Threshold detection: matching statistical methodology to ecological questions and conservation planning objectives

Toms, Judith D.; Villard, Marc-Andr

doi:10.5751/ace-00715-100102

Cited by 55 publications

(45 citation statements)

References 63 publications

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“…To identify a threshold value for suitable sea ice algae habitat, we used piecewise “hockey stick” regression (Toms & Lesperance, ; Toms & Villard, ) between the natural logarithm‐transformed transmittance (ln[ T ]) and chl a biomass for the ice core locations. Hockey stick regression identifies the change point value (i.e., threshold) of the calculated transmittance, which separates regions of high chl a biomass (hereafter referred to as suitable habitat) from regions of low chl a biomass (hereafter referred to as not‐suitable habitat).…”

Section: Methodsmentioning

confidence: 99%

Pan‐Arctic sea ice‐algal chl a biomass and suitable habitat are largely underestimated for multiyear ice

Lange

Flores

Michel

et al. 2017

Global Change Biology

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There is mounting evidence that multiyear ice (MYI) is a unique component of the Arctic Ocean and may play a more important ecological role than previously assumed. This study improves our understanding of the potential of MYI as a suitable habitat for sea ice algae on a pan-Arctic scale. We sampled sea ice cores from MYI and first-year sea ice (FYI) within the Lincoln Sea during four consecutive spring seasons. This included four MYI hummocks with a mean chl a biomass of 2.0 mg/m 2 , a value significantly higher than FYI and MYI refrozen ponds. Our results support the hypothesis that MYI hummocks can host substantial ice-algal biomass and represent a reliable ice-algal habitat due to the (quasi-) permanent lowsnow surface of these features. We identified an ice-algal habitat threshold value for calculated light transmittance of 0.014%. Ice classes and coverage of suitable ice-algal habitat were determined from snow and ice surveys. These ice classes and associated coverage of suitable habitat were applied to pan-Arctic CryoSat-2 snow and ice thickness data products. This habitat classification accounted for the variability of the snow and ice properties and showed an areal coverage of suitable icealgal habitat within the MYI-covered region of 0.54 million km 2 (8.5% of total ice area). This is 27 times greater than the areal coverage of 0.02 million km 2 (0.3% of total ice area) determined using the conventional block-model classification, which assigns single-parameter values to each grid cell and does not account for subgrid cell variability. This emphasizes the importance of accounting for variable snow and ice conditions in all sea ice studies. Furthermore, our results indicate the loss of MYI will also mean the loss of reliable ice-algal habitat during spring when food is sparse and many organisms depend on ice-algae. K E Y W O R D SCryoSat-2, habitat classification, hockey stick regression, light transmittance, piecewise regression, sea ice algae, sea ice bio-optics, the Last Ice AreaThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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Section: Methodsmentioning

confidence: 99%

Pan‐Arctic sea ice‐algal chl a biomass and suitable habitat are largely underestimated for multiyear ice

Lange

Flores

Michel

et al. 2017

Global Change Biology

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“…All else being equal, the sensitivity of management decisions to error increases with uncertainty in the slope and location of thresholds. Unfortunately, statistical power to identify thresholds—or differentiate linear versus nonlinear responses—may be limited in many systems (Poff et al., ; Toms & Villard, ). Low power to explain variance if often a consequence of multiple (unmeasured) causative drivers, leading to the increasing use of quantile regression to define the upper bounds of flow–ecology relationships (e.g.…”

Section: Shape and Defining Attributes Of Flow–ecology Relationshipsmentioning

confidence: 99%

“…Inadvertently crossing a threshold may cause a large decline in ecological response relative to a similar error for a linear function. This will increase the likelihood of ecological surprises in the presence of nonlinearities (Gordon et al., ), necessitating a more precautionary approach in the neighbourhood of thresholds under high uncertainty (Bennett & Radford, ; Radford et al., ; Toms & Villard, ).…”

Section: Implications Of Nonlinearity For Threshold Versus Proportionmentioning

confidence: 99%

Developing flow–ecology relationships: Implications of nonlinear biological responses for water management

