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2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 01 + 2025 + + + 10 + + 105 + + + + ssdtools v2: An R package to fit Species Sensitivity Distributions + + + + Joe + Thorley + + Poisson Consulting, Canada + + https://orcid.org/0000-0002-7683-4592 + + + Rebecca + Fisher + + Australian Institute of Marine Science, Australia + Oceans Institute, The University of Western Australia, Australia + + https://orcid.org/0000-0001-5148-6731 + + + David + Fox + + The University of Melbourne, Australia + Environmetrics Australia, Australia + + https://orcid.org/0000-0002-3178-7243 + + + Carl + Schwarz + + Simon Fraser University, Canada + + https://orcid.org/0000-0002-8525-862X + + + + 01 + 15 + 2025 + + + 7492 + + + 10.21105/joss.07492 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.14609128 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/7492 + + + + 10.21105/joss.07492 + https://joss.theoj.org/papers/10.21105/joss.07492 + + + https://joss.theoj.org/papers/10.21105/joss.07492.pdf + + + + + + Applying species-sensitivity distributions in ecological risk assessment: Assumptions of distribution type and sufficient numbers of species + Newman + Environmental Toxicology and Chemistry + 2 + 19 + 10.1002/etc.5620190233 + 2000 + Newman, M. C., Ownby, D. R., Mézin, L. C. A., Powell, D. C., Christensen, T. R. L., Lerberg, S. B., & Anderson, B.-A. (2000). Applying species-sensitivity distributions in ecological risk assessment: Assumptions of distribution type and sufficient numbers of species. Environmental Toxicology and Chemistry, 19(2), 508–515. https://doi.org/10.1002/etc.5620190233 + + + shinyssdtools: A web application for fitting Species Sensitivity Distributions (SSDs) + Dalgarno + Journal of Open Source Software + 57 + 6 + 10.21105/joss.02848 + 2475-9066 + 2021 + Dalgarno, S. (2021). shinyssdtools: A web application for fitting Species Sensitivity Distributions (SSDs). Journal of Open Source Software, 6(57), 2848. https://doi.org/10.21105/joss.02848 + + + Improving Statistical Methods for Modeling Species Sensitivity Distributions + Schwarz + 2019 + Schwarz, C., & Tillmanns, A. (2019). Improving Statistical Methods for Modeling Species Sensitivity Distributions (No. WSS2019-07). Province of British Columbia. https://a100.gov.bc.ca/pub/acat/documents/r57400/2_1568399094009_8398900200.pdf + + + Species sensitivity distributions in ecotoxicology + Posthuma + 10.1002/etc.4373 + 2001 + Posthuma, L., Suter II, G., & Traas, T. (2001). Species sensitivity distributions in ecotoxicology. CRC press. https://doi.org/10.1002/etc.4373 + + + fitdistrplus: An R package for fitting distributions + Delignette-Muller + Journal of Statistical Software + 4 + 64 + 10.18637/jss.v064.i04 + 2015 + Delignette-Muller, M., & Dutang, C. (2015). fitdistrplus: An R package for fitting distributions. Journal of Statistical Software, 64(4), 1–34. https://doi.org/10.18637/jss.v064.i04 + + + ggplot2: Elegant graphics for data analysis + Wickham + 10.1007/978-0-387-98141-3 + 978-3-319-24277-4 + 2016 + Wickham, H. (2016). ggplot2: Elegant graphics for data analysis. 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Wiley. https://doi.org/10.1002/9780470094846 + + + ssddata: Species Sensitivity Distribution Data + Fisher + 10.32614/cran.package.ssddata + 2021 + Fisher, R., & Thorley, J. (2021). ssddata: Species Sensitivity Distribution Data. https://doi.org/10.32614/cran.package.ssddata + + + TMB: Automatic differentiation and laplace approximation + Kristensen + Journal of Statistical Software + 5 + 70 + 10.18637/jss.v070.i05 + 2016 + Kristensen, K., Nielsen, A., Berg, C., Skaug, H., & Bell, B. (2016). TMB: Automatic differentiation and laplace approximation. Journal of Statistical Software, 70(5), 1–21. https://doi.org/10.18637/jss.v070.i05 + + + ssdtools: An R package to fit species sensitivity distributions + Thorley + Journal of Open Source Software + 31 + 3 + 10.21105/joss.01082 + 2018 + Thorley, J., & Schwarz, C. (2018). ssdtools: An R package to fit species sensitivity distributions. Journal of Open Source Software, 3(31), 1082. https://doi.org/10.21105/joss.01082 + + + Burrlioz 2.0 manual + Barry + Commonwealth Science and Industrical Research Organisation + 2012 + Barry, S., & Henderson, B. (2012). Burrlioz 2.0 manual. Commonwealth Science and Industrical Research Organisation. https://research.csiro.au/software/burrlioz + + + Recent Developments in Species Sensitivity Distribution Modeling + Fox + Environmental Toxicology and Chemistry + 2 + 40 + 10.1002/etc.4925 + 0730-7268 + 2021 + Fox, D., van