Modeling control of Common Carp (Cyprinus carpio) in a shallow lake–wetland system

Abstract

The introduction of Common Carp (Cyprinus carpio) into North American waterways has led to widespread alteration of aquatic ecosystems. Control of this invader has proven extremely difficult due to its capacity for rapid population growth. To help understand how Common Carp can potentially be controlled we developed a population dynamics model (CarpMOD) to explore the efficacy of active and passive control measures that impose mortality on multiple life stages (embryos, juveniles and adults). We applied CarpMOD to Common Carp in Malheur Lake, a large shallow lake in Southeast Oregon, USA. Simulated control measures included commercial harvest of adults, trapping of juveniles, embryo electroshocking, and passive removal imposed via avian predation. Results from CarpMOD suggest that no single active removal method would decrease Common Carp biomass below the targeted 50 kg/ha threshold. Combinations of two or all three active removal methods could, however, reduce biomass below the desired threshold due to cumulative mortality on multiple life stages. CarpMOD simulations suggest that the level of carp removal necessary to reach the desired biomass threshold is approximately 40% at each life-stage, which may be unrealistic to maintain over longer time scales. Passive removal via avian predation may also contribute to suppression of Common Carp, but was not sufficient in isolation to reduce biomass below the desired threshold. Collectively, our results indicate control of Common Carp as a sole means of ecosystem restoration is unlikely to be effective in the system we modeled. This suggests additional means of restoration may be warranted, perhaps in combination with control of Common Carp, or development of more effective control measures.

Appendices

Appendix 1: CarpMOD—population dynamics model equations and parameters

State variable equations

Carp population dynamics at time (t) can be described as:

[Age 1 Abundance]_t = [Age 1 Abundance]_t−1 + [Recruitment]_t−[Age 1 Mortality]_t−[Age 1 Survival]_t.

[Age x Abundance]_t = [Age x Abundance]_t−1 + [Age x−1 Survival]_t−[Age x Mortality]_t−[Age x Survival]_t.

X = Age 2, 3, 4, …. 20.

However, because CarpMOD is ran on an annual timestep, the above equations can be simplified to:

[Age 1 Survival] = [Recruitment]−[Age 1 Mortality].

[Age X Survival] = [Age X−1 Survival]−[Age X−1 Mortality].

X = Age 2, 3, 4, …. 20.

Von Bertlanffy growth model

The Von Bertalanffy’s Growth Model (VBGM) was used to describe the average yearly growth in length of individual carp in the population (Von Bertalanffy 1938). The VBGM equation is:

$$L_{\left( A \right)} = L_{\infty } \left( {1 - e^{{ - k\left( {A - t_{0} } \right)}} } \right)$$

where L_(A) is the length (mm) of the carp at age, L_∞ is theoretical maximum length, k is the growth coefficient, and t₀ is the theoretical length of the carp at age zero (Von Bertalanffy 1938; Quist et al. 2012). The Malheur National Wildlife Refuge (MNWR) staff collected 88 carp of varying sizes (190–740 mm), over a two year time frame (June 2010–July 2011), using multiple gear types (i.e. electrofishing, dip netting, minnow trapping, angling, trammel netting, and cast netting). The MNWR staff recorded the total length (mm) of each individual carp and then removed the otoliths using standard removal methods (Secor et al. 1991). Otoliths were processed at Iowa State University and ages were estimated for each individual carp collected (Colvin et al. 2012a). The VBGM was fit using the length and age data in the fisheries stock assessment package (FSA), using the R statistical computing software (mean ± Standard Error (SE); L_∞ = 818.02754 ± 41.3931, k = 0.13327 ± 0.01938, and t₀= −0.5482 ± 0.25022; R Development Core Team 2017; Ogle 2017, Ogle et al. 2017).

