Issue |
Aquat. Living Resour.
Volume 32, 2019
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|
---|---|---|
Article Number | 20 | |
Number of page(s) | 11 | |
DOI | https://doi.org/10.1051/alr/2019018 | |
Published online | 26 August 2019 |
Short Communication
Assessing attribute redundancy in the application of productivity-susceptibility analysis to data-limited fisheries
Inter-American Tropical Tuna Commission,
8901 La Jolla Shores Dr., La Jolla,
CA
92037-1509, USA
* Corresponding author: lduffy@iattc.org
Handling Editor: Flavia Lucena Fredou
Received:
27
September
2018
Accepted:
11
July
2019
Productivity-susceptibility analysis (PSA) is a widely used data-limited method to assess the relative vulnerability of species impacted by fisheries. Despite its widespread use, few authors have evaluated the impacts of attribute weightings and correlation of productivity attributes that may bias species' vulnerability scores. We evaluated the PSA methodology and performed sensitivity analyses to determine the impacts of correlation among productivity attributes used in the PSA, given that several of these attributes are strongly correlated. A PSA for species caught in the eastern Pacific Ocean tuna purse-seine fishery was used as an example to assess potential bias introduced by attribute weightings and correlation of productivity attributes on species' vulnerability scores. Redundancy was observed among three pairs of attributes. We demonstrated that manipulation of attribute weightings and removal of correlated attributes did not appreciably change any species' overall vulnerability status. Our results suggest that after removal of redundant attributes, PSAs can be conducted more rapidly with fewer data inputs than previous implementations, while retaining comparable vulnerability scores.
Key words: Ecological risk assessment / tuna fishery / correlation / life history
© EDP Sciences 2019
1 Introduction
Ecological risk assessment (ERA) is a popular approach used to assess the impact of fishing on taxa that generally lack sufficient information for more traditional population assessment approaches, such as stock assessment models. ERA approaches range from qualitative consequence-likelihood methods using information from various data sources from expert opinion to precise field data (Fletcher, 2005), to quantitative population models that are more data-intensive (Zhou and Griffiths, 2006). However, attribute-based ERA methods that utilize semi-quantitative data are being increasingly used, in particular the productivity-susceptibility analysis (PSA) (Milton, 2001; Stobutzki et al., 2001).
PSA measures the relative vulnerability of individual species by ranking them based on attributes characterising their susceptibility to being captured in a particular fishery (e.g., gear selectivity), and the capacity of the population to recover following depletion, based on the species' productivity (e.g., natural mortality). Attributes are scored categorically as 1, 2 or 3 using best available data – ranging from highly precise species-specific data to subjective expert opinion. Attribute scores are then averaged, or multiplied (Walker, 2005), and the species having the lowest productivity and highest susceptibility scores across all attributes are considered to be most vulnerable (Stobutzki et al., 2001; Hobday et al., 2007). Although the use of traditional fisheries biological reference points (e.g., F msy, F 0.1) is not possible in PSA to define stock status, PSA practitioners generally use a pre-defined vulnerability score (v) – calculated from the productivity and susceptibility scores – to identify the most vulnerable species (e.g., v ≥ 2.0 is considered “high concern”; see Cope et al., 2011). Boundaries of relative vulnerability have also been identified through contour lines that divide a PSA plot into areas of low, moderate, and high whereby species with similar vulnerability levels are grouped and those furthest from the plot's origin are considered most vulnerable (Hobday et al., 2007).
The flexibility and minimal data requirements of PSA has led to the method being used in a diversity of fisheries worldwide and applied to a wide range of taxonomic groups, including teleosts, elasmobranchs, sea snakes, sea turtles, and seabirds (Stobutzki et al., 2001; Kirby, 2006; Arrizabalaba et al., 2011; Lucena Frédou et al., 2017). However, surprisingly few studies have conducted sensitivity analyses to determine the validity of attribute inclusion/exclusion and attribute weightings used in the PSA (but see Griffiths et al., 2006), given that several commonly-used attributes (e.g., maximum size and maximum age) are strongly correlated (Froese and Binohlan, 2000). This effectively generates implicit weighting – additional to any applied statistical weighting – of correlated attributes, creating a potential positive bias in productivity scores and thus, causing a species' productivity to be overestimated and a fishery's impact underestimated.
