Corresponding author: Giovanni Vimercati ( gvimercati@outlook.com ) Academic editor: Jonathan Jeschke
© 2021 Giovanni Vimercati, Sarah J. Davies, Cang Hui, John Measey.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Vimercati G, Davies SJ, Hui C, Measey J (2021) Cost-benefit evaluation of management strategies for an invasive amphibian with a stage-structured model. NeoBiota 70: 87-105. https://doi.org/10.3897/neobiota.70.72508
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Management strategies for invasive populations should be designed to maximise efficacy and efficiency, i.e. to accomplish their goals while operating with the least resource consumption. This optimisation is often difficult to achieve in stage-structured populations, because costs, benefits and feasibility of removing individuals may vary with stage. We use a spatially-explicit stage-structured model to assess efficacy of past, present and alternative control strategies for invasive guttural toads, Sclerophrys gutturalis, in Cape Town. The strategies involve removal of variable proportions of individuals at different life-history stages and spatial scales. We also quantify the time necessary to implement each strategy as a proxy of financial resources and we correct strategy outcomes by implementation of time to estimate efficiency. We found that the strategy initially pursued in Cape Town, which did not target any specific stage, was less efficient than the present strategy, which prioritises adult removal. The initial strategy was particularly inefficient because it did not reduce the population size despite allocating consistent resources to remove eggs and tadpoles. We also found that such removal might be detrimental when applied at high levels. This counter-intuitive outcome is due to the ‘hydra effect’: an undesired increase in population size caused by removing individuals before overcompensatory density dependence. Strategies that exclusively remove adults ensure much greater management efficiency than those that also remove eggs and tadpoles. Available management resources should rather be allocated to increase the proportion of adult guttural toads that are removed or the spatial extent at which this removal is pursued.
Density dependence, hydra effect, invasive species, management costs, overcompensation, spatially-explicit model
Management strategies for invasive populations often aim to eradicate or control the number of invasive individuals in order to minimise their impacts on native species, ecosystems and human activities (
Numerous invasive populations are characterised, at any given time, by cohorts of different life-history stages (also called stage-structured populations;
Stage-related differences may affect not only the number of individuals that can be detected (detection probability) or removed after detection (intervention success rate), but also how many individuals from different stages can be removed per unit of resource invested (
Invasion dynamics can be reconstructed using a range of mathematical models operating at both individual and population level in accordance with predefined ecological and evolutionary rules (
In this paper, we assess efficacy and efficiency of alternative management strategies for an invasive population of the guttural toad, Sclerophrys gutturalis (Power, 1927), in a peri-urban residential area of Cape Town (
In this study, we explain the rationale behind the decision to change strategies in the control operation of the guttural toad in Cape Town. For management strategies involving the removal of variable proportions of individuals at different life-history stages, efficacy and efficiency were assessed here by the use of a spatially-explicit stage-structured model, which has already been parameterised and validated for this invasive population with field data (
The stage-structured model proposed by
In brief, an average of 13000 eggs are laid twice a year by each female from late spring (October-November) to late summer (February), with the probability for females to lay eggs in a pond that varies with pond size (
As the population size is reasonably large, demographic stochasticity can be safely ignored; the peri-urban environment has further reduced any effects from environmental fluctuation and uncertainty. First, invasive guttural toads in Cape Town use only permanent, mainly artificial, ponds, thus justifying the assumption that the pond network does not change over time. Second, given the small spatial scale of the invaded area, the climate can be considered homogeneous across the whole pond network, while the landscape structure has not been altered since the first introduction of the species in Cape Town (
The model structure allows the alteration of mortality rate of any stage at any point in space (different ponds) and time (different years). As a consequence, this model can be used to test alternative management strategies based on different rates of removal across stages (
First, we designed a management strategy named “initial removal”, which realistically simulates removal of the guttural toad in Cape Town from accessible ponds as pursued from 2011 to 2016 by the implementation team (i.e. 128 ponds, see also
Proportions of guttural toads, Sclerophrys gutturalis, removed in Cape Town from ponds accessible by implementers according to the “initial removal” strategy simulated with the stage-structured model. For each stage, the proportion of individuals removed has been estimated by considering: the removal capacity by the implementation team; the spatial and temporal occurrence of the stage in the property visited by the team. Removal proportions have been confirmed by using evidence collected from field data and surveys.