Length–weight relationship

A length to weight relationship was created using data collect during a five day commercial fishing effort (2014) in Malheur Lake, in which 6797 carp were caught and a subsample of 880 carp (85–853 mm) were sampled for their length (mm) and weights (g). This data was analyzed via a logarithmic weight to length relationship created in the FSA package using the R statistical computing software (Bister et al. 2000; Carlander 1969; Ogle 2017). The length–weight relationship equation is,

$$W = aL^{b}$$

where W is the weight (g), L is the length (mm), a and b are constants that are estimated by linear relationship described above (mean ± SE; a = 4.531975 ± 0.03952 and b = 2.869073 ± 0.01461; Schneider et al. 2000; Ogle 2017).

Probability of maturity

Carp mature at different rates, therefore an equation that uses length to determine probability of maturity at each age in the carp population was necessary in this model. The probability of maturity equation is,

$$\rho_{i} = \left( {1 + e^{{{\raise0.7ex\hbox{${\ln \left( {\left( {19} \right)\left( {L_{\left( A \right)} } \right) - LM50} \right)}$} \!\mathord{\left/ {\vphantom {{\ln \left( {\left( {19} \right)\left( {L_{\left( A \right)} } \right) - LM50} \right)} {\left( {LM50 - LM95} \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\left( {LM50 - LM95} \right)}$}}}} } \right)^{ - 1}$$

where ρ_ί is the probability of maturity, L_(A) is the length at age, LM50 is the length (mm) at 50% maturity, and LM95 is the length at 95% maturity (Brown et al. 2003). The values for the parameters used in this model were derived from the means and standard deviations of the LM50 and LM95 of the female populations used in CarpSIM (mean ± standard deviation (SD); LM50 = 309.667 ± 31.754 and LM95 = 364.667 ± 47.343 mm; Brown and Walker 2004; Brown and Gilligan 2014).

Ricker recruitment equation

Recruitment is thought to be density dependent due to the yearly suppressing of age 0 carp via spawning habitat degradation or competition for resources with large adult carp (Rose et al. 2001; Weber et al. 2016). The Ricker Recruitment equation has been demonstrated to be suitable for carp population models (Bajer et al. 2015; Weber and Brown 2013). The recruitment equation is,

$$R = a*S*\exp^{{\left( { - \beta *S} \right)}}$$

where R is the total annual individual recruits per hectare, S is the numbers of mature individuals per hectare, α is the coefficient that is density-independent, and β is the coefficient that is density-dependent (Ricker 1954). The Ricker Recruitment is recalculated at each progressive time step in order to increase and decrease the recruits into the model as the carp population fluctuates over time. The Ricker Recruitment equation parameters that were used in this model were established by deriving the means and standard deviations of α and β coefficients used to model the carp populations in CarpSIM (mean ± SD; α = 20.0825 ± 16.1242 and β= 0.0162 ± 0.0039; Brown and Walker 2004; Brown and Gilligan 2014).

Annual natural mortality

The annual mortality rate is thought to be density dependent; therefore, an annual mortality rate that fluctuates with the density of carp was necessary in this model. The annual natural mortality rate equation is,

$$V_{\left( A \right)} = 1 - e^{{ - 0.006\left( { - \frac{{L_{\left( A \right)} }}{{L_{\infty } }}} \right) - 1.5}} + 10^{ - 4} \cdot D$$

where V is the annual mortality, A is the age of carp, D is the density of age 1 + carp (kg/ha), L_(A) is the average length (mm) of carp at age, and L_∞ is theoretical maximum length of carp in the population (Charnov et al. 2013; Bajer et al. 2015). The annual mortality rate is recalculated at each progressive time step in order to increase and decrease the mortality as the carp density fluctuates over time.

Appendix 2: Modeled avian piscivory

Avian predation was added to the carp population model in order to more accurately depict the annual mortality imposed on carp by native avian piscivores (Double-crested Cormorant (Phalacrocorax auritus), American White Pelican (Pelecanus erythrorhynchos), and Caspian Tern (Hydroprogne caspia). The addition of avian predation into the model brings more realism to the carp population model as well as enables managers to simulate removal strategies that include increasing the avian populations (e.g., by enhancing nesting habitat). In order to add avian predation into the model we used a bioenergetics approach to estimate the annual consumption of the three avian species (Wiens and Scott 1975; Roby et al. 2003).