Dam, R., Fisher, R., Batley, G., Tillmanns, A., Thorley, J., Schwarz, C., Spry, D., & McTavish, K. (2021). Recent Developments in Species Sensitivity Distribution Modeling. Environmental Toxicology and Chemistry, 40(2), 293–308. https://doi.org/10.1002/etc.4925 + + + Joint investigation into statistical methodologies underpinning the derivation of toxicant guideline values in Australia and New Zealand + Fox + 10.25845/fm9b-7n28 + 2022 + Fox, D., Fisher, R., Thorley, J., & Schwarz, C. (2022). Joint investigation into statistical methodologies underpinning the derivation of toxicant guideline values in Australia and New Zealand. Environmetrics Australia; Australian Institute of Marine Science. https://doi.org/10.25845/fm9b-7n28 + + + Final report of the joint investigation into SSD modelling and ssdtools implementation for the derivation of toxicant guidelines values in Australia and New Zealand. Report prepared for the department of climate change, energy, the environment and water + Fox + 10.25845/xtvt-yc51 + 2024 + Fox, D., Fisher, R., & Thorley, J. (2024). Final report of the joint investigation into SSD modelling and ssdtools implementation for the derivation of toxicant guidelines values in Australia and New Zealand. Report prepared for the department of climate change, energy, the environment and water. Environmetrics Australia; Australian Institute of Marine Science. https://doi.org/10.25845/xtvt-yc51 + + + Revised Method for Deriving Australian and New Zealand Water Quality Guideline Values for Toxicants – update of 2015 version. + Warne + 2018 + Warne, M., Batley, GE, van Dam, R., Chapman, J., Fox, D., Hickey, C., & Stauber, J. (2018). Revised Method for Deriving Australian and New Zealand Water Quality Guideline Values for Toxicants – update of 2015 version. Prepared for the Revision of the Australian and New Zealand Guidelines for Fresh and Marine Water Quality. Australian and New Zealand Governments and Australian state and territory governments, Canberra, 48 pp. https://www.waterquality.gov.au/sites/default/files/documents/warne-wqg-derivation2018.pdf + + + Manual on the methodological framework to derive environmental quality standards for priority substances in accordance with article 16 of the water framework directive (2000/60/EC) + Lepper + Schmallenberg, Germany: Fraunhofer-Institute Molecular Biology and Applied Ecology + 15 + 2005 + Lepper, P. (2005). Manual on the methodological framework to derive environmental quality standards for priority substances in accordance with article 16 of the water framework directive (2000/60/EC). Schmallenberg, Germany: Fraunhofer-Institute Molecular Biology and Applied Ecology, 15, 51–52. https://www.wrrl-info.de/docs/manual-derivation-qs.pdf + + + Derivation of Water Quality Guidelines for the Protection of Aquatic Life in British Columbia. Water quality guideline series, WQG‐06 + BC Ministry of Environment and Climate Change Strategy + 2019 + BC Ministry of Environment and Climate Change Strategy. (2019). Derivation of Water Quality Guidelines for the Protection of Aquatic Life in British Columbia. Water quality guideline series, WQG‐06. Province of British Columbia, Victoria, BC, Canada. https://www2.gov.bc.ca/assets/gov/environment/air-land-water/water/waterquality/water-quality-guidelines/derivation-protocol/bc_wqg_aquatic_life_derivation_protocol.pdf + + + Species sensitivity distribution (SSD) toolbox + US EPA + 10.23645/epacomptox.11971392.v2 + 2020 + US EPA. (2020). Species sensitivity distribution (SSD) toolbox. 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    + + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +7492 +10.21105/joss.07492 + +ssdtools v2: An R package to fit Species Sensitivity +Distributions + + + +https://orcid.org/0000-0002-7683-4592 + +Thorley +Joe + + +* + + +https://orcid.org/0000-0001-5148-6731 + +Fisher +Rebecca + + + + + +https://orcid.org/0000-0002-3178-7243 + +Fox +David + + + + + +https://orcid.org/0000-0002-8525-862X + +Schwarz +Carl + + + + + +Poisson Consulting, Canada + + + + +Australian Institute of Marine Science, +Australia + + + + +Oceans Institute, The University of Western Australia, +Australia + + + + +The University of Melbourne, Australia + + + + +Environmetrics Australia, Australia + + + + +Simon Fraser University, Canada + + + + +* E-mail: + + +11 +12 +2024 + +10 +105 +7492 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2025 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +ssdtools +species sensitivity distributions +R +maximum likelihood +model averaging +hazard concentration + + + + + + Summary +