Rosenfeld

2017

Freshwater Biology

111

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Empirical relationships between stream flow and ecological responses (flow–ecology relationships) are essential for establishing environmental flows and evaluating tradeoffs between instream values and out‐of‐stream uses. Establishing the shape of flow–ecology relationships (i.e. slope, linearity versus nonlinearity) is particularly important to avoid crossing ecological thresholds in water management. This review focuses on ecological responses to discharge at low summer flows when out‐of‐stream water demand is often highest, and identifying ecological contexts where nonlinearities are most likely. Most physical attributes (temperature, dissolved oxygen, available habitat) and ecological responses (energy flow, fish survival, recruitment, community structure) show at least some evidence of nonlinear relationships with flow, although assumptions of linearity may be reasonable across limited discharge ranges which may include low flows. Nonlinearities are most likely in systems that are near existing thresholds (e.g. cold‐water transitional fish communities that are close to upper thermal tolerances). The probability of nonlinearities is likely to increase under future landuse and climate change scenarios, particularly in combination with other stressors, such as eutrophication, which may greatly accelerate temperature‐related decline in dissolved oxygen under climate warming. Managers need to anticipate changes in flow–ecology relationships and develop management systems that are robust to change. Field programmes to establish the slope and linearity of local flow–ecology relationships are essential for regional management, but developing generalisable flow–ecology relationships that are transferrable to regions with limited resources also needs to be a priority. Generalised relationships can be generated through meta‐analysis of empirical flow–ecology relationships, and may prove especially useful if they can capture how environmental and ecological context (channel size and morphology, landuse, flow regime, antecedent conditions, habitat or taxonomic guild) affect flow–ecology relationships. For instance, linking empirical data from flow–ecology relationships to available habitat predicted by physical habitat simulation models (e.g. PHABSIM) may provide a better mechanistic basis for modelling ecological responses, while providing much needed validation for habitat simulation approaches. This would also help bridge the gap between emerging holistic environmental flow modelling approaches and more traditional habitat simulation methods.

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“…Similarly, Radford et al () show evidence for a threshold response in species richness of woodland‐dependent birds to habitat cover in Victoria, Australia. Despite the growing evidence for ecological thresholds, species populations or assemblages may not always show a sudden response to change in their environment and if they do show a response the shapes of these responses can be quite different (Swift and Hannon , Toms and Villard ). How to detect such thresholds or sensitive zones has been a challenging problem but is critically important to ecosystem management (Svancara et al , Ficetola and Denoël , Suding and Hobbs , Rondinini and Chiozza , Samhouri et al , Swift and Hannon , Matthews et al ).…”

Section: A Summary Of Tools For Identifying Ecological Thresholds Thmentioning

confidence: 99%

“…While ecological thresholds are usually defined as ‘points or zones of abrupt change in relationships’ (Huggett , Toms and Villard ), the identification of thresholds varies from different types of response curves. For V‐shaped thresholds, the point at which the two lines join is commonly defined as the threshold and several statistical methods have been developed to identify V‐shaped thresholds, for example, bent‐cable regression (Chiu ), a nonparametric method based on the reduction of deviance (Qian et al ), and piecewise regression (Toms and Lesperance ).…”

Section: A Summary Of Tools For Identifying Ecological Thresholds Thmentioning

confidence: 99%

Methods and models for identifying thresholds of habitat loss

Yin

Leroux

2016

Ecography

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There is mounting evidence that many taxa respond in non‐linear ways to perturbation (i.e. deviations from a natural trajectory brought on by an external agent), and many statistical, physical and ecological methods have been developed to detect the critical points or thresholds of perturbation. The majority of these methods define thresholds as the perturbation points causing abrupt ecological response, but in reality most species or ecosystems do not show a break point response but more gradual transitional change to perturbation. We develop a new method which delineates thresholds as a region in which the slope of the relationship between ecological response (y) and perturbation (x; e.g. habitat loss) is larger than 1: |dy/dx|≥ 1, where both x‐ and y‐axes are scaled to (0, 1) range. The lower end of threshold zones so defined is of particular ecological interest because it is the smallest x that may trigger impending catastrophic response to a small change in x. We derived two landscape models (edge length and the number of patches of species distribution) and two biodiversity models (endemics–area relationship and half‐population curve) to test this method. We applied our zonal thresholding method to these four models fit to empirical data of two forest plots to detect thresholds of species distribution to habitat loss. The two landscape metric models predict that no species could tolerate more than 40% of habitat loss and these thresholds can be much lower for relatively rare species with occupancy < 0.4 and for aggregated habitat loss compared to random habitat loss. The half‐population model leads to a similar threshold level of 40% habitat loss. Overall, we suggest the maximum permissible habitat loss threshold to be between 0–40%, depending on the pre‐disturbed occupancy (or abundance) of a species. This habitat loss threshold falls within the otherwise wide range of thresholds calculated from conventional methods. Our study contributes novel methods and models to quantify the effect of habitat loss on species distribution and diversity in landscapes with potential for conservation applications.

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Threshold detection: matching statistical methodology to ecological questions and conservation planning objectives

Cited by 55 publications

References 63 publications

Pan‐Arctic sea ice‐algal chl a biomass and suitable habitat are largely underestimated for multiyear ice

Pan‐Arctic sea ice‐algal chl a biomass and suitable habitat are largely underestimated for multiyear ice

Developing flow–ecology relationships: Implications of nonlinear biological responses for water management

Methods and models for identifying thresholds of habitat loss

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