hypothesis Stock-Recruitment model Ricker Beverton-Holt 퐶푅 Recruitment compensation ratio 10 20 6 휎 Strength of density-dependent growth 퐵50⁄4 10 -1 푀푟푒푓 Natural mortality rate at 푇퐿푟푒푓 (yr ) 0.38 0.80 퐴푚푎푡 Age at maturation (years) 2 1

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 31

Figures

25000 15000 virgin recruitment

Ricker, CR = 20

Ricker, CR = 10

5000 Index of age-1 recruits age-1 of Index

BH, CR = 20 stock virgin 0

0e+00 4e+07 8e+07

Index of spawning biomass

Fig. 1. Stock recruitment relationships modeled for Lake Purrumbete redfin perch. “Ricker, CR = 20” is used in our based modeling scenarios. “Ricker, CR = 10” and “BH, CR = 20” (Beverton-Holt) were evaluated in our sensitivity analysis.

350

75% decrease 25% decrease

Virgin biomass

300

250

Average asymptotic length (mm) length asymptotic Average 200 -100 -50 0 50 100

Percent change in biomass from virgin state

Fig. 2. Density-dependent growth response curve. The blue dotted line indicates the average asymptotic length at the unexploited equilibrium state. The green and red dotted lines indicate the average asymptotic length when the population biomass is reduced by 25% and 75% from the unexploited state.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 32

0.5 Fishbase reported values

Model prediction

0.4

0.3

0.2

0.1 von Bertalanffy growth coefficient (yr-1) coefficient growth Bertalanffy von 200 300 400 500 600

Asymptotic length (mm)

Fig. 3. The relationship between the von Bertalanffy growth coefficient 푘 and the mean asymptotic length 퐿∞ across 휂0+휂1log(퐿̅∞) redfin perch population. The solid line represents predicted values from the linear equation 푘푝푟푒푑푖푐푡푒푑 = 푒 , 2 where the parameter values were estimated as 휂0 = 1.7123 and 휂1 = −0.9328 (f = 63.54, p < 0.001, R = 0.4033) with least squares regression.

Fig. 4. Growth predictions for simulated redfin perch population. Panel (a) shows the minimum (dashed line) and maximum (solid line) average modeled growth rates with their 95% probability regions of growth variation. Panel (b) shows the length/weight relationship predicted for Lake Purrumbete redfin perch.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 33

L 150mm L 150mm All lengths

(a) (b) (c)

8000

4000

Smallundesirable fish 0

(d) (e) (f)

rowMeans(out1a$SmallN[, 30:Ymax]) rowMeans(out1a$SmallN[, 30:Ymax]) rowMeans(out1b$SmallN[, 30:Ymax]) rowMeans(out1c$SmallN[,

60 Utest Utest Utest Yearly

3-year 40

Predicted abundancePredicted 5-year

10-year

20

Largedesirable fish 0

0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6

rowMeans(out1a$TrophN[,30:Ymax]) rowMeans(out1b$TrophN[,30:Ymax]) rowMeans(out1c$TrophN[,30:Ymax]) Exploitation rate Utest Utest Utest Fig. 5. Predicted abundance of small undesirable (100-300mm) and large desirable (>300mm) redfin perch under a variety of removal scenarios.

L 150mm L 150mm All lengths (a) (b) (c)

3000 Yearly 3-year 5-year

2000 10-year

1000

Smallundesirable fish

variation(out1a$SmallN) variation(out1b$SmallN) variation(out1c$SmallN) 0

8 (d) (e) (f)

6 Utest Utest Utest

4

2

Largedesirable fish

variation(out1a$TrophN) variation(out1b$TrophN) variation(out1c$TrophN) 0

Predicted annualPredictedinabundancevariation 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 Exploitation rate Utest Utest Utest Fig. 6. Predicted annual variation of small undesirable (100-300mm) and large desirable (>300mm) redfin perch under a variety of removal scenarios.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 34

U = 0.2 U = 0.6 Annual Every 5th Annual Every 5th (a) (b) (c) (d) BH SR

CR = 10

= 0

Mref = 0.6

Amat = 1

Base Smallundesirable fish

0 4000 10000 0 4000 10000 0 6000 0 4000 10000

(e) (f) (g) (h) BH SR

CR = 10

= 0 All sizes Mref = 0.6 >150mm <150mm Amat = 1

Large desirableLarge fish Base

0 20 40 60 0 5 10 15 0 20 60 0 10 25 Predicted abundance

Fig. 7. Results from model sensitivity analysis.

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 35

Managing redfin perch in Lake Purrumbete – Modelling impacts of fish reduction • Recreational Fishing Grants Program 36

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