The purpose of this paper was to evaluate the PSA methodology by using an example PSA developed for the tuna purse-seine fishery in the eastern Pacific Ocean (EPO) (Duffy et al., 2019) to determine: (i) which PSA productivity attributes are correlated and (ii) the impacts of attribute weightings and removal of correlated attributes on species vulnerability scores. The goal was to optimize the reliability of results from the PSA method, while potentially decreasing data requirements to further expedite this assessment approach for data-limited fisheries.
2 Materials and methods
2.1 Example PSA and attribute weighting
Details of the example PSA for the EPO purse-seine fishery used here are described in Duffy et al. (2019). In brief, 27 species caught during 2005–2013 were included in the PSA composed of 9 productivity (Tab. 1) and 7 susceptibility (Tab. 2) attributes, following the approach of Patrick et al. (2009; 2010), and analysed with the U.S. National Marine Fisheries Service “PSA” analysis package. 1 Data values for each attribute and species were obtained from published and unpublished literature, EPO fisheries data held by the IATTC, web-based sources (e.g., FishBase) and expert opinion from experienced scientists and fishers. Scoring thresholds for productivity (p) attributes were derived by dividing the range of values for a particular attribute into 1/3 percentiles, while those for susceptibility (s) attributes were either taken from Patrick et al. (2009; 2010) or modified as applicable to the EPO purse-seine fishery. The attribute weighting system of Patrick et al. (2009; 2010) was used, ranging between 0 (no importance) and 4 (high importance) with a default value of 2, which was used in the EPO PSA (Duffy et al., 2019).
We conducted sensitivity analyses to determine whether the v score and associated vulnerability status of each species changed when weighting values were manipulated. Categories of relative vulnerability were defined as “low” (v ≤ 1), “moderate” (1 < v > 2) and “high” (v ≥ 2) – with the “high” threshold following the recommendation of Cope et al. (2011) – and identified by vulnerability isopleths starting from the origin of the plot (productivity score = 3, high; susceptibility score = 1, low) (Patrick et al., 2009) (Fig. 1). We manipulated productivity attribute weights in four scenarios (Tab. 3). The attributes maximum size (L max), von Bertalanffy growth rate coefficient (K), and intrinsic rate of population growth (r) were each up-weighted from 2 to 3 (p wtd3, scenario 1) and 4 (p wtd4, scenario 2). Lucena Frédou et al. (2016) found that patterns and covariation between life history traits were mostly explained by L max and K, while r is a combination of many attributes and should take precedence over others, if a reliable estimate is available (Musick, 1999). We also explored a scenario where each of these attributes were down-weighted from 2 to 1 (p wtd1, scenario 3). In the final scenario, we allocated a weight of between 1 and 4 to each productivity attribute by randomly selecting a weighting value from a uniform distribution (minimum 1 to maximum 4) during each iteration of 10,000 Monte Carlo simulations to derive a mean vulnerability score (scenario 4: p wtd random).
Productivity attributes and scoring thresholds used in the example PSA of the eastern Pacific Ocean purse-seine fishery (Duffy et al., 2019). Attribute definitions taken from Table 1 in Patrick et al. (2010) and refined when appropriate.
Susceptibility attributes and scoring thresholds used in the example PSA of the eastern Pacific Ocean purse-seine fishery (Duffy et al., 2019). Attribute definitions taken from Table 2 in Patrick et al. (2010) with the exception of areal overlap taken from Griffiths et al. (2018).
Fig. 1 Scatterplot depicting results of the productivity-susceptibility analysis (PSA) for the purse-seine fishery in the eastern Pacific Ocean. Vulnerability (v) isopleths (dashed lines) with values of 0.5, 1.0, 1.5, 2.0 define the boundaries of “low” (v ≤ 1.0, green), “moderate” (1 < v < 2, yellow), and “high” (v ≥ 2.0, red) relative vulnerability. The proportion contribution by each species to the catch by purse-seine set type is displayed in the pie charts. Coloured boxes represent mean data quality (DQ) score: green = high (DQ < 2), yellow = moderate (3 < DQ ≥ 2), red = low (DQ ≥ 3). Figure and caption from Duffy et al. (2019). Species codes are defined in Table 3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) |
Weighting applied to productivity attributes for each PSA analysis scenario. Productivity (p) and susceptibility (s) scores were used to compute vulnerability (v) scores. Original productivity (p orig) and susceptibility (s orig) scores (using the default weight of 2) were used to compute vulnerability (v orig) scores for a PSA of the purse seine fishery in the eastern Pacific Ocean (Duffy et al., 2019). p scores for maximum size (L max), intrinsic rate of population increase (r), and the von Bertalanffy growth rate coefficient (K) were up-weighted in scenario 1 from 2 to 3 (p wtd3), scenario 2 from 2 to 4 (p wtd4), and down-weighted in scenario 3 from 2 to 1 (p wtd1). In scenario 4, weights ranging from 1 to 4 were randomly allocated to productivity attributes (p wtd random) using a uniform distribution in 10,000 Monte Carlo simulations of the data to produce a mean v score for each species. Vulnerability status: green = low (v ≤ 1), yellow = moderate (1 < v < 2), red = high (v ≥ 2). (For interpretation of the references to colour in this table, the reader is referred to the web version of this article.)