In order to quantify the total carp consumed annually, we estimated the annual intake of carp needed to sustain the avian predator populations using a variety of input data. Some required data were available as a product of unrelated studies (Bird Research Northwest 2013, 2014, 2015); where data were not available from Malheur Lake, values were derived from the literature (Table 3).

Table 3 Parameters used as inputs into the avian bioenergetics for the three avian piscivores (Double-crested Cormorant, American White Pelican, and Caspian Tern)

Rearing chicks were not taken into account in this model because the overall bird productivity at Malheur Lake is poor compared to other nesting locations.

Caspian Tern diet composition was estimated using visual identification of prey species carried back to the colony (for mates or offspring) in the Caspian Tern bill by observers using binoculars from blinds adjacent to the breeding colony (Bird Research Northwest 2013, 2014, 2015). Prior research has demonstrated that the prey species transported back to the colony by Caspian Terns consists of the same general taxonomic composition as their individual diet (Collis et al. 2002). The length of each prey was estimated by comparing the length of fish to that of the Caspian Tern’s bill (~ 8 cm; Antolos et al. 2005; Bird Research Northwest 2013, 2014, 2015). We translated the lengths of carp consumed into biomass of carp consumed using a previously documented weight–length relationship (Schneider et al. 2000), which allowed Caspian Tern consumption of carp to be broken down by carp age class.

Diet data for cormorants and pelicans were lacking for Malheur Lake. The diet composition established for terns was used for cormorants because the two species have displayed generally similar diets in other locations (Collis et al. 2002; Lyons 2010), particularly in shallow water environments. The diet composition of pelicans was assumed to be 50% carp, consistent with limited empirical evidence from a somewhat similar Great Basin large water body (Pyramid Lake, Nevada) that had also been previously invaded by nonnative carp (Hall 1925). The age distribution of carp consumed by pelicans was assumed to be split between two age groupings: 90% juveniles (age 0–3) and 10% adults (age 4+). We calculated the relative diet composition of pelicans contributed by each specific age class using the following equation, which assumed consumption was proportional to the relative availability of each age class:

$$\Pr_{x} = D_{y} \left( {\frac{{B_{x} }}{{B_{y} }}} \right)$$

where x denotes individual age class (i.e. age 1, 2, 3, …) and y denotes the age grouping (juveniles or adults), B_x is the biomass of each individual age class, B_y is the biomass of each age grouping (juveniles or adults), D_y is the diet composition for each age grouping, and Pr_x is the resulting proportional diet composition of each age class. The sensitivity of model output to this distributional breakdown was tested by running multiple scenarios assuming different age class (length) distributions of carp consumed. We determined that shifts in the age/size of the pelican’s prey had little to no effect on the output of carp biomass over time; therefore, we only considered the above distribution in subsequent analyses.

Avian piscivore diets were allowed to shift in response to fluctuations in carp densities that will occur as simulated removal actions are implemented following a predator–prey functional response. Diet shifts associated with changes in prey densities have been seen previously in piscivorous waterbird populations. For instance, Double-crested Cormorants shifted their diets away from largely limnetic fish species [Alewife (Alosa pseudoharengus), Yellow perch (Perca flavescens), and three spine stickleback (Gasterosteus aculeatus)] to a benthic fish species [Round goby (Apollonia melanostoma)] during the Goby’s proliferation and subsequent invasion of the Great Lakes (Johnson et al. 2015). We investigated multiple functional response relationships (constant, type 1 [linear], type 2 [saturation], type 3 [sigmoid]) between diet and juvenile carp densities. We determined that the type 1 functional response (% of diet that was carp = 0.0041 multiplied by the juvenile carp biomass) adequately described the likely diet shifts that would take place as carp densities varied as removal efforts were implemented and parsimoniously minimized the number of additional assumptions needed (i.e. rate of saturation or sigmoid shape).