Second, we test a management strategy named “adult removal”, which simulates the exclusive removal of adults from ponds accessible to the implementation team. This strategy is currently being pursued in Cape Town, shares with the “initial removal” strategy the proportion of adults removed from each pond (0.8), but differs in that no other stages are targeted for removal. To test whether individuals at early life-history stages should be prioritised over adults, we additionally simulated a third “pre-metamorphic removal” strategy, which is based on the exclusive removal of the same proportion of eggs and tadpoles (0.8) from accessible ponds. We also simulated the hypothetical application of the above three strategies across all ponds (i.e. accessible and not-accessible ponds) in order to explore how management efficacy and efficiency vary with restricted access. Analogous to
For each management strategy, we estimate efficacy (i.e. the degree to which a strategy accomplishes its goal) and net efficiency (i.e. the efficacy of a strategy corrected by the time [as a proxy for cost spent] on its implementation). As the goal of the initial management programme in Cape Town was to decrease the total number of invasive individuals to zero (i.e. full eradication,
Proportions of guttural toads, Sclerophrys gutturalis, removed from each pond according to the different management strategies simulated with a stage-structured model. For each simulated strategy, number of ponds in which the removal is performed, rationale and total time necessary to perform the removal in one year (T) are reported. Please note that the “initial removal” strategy describes the ongoing management of the invasive population in Cape Town (see Table
Management strategy simulated through the stage-structured model described in |
Proportion of individuals removed from each stage in the simulated strategy | Number of ponds visited by the implementation team (Np) / Total number of ponds in the area | Rationale behind the simulated strategy | Estimated total yearly time T (in hours) spent by the implementation team to remove individuals from different stages while visiting properties, as expressed in the formula (3): (Taj + Tm + Tte) × 2 × Np = T | ||||
---|---|---|---|---|---|---|---|---|
Ad. | Juv. | Met. | Tad. | Eggs | ||||
“Initial removal” | 0.8 | 0.05 | 0.25 | 0.25 | 0.05 | 128/415 | Estimate of the initial management strategy in which the implementation team remove individuals at different stages from accessible ponds (See also Table |
(1 + 0.25 + 0.5) × 2 × 128 = 448 |
“Adult removal” (current strategy) | 0.8 | 0 | 0 | 0 | 0 | 128/415 | Fictional management strategy in which the implementation team removes only adults from accessible ponds | (1 + 0 + 0) × 2 × 128 = 256 |
“Pre-metamorphic removal” | 0 | 0 | 0 | 0.8 | 0.8 | 128/415 | Fictional management strategy in which the implementation team removes only eggs and tadpoles from accessible ponds | (0 + 0 + 1.5) × 2 × 128 = 384 |
“Initial removal in all ponds” | 0.8 | 0.05 | 0.25 | 0.25 | 0.05 | 415/415 | Estimated initial management strategy in which the implementation team removes individuals at different stages from all ponds | (1 + 0.25 + 0.5) × 2 × 415 = 1453 |
“Adult removal in all ponds” | 0.8 | 0 | 0 | 0 | 0 | 415/415 | Fictional management strategy in which the implementation team removes only adults from all ponds | (1 + 0 + 0) × 2 × 415 = 830 |
“Pre-metamorphic removal in all ponds” | 0 | 0 | 0 | 0.8 | 0.8 | 415/415 | Fictional management strategy in which the implementation team removes only eggs and tadpoles from all ponds | (0 + 0 + 1.5) × 2× 415 = 1245 |
“No removal” | 0 | 0 | 0 | 0 | 0 | 0/415 | Fictional strategy in which the implementation team does not remove any individual | (0 + 0 + 0) × 0 × 0 = 0 |
“Successful eradication” | 0.95 | 0 | 0 | 0.8 | 0.8 | 415/415 | Fictional management strategy in which the implementation team removes most adults, eggs and tadpoles from all ponds | (2 + 0 + 1.5) × 2 × 415 = 2905 |
E = (S0 – Si) (1)
In other words, E reflects how many invasive individuals would theoretically be removed from the population as a consequence of a given management strategy. For ease of comparison, we also calculate the efficacy in percentage (E%) from the ratio between E and S0:
E% = (S0 – Si) * 100 / S0 (2)
For each strategy, we measured efficiency F as the ratio between E and the strategy implementation cost T expressed in hours. Implementation costs can be estimated in various ways, for instance, by measuring average personnel salary or equipment cost. Here we assume that the management effort invested to control the guttural toad in Cape Town is linearly related to the time spent by the implementation team to remove the toads. This assumption is supported by the observation that the management of guttural toads is done manually without using expensive equipment, while the total salary costs of the implementation team reflect the time spent for removal. We thus conducted field surveys in 2014, 2015 and 2016 to estimate the time (in hours) spent by a manager to target each stage during the initial strategy of removal. We found that at each visit, 1, 0.25 and 0.5 hours have been, on average, allocated to remove adults and juveniles (Taj), metamorphs (Tm) and tadpoles and eggs (Tte), respectively.
The removal of adults and juveniles was more time-consuming than the removal of metamorphs: while adults and juveniles can be detected only through a detailed walking survey of the area around the pond, metamorphs are generally found only within 1 to 5 metres from the pond edge, where they congregate to minimise desiccation risk (
T = (Taj + Tm + Tte) × Np × 2 (3)
where the time spent each night to remove individuals across different stages in a single property is multiplied by the number of properties that can be visited (Np) in one year and by two, which is the average number of properties visited each night. The limited number of properties that can be visited each night by the team (i.e. two properties) is due to the necessity to remove toads when they are mostly active (i.e. within three-four hours after sunset) and the obligation to gain access to a private property at a time that suits the owner (e.g. no later than midnight). As the guttural toad management programme employed only one team to remove toads in 2014, 2015 and 2016, all calculations are based on a single team visiting properties in the evening.