2.2 Assessing redundancy
To explore potential redundancy in PSA attributes, we evaluated relationships between pairs of productivity attributes using a scatterplot matrix and linear regressions. To confirm linearity, we fit generalized additive models (GAMs) to the data of attribute pairs in R (R Development Core Team, 2017).
2.3 Removal of attributes
Prior to exploring scenarios of attribute removal, it was necessary to determine which weighting scenario would be used for the productivity attributes to then compute an overall vulnerability score and associated vulnerability status. Each species' vulnerability score was similar across all weighting scenarios described in Section 2.1 “Example PSA and attribute weighting” (i.e. v orig, v wtd3, v wtd4, v wtd1, v wtd random; Fig. 2). Two exceptions involved slight shifts in vulnerability status for Thunnus obesus, whose vulnerability status shifted from moderate to low in the down-weighted scenario 3 (v wtd1 = 0.99), and Sphyrna lewini, whose vulnerability status decreased from high to moderate in the upweighted scenario 2 (v wtd3 = 1.97) (Tab. 3). Because vulnerability status was on the borderline of moderate (T. obesus) and high (S. lewini) and that of all other species remained the same, we used the default weight of 2 for productivity attributes in p 1 to p 4 in four subsequent scenarios involving correlated attributes that we sequentially removed in a stepwise approach. These p and susceptibility (s orig) scores were used to calculate a vulnerability score after attribute removal, in v 1 to v 4 to compare with v orig (Tab. 4). Vulnerability status was determined by v scores and defined as low (v ≤ 1.0), moderate (1 < v < 2), and high (v ≥ 2.0) as described in Section 2.1.
Scenarios of attribute removal include: v 1 without mean trophic level (TL); v 2 without TL and r; v 3 without TL, r, and maximum age (A max); and v 4 without TL, r, A max and natural mortality (M). In scenario v 1, we did not consider mean trophic level (TL) to be an independent measure of biological productivity, because it describes the contribution of prey from other trophic levels to a predator's diet (Christensen and Pauly, 1992). Although maximum size and longevity generally increase with trophic level, there are many exceptions. For example, several species of mysticete whales (e.g., northern and southern right whales and blue whales) consume primarily planktonic or micronectonic crustaceans (e.g., krill) and occupy low trophic levels (TL = 3.2) (Pauly et al., 1998; Croll et al., 2018). Given that composition of a species' diet is not a direct measure of productivity, we considered this attribute to be irrelevant in PSA analyses.
Fig. 2 Comparison of vulnerability scores using the default attribute weight of 2 for all productivity and susceptibility attributes used in the calculation of overall vulnerability scores (v orig) and those derived from various scenarios of weighting productivity attributes. Scenarios 1 and 2 involved maximum size (L max), intrinsic rate of population growth (r), and the von Bertalanffy growth rate coefficient (K) being upweighted to 3 (v wtd3) and 4 (v wtd4), respectively. Scenario 3 down-weighted these attributes to 1 (v wtd1). Scenario 4 randomly weighted each productivity attribute from 1 to 4 (v wtdr). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) |
Productivity (p) and susceptibility (s) scores used to compute vulnerability (v) scores. Original productivity (p orig) and susceptibility (s orig) scores (using the default weight of 2) were used to compute vulnerability (v orig) scores from a PSA of the purse seine fishery in the eastern Pacific Ocean (Duffy et al., 2019). The default weight of 2 was used in scenarios of attribute removal. p 1 = without trophic level (TL), p 2 = attributes in p 1 and without intrinsic rate of population increase (r), p 3 = attributes in p 2 and without maximum age (A max), p 4 = attributes in p 3 and without natural mortality (M). Vulnerability status: green = low (v ≤ 1), yellow = moderate (1 < v < 2), red = high (v ≥ 2). v scores are ranked in descending order, where bold numbers identify v scores that are different to the original vulnerability scores (v orig). (For interpretation of the references to colour in this table, the reader is referred to the web version of this article.)
3 Results
We observed non-linear relationships between most productivity attribute scores indicating these attributes should be retained in the PSA because if removed, a species' productivity score could cause a change in its vulnerability score and potentially shift it into a higher or lower vulnerability category. Linear regressions showed three pairs of productivity attributes had strong linear correlations (adjusted R 2 > 0.5): (1) age at maturity (A mat) and A max (R 2 = 0.71); (2) K and r (R 2 = 0.57); and (3) M and r (R 2 = 0.56) (Fig. 3), suggesting that two attributes may contain similar information, and if one attribute in the pair was removed, the vulnerability status and species' position in the PSA plot would not significantly change. The GAM analysis confirmed that the relationships between these attribute pairs were linear.
Overall, v scores in the various scenarios of attribute removal produced similar results (Figs. 4 and 5) and vulnerability status stayed the same or remained on the vulnerability status boundaries for most species, with comparable ranks for the most vulnerable species (Tab. 4). For example, slight decreases in v scores were observed for Carcharhinus falciformis (high: v orig = 2.07, v 1 = 2.03 to moderate: v 2 = 1.97, v 3 = 1.91, v 4 = 1.95) and Sphyrna lewini (high: v orig = 2.03, v 1 = 2.00, v 2 = 2.07, v 3 = 2.03 to moderate: v 4 = 1.98). Istiophorus platypterus slightly shifted from moderate (v orig = 1.06; v 1 = 1.03) to low vulnerability (v 2–v 4 = 0.95, 0.96 and 0.99, respectively), Thunnus obesus (v orig = 1.03, v 1 = 1.00, v 2 = 0.97, v 3 = 0.93, v 4 = 0.99) was on the boundary of moderate and high, while Sectator ocyurus was on the boundary of low and moderate (v orig, v 3 and v 4 = 0.95, 1.00 and 0.97, respectively and v 1–v 2 = 1.03 and 1.02, respectively).
Removal of the TL attribute did not result in a change in vulnerability status for any species, although v scores for Manta birostris increased from 2.21 (v orig) to 2.39 (v 1–v 4) due to its consumption of low-trophic level plankton at the base of the food web.
Fig. 3 Linear regressions of productivity attribute pairs with corresponding equations. Multiple R-square value (Mul R-sq) and adjusted R-square value (Adj R-sq) shown for each model fit. Bold equations indicate correlated attribute pairs. |
Fig. 4 Comparison of the original vulnerability scores (v orig) – all attributes included in the productivity-susceptibility analysis – with the four scenarios involving attribute removal: v 1 = no mean trophic level (TL); v 2 = attributes in v 1 and without the intrinsic rate of population growth (r); v 3 = attributes in v 2 and without maximum age (A max); v 4 = attributes in v 3 and without natural mortality (M). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) |
Fig. 5 Scatterplots of PSA results involving productivity attribute reduction: (a) v 1 = no mean trophic level (TL); (b) v 2 = attributes in v 1 and without the intrinsic rate of population growth (r); (c) v 3 = attributes in v 2 and without maximum age (A max); (d) v 4 = attributes in v 3 and without natural mortality (M). Species codes are defined in Table 3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) |
4 Discussion
ERA methods such as PSA are often employed by researchers and managers faced with the common problem of having insufficient biological and/or fishery data or resources to assess the sustainability of bycatch species but require a rapid and inexpensive prioritisation tool that can identify the most vulnerable species impacted by fishing activities. This paper assessed specific aspects of the statistical rugosity of PSA – using common practices of attribute and weighting manipulation – to determine an appropriate and parsimonious approach for future use.
We found no evidence that attribute weighting – as used here – resulted in any appreciable change in any species' vulnerability status. Weightings used in PSAs (Stobutzki et al., 2001; Patrick et al., 2009, 2010) appear to be subjectively applied to emphasise the perceived importance of an attribute by the practitioner or fishery stakeholders, with apparently little consideration given to the potential for excessive weighting of attributes that are already implicitly weighted due to their correlation with one or more related attributes. Based on our results, we recommend that future PSAs do not use attribute weightings but rather dedicate greater focus on the category splits within each attribute to maximize the differentiation of scores between species (e.g., using a quantile method as in Lucena Frédou et al., 2017), particularly those with vast differences in life history characteristics (e.g., teleosts versus marine mammals).