The removal of most adult toads (80%) from accessible ponds (“adult removal” strategy) currently pursued in Cape Town is as effective as the initial strategy (Table
Population size at the end of management, efficacy, efficacy in percentage, cost T (in hours) and efficiency obtained by simulating different strategies with a stage-structured model for the invasive population of guttural toad, Sclerophrys gutturalis, in Cape Town. Note that the “initial removal” and “adult removal” strategies describe, respectively, the initial strategy (2011–2016, Table
Strategy | Population size at the end of management (2011) | Strategy efficacy E, as expressed in the formula (1) | Strategy efficacy E%, as expressed in the formula (2) | Strategy Implementation cost T expressed in hours (as reported in Table |
Strategy efficiency F expressed as the ratio between E and T |
---|---|---|---|---|---|
“No removal” | 2973 | – | 0 | 0 | – |
“Initial removal” | 2162 | 811 | 27% | 448 | 1.81 |
“Adult removal” | 2197 | 776 | 26% | 256 | 3.03 |
“Pre-metamorphic removal” | 3318 | - 345 | Counter-effective | 384 | Counter-effective |
“Initial removal in all ponds” | 494 | 2479 | 83% | 1453 | 1.71 |
“Adult removal in all ponds” | 465 | 2508 | 84% | 830 | 3.02 |
“Pre-metamorphic removal in all ponds” | 3897 | - 924 | Counter-effective | 1245 | Counter-effective |
“Successful eradication” | 0 | 2973 | 100% | 2905 | 1.02 |
Population size of invasive toads estimated by a stage-structured model simulating alternative management strategies. Adult population size of invasive guttural toads, Sclerophrys gutturalis, in Cape Town estimated by a stage-structured model that simulates potential management strategies, as listed in Table
We found that the efficiency of the initial strategy adopted in Cape Town to control the guttural toad was impaired by the removal of eggs and tadpoles; their removal did not noticeably affect the population demography (Fig.
Population size of invasive toads estimated by a stage-structured model simulating different removal proportions of pre-metamorphic individuals. Adult population size of invasive guttural toads, Sclerophrys gutturalis, in Cape Town estimated by a stage-structured model that simulates different removal proportions of pre-metamorphic individuals (eggs and tadpoles). Colours indicate different proportions of removal expressed in percentage. Black indicates a no-removal scenario. Management was simulated to start in 2011 and to be interrupted in late 2020 (removal phase), after which the model simulating the invasive population would be allowed to run for a further 10 years until 2030.
The counter-intuitive observation that a sustained removal of eggs and tadpoles may increase, rather than decrease, the adult population size can be explained by the occurrence of the ‘hydra effect’; i.e. “the phenomenon of a population increasing in response to an increase in its per-capita mortality rate” (
Since density dependence in tadpoles is also followed by density dependence in metamorphs, our study also shows that this condition promotes a relaxation of the density-dependent bottleneck; as a consequence, a higher equilibrium density is reached (
The occurrence of a strong positive mortality effect at the population level implies that management actions to control the guttural toad should target eggs and tadpoles only when it is possible to fully remove them (Fig.
Multiple studies on amphibians have shown that variations in the survival rate of juveniles and sub-adults may have severe population-level effects (
Here, we have shown that the strategy currently adopted to control the invasive guttural toad in Cape Town ensures much greater management efficiency than the strategy initially adopted in 2011. By removing only adults, the implementation team can maximise the reduction of population size without dissipating resources for removal of other stages or causing unwanted consequences, such as those associated with the hydra effect. The management resources, saved by not removing pre-metamorphic individuals, should rather be allocated to increase the proportion of adults that are removed or the spatial scale at which this removal is pursued. Overall, our study demonstrates that simulation models, combining complex population dynamics with management costs and field data, represent valuable tools to guide and improve management decisions for stage-structured invasive populations.
We would like to thank David Richardson, James Vonesh and Mohlamatsane Mokhatla for fruitful discussions throughout the preparation of the manuscript. We would like also to thank Jonathan Bell, Richard Burns, Michael Hoarau and Scott Richardson for their help in the field and Jonathan Jeschke, Benedikt Schmidt and an anonymous reviewer for improving the quality of the manuscript. The study was supported by the Department of Science and Technology-National Research Foundation Centre of Excellence for Invasion Biology (NRF grant no. 41313). G.V. would like to acknowledge funding from the South Africa’s National Research Foundation (NRF) through the NRF Innovation Doctoral Scholarships programme (NRF grant no. 88676) and from the Swiss National Science Foundation (NSF grant no. 31BD30_184114) and the Belmont Forum – BiodivERsA International joint call project InvasiBES (PCI2018–092939). C.H. is supported by the South African Research Chairs Initiative (NRF grant no. 89967).