Our sensitivity analyses revealed redundancy among some pairs of productivity attributes: A mat and A max, K and r, and M and r. Two of these, r and K, characterize the rate of population growth. However, r is difficult to measure, because it incorporates age- or life stage-specific growth, survivorship, and in particular natural mortality and fecundity. For pelagic fishes that produce millions of oocytes per spawning, the latter is almost impossible to estimate with confidence. Recently, methods for estimating r, particularly for long-lived species like sharks, have been proposed (Dillingham et al., 2016; Pardo et al., 2016) and may be useful should more easily obtained parameters (e.g., K) be deemed less reliable for describing population growth for a particular species (see Denney et al., 2002). Since reliable estimates of r are typically unavailable for most non-target teleosts we recommend using K over r.
Similar to K, M was correlated with r in our study and has been identified as a correlate of several other life history parameters (Pascual and Iribarne, 1993; Jennings et al., 1998; Denney et al., 2002; Zhou et al., 2012). Although M is a notoriously difficult parameter to measure in practice, its requirement in most stock assessment models has resulted in improvement of estimates derived from empirical models based on various combinations of von Bertalanffy growth parameters (e.g., L ∞ and K) and longevity (A max) (Pauly, 1980; Pascual and Iribarne, 1993; Then et al., 2015). Given that fewer parameters are required in the estimation of M compared to r, we recommend the use of M in preference to r.
The third pair of correlated attributes, A mat and A max, are less problematic in that both can be estimated with reasonable confidence through field studies, but in data-limited settings, both can be estimated using various empirical equations that use von Bertalanffy growth model parameters (Froese and Binohlan, 2000). Therefore, we recommend using the parameter for which the highest quality data is available.
Despite several demonstrations of correlations among life history traits in the literature (Cortés, 2000; Froese and Binohlan, 2000; Lucena Frédou et al., 2016; Thorson et al., 2017), our study is the first to explicitly demonstrate how these correlations can affect the outcomes of PSA. The redundancy we observed in productivity attributes indicates that PSAs can be conducted more rapidly and cost-effectively, due to fewer data requirements, than in previous implementations, and with no compromise in species vulnerability status. For teleosts and elasmobranchs, we recommend the use of no more than one attribute to describe each of the following five principal components of productivity: (1) the rate of population growth (e.g., K or r), (2) maximum extent of growth in terms of age (A max) or length (L ∞ or L max), (3) timing of reproductive maturity in terms of length (L 50) or age (A 50) at which half of the population is mature (ideally for females), (4) reproductive output (e.g., fecundity), and (5) frequency of reproductive output (e.g., seasonally, annually). For some groups, such as marine mammals or seabirds, additional productivity attributes may be required, and possibly separate PSAs using attributes specific to the life histories of these groups.
Although our analyses were restricted to one fishery, our results serve as a caution to other PSA practitioners who may not fully appreciate the potential impacts of manipulating attributes and weightings on PSA outcomes. Despite the manipulations of the attributes used in the present study showed little influence of weighting or removal of correlated attributes on species vulnerability status, researchers using different or additional attributes may experience different results. Therefore, we recommend disregarding attribute weighting and undertaking preliminary analyses prior to finalizing PSAs to ensure attribute values are not correlated, which may cause cryptic weightings that may introduce biases and compromise assessment results.
Acknowledgements
We thank Cleridy Lennert-Cody for assistance with the statistical analysis, Christine Patnode for assistance with graphics, and Nick Webb, Alexandre Aires-da-Silva and Guillermo Compean for reviewing drafts of the manuscript.
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Cite this article as: Duffy LM, Griffiths SP. 2019. Assessing attribute redundancy in the application of productivity-susceptibility analysis to data-limited fisheries. Aquat. Living Resour. 32: 20
All Tables
Productivity attributes and scoring thresholds used in the example PSA of the eastern Pacific Ocean purse-seine fishery (Duffy et al., 2019). Attribute definitions taken from Table 1 in Patrick et al. (2010) and refined when appropriate.
Susceptibility attributes and scoring thresholds used in the example PSA of the eastern Pacific Ocean purse-seine fishery (Duffy et al., 2019). Attribute definitions taken from Table 2 in Patrick et al. (2010) with the exception of areal overlap taken from Griffiths et al. (2018).
Weighting applied to productivity attributes for each PSA analysis scenario. Productivity (p) and susceptibility (s) scores were used to compute vulnerability (v) scores. Original productivity (p orig) and susceptibility (s orig) scores (using the default weight of 2) were used to compute vulnerability (v orig) scores for a PSA of the purse seine fishery in the eastern Pacific Ocean (Duffy et al., 2019). p scores for maximum size (L max), intrinsic rate of population increase (r), and the von Bertalanffy growth rate coefficient (K) were up-weighted in scenario 1 from 2 to 3 (p wtd3), scenario 2 from 2 to 4 (p wtd4), and down-weighted in scenario 3 from 2 to 1 (p wtd1). In scenario 4, weights ranging from 1 to 4 were randomly allocated to productivity attributes (p wtd random) using a uniform distribution in 10,000 Monte Carlo simulations of the data to produce a mean v score for each species. Vulnerability status: green = low (v ≤ 1), yellow = moderate (1 < v < 2), red = high (v ≥ 2). (For interpretation of the references to colour in this table, the reader is referred to the web version of this article.)
Productivity (p) and susceptibility (s) scores used to compute vulnerability (v) scores. Original productivity (p orig) and susceptibility (s orig) scores (using the default weight of 2) were used to compute vulnerability (v orig) scores from a PSA of the purse seine fishery in the eastern Pacific Ocean (Duffy et al., 2019). The default weight of 2 was used in scenarios of attribute removal. p 1 = without trophic level (TL), p 2 = attributes in p 1 and without intrinsic rate of population increase (r), p 3 = attributes in p 2 and without maximum age (A max), p 4 = attributes in p 3 and without natural mortality (M). Vulnerability status: green = low (v ≤ 1), yellow = moderate (1 < v < 2), red = high (v ≥ 2). v scores are ranked in descending order, where bold numbers identify v scores that are different to the original vulnerability scores (v orig). (For interpretation of the references to colour in this table, the reader is referred to the web version of this article.)
All Figures
Fig. 1 Scatterplot depicting results of the productivity-susceptibility analysis (PSA) for the purse-seine fishery in the eastern Pacific Ocean. Vulnerability (v) isopleths (dashed lines) with values of 0.5, 1.0, 1.5, 2.0 define the boundaries of “low” (v ≤ 1.0, green), “moderate” (1 < v < 2, yellow), and “high” (v ≥ 2.0, red) relative vulnerability. The proportion contribution by each species to the catch by purse-seine set type is displayed in the pie charts. Coloured boxes represent mean data quality (DQ) score: green = high (DQ < 2), yellow = moderate (3 < DQ ≥ 2), red = low (DQ ≥ 3). Figure and caption from Duffy et al. (2019). Species codes are defined in Table 3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) |
|
In the text |
Fig. 2 Comparison of vulnerability scores using the default attribute weight of 2 for all productivity and susceptibility attributes used in the calculation of overall vulnerability scores (v orig) and those derived from various scenarios of weighting productivity attributes. Scenarios 1 and 2 involved maximum size (L max), intrinsic rate of population growth (r), and the von Bertalanffy growth rate coefficient (K) being upweighted to 3 (v wtd3) and 4 (v wtd4), respectively. Scenario 3 down-weighted these attributes to 1 (v wtd1). Scenario 4 randomly weighted each productivity attribute from 1 to 4 (v wtdr). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) |
|
In the text |
Fig. 3 Linear regressions of productivity attribute pairs with corresponding equations. Multiple R-square value (Mul R-sq) and adjusted R-square value (Adj R-sq) shown for each model fit. Bold equations indicate correlated attribute pairs. |
|
In the text |
Fig. 4 Comparison of the original vulnerability scores (v orig) – all attributes included in the productivity-susceptibility analysis – with the four scenarios involving attribute removal: v 1 = no mean trophic level (TL); v 2 = attributes in v 1 and without the intrinsic rate of population growth (r); v 3 = attributes in v 2 and without maximum age (A max); v 4 = attributes in v 3 and without natural mortality (M). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) |
|
In the text |
Fig. 5 Scatterplots of PSA results involving productivity attribute reduction: (a) v 1 = no mean trophic level (TL); (b) v 2 = attributes in v 1 and without the intrinsic rate of population growth (r); (c) v 3 = attributes in v 2 and without maximum age (A max); (d) v 4 = attributes in v 3 and without natural mortality (M). Species codes are defined in Table 3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) |
|
In the text |
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