    Species sensitivity distributions (SSDs) are cumulative probability + distributions that are used to estimate Hazard Concentrations + ( + + HCx) + - the concentration of a chemical that is expected to affect a given + + + x% + of species. + + HC5 + values, which are intended to protect 95% of species, are often used + for the derivation of environmental quality criteria and ecological + risk assessment for contaminated ecosystems + (Posthuma + et al., 2001). The Hazard Proportion + ( + + HPu) + is the proportion of species affected by a given concentration + + + x.

    +

    ssdtools is an R package + (R Core + Team, 2024) to fit SSDs using Maximum Likelihood + (Millar, + 2011) and estimate + + HCx + and + + HPu + values by model averaging + (Schwarz + & Tillmanns, 2019) across multiple distributions + (Thorley + & Schwarz, 2018). The shinyssdtools + R package + (Dalgarno, + 2021) provides a Graphical User Interface to + ssdtools.

    +

    Since the publication of Thorley & Schwarz + (2018), + the ssdtools R package has undergone two major + updates. The first update (v1) included the addition of four new + distributions (inverse Pareto, Burr Type III and the log-normal + log-normal and log-logistic log-logistic mixtures) and a switch to the + R package TMB + (Kristensen + et al., 2016) allowing full control over model specification. + The second major release (v2) includes critical updates to ensure that + the + + HCx + and + + HPu + estimates satisfy the inversion principle as well as + bootstrap methods to obtain confidence intervals (CIs) with more + appropriate coverage + (Fox + et al., 2024).

    +
    + + Statement of need +

    SSDs are a practical tool for the determination of safe threshold + concentrations for toxicants in fresh and marine waters, and are + implemented in some form for risk assessment and water quality + criteria derivation throughout multiple jurisdictions globally + (BC + Ministry of Environment and Climate Change Strategy, 2019; + Lepper, + 2005; + US EPA, + 2020; + Warne + et al., 2018).

    +

    The selection of a suitable distribution has been identified as one + of the most important and difficult choices in the use of SSDs + (Newman + et al., 2000). Since the original implementation (v0), + ssdtools + (Thorley + & Schwarz, 2018) has used model averaging to allow + estimation of + + HCx + and + + HPu + values using multiple distributions + (Schwarz + & Tillmanns, 2019). The method, which is described in + detail by Fox et al. + (2021) + in the SSD context, provides a level of flexibility and parsimony that + is difficult to achieve with a single distribution.

    +
    + + Technical details + + Distributions +

    Ten distributions are currently available in + ssdtools. The original version (v0) of + ssdtools provided the two parameter + log-normal (lnorm), log-logistic + (llogis), log-Gumbel + (lgumbel, also known as the inverse Weibull), + gamma (gamma), Weibull + (weibull) and Gompertz + (gompertz) distributions. In the first major + update (v1), the two parameter inverse Pareto + (invpareto), three parameter Burr Type III + (burrIII3) and five parameter log-normal + log-normal (lnorm_lnorm) and log-logistic + log-logistic (llogis_llogis) mixture + distributions were added. Together with the Burr Type III, the + inverse Pareto and inverse Weibull provide the underlying + distributions of the SSD fitting software + Burrlioz + (Barry + & Henderson, 2012) while the mixture distributions were + added to accommodate bimodality + (Fox + et al., 2021). Since v1, ssdtools has + by default fitted the lnorm, + llogis, lgumbel, + gamma, weibull and + lnorm_lnorm distributions.

    +
    + + Model Fitting +

    In the first major update (v1), the dependency + fitdistrplus + (Delignette-Muller + & Dutang, 2015) was replaced by + TMB + (Kristensen + et al., 2016) for fitting the available distributions via + Maximum Likelihood + (Millar, + 2011). The move to TMB means the + likelihood function is hand coded in C++, + which allows full control over model specification and improved + handling of censored data. The change is internal and does not + directly affect the user interface.

    +
    + + Model Averaging +

    In both the original + (Thorley + & Schwarz, 2018) and updated versions, the Akaike + Information Criterion (AIC), AIC corrected for small sample size + (AICc) and Bayesian Information Criterion (BIC) can be calculated + for each distribution + (Burnham + & Anderson, 2002). Information criterion based model + weights have the properties + + 0wi1 + and + + i=1mwi=1 + where + + wi + is the weight of the + + ith + of the + + m + models + (Burnham + & Anderson, 2002). Except in the case of censored data, + ssdtools uses AICc based weights for model + averaging.

    +

    The first two implementations of ssdtools + used the weighted arithmetic mean to obtain a model-averaged + estimate of + + HCx: + + + HC̃x=i=1mwiHCx{i} + where + + HCx{i} + is the + + HCx + estimate for the + + ith + model.

    +

    The weighted arithmetic mean is conventionally used for averaging + model parameters or estimates + (Burnham + & Anderson, 2002). However, in the case of + + + HCx + and + + HPu + values, the estimator + + HC̃x + fails to satisfy the inversion principle + (Fox + et al., 2024) which requires + + [HPu]u=HCθ=θ + This inconsistency has been rectified in + ssdtools v2 by estimating the model-averaged + + + HCx + (denoted + + HĈx) + directly from the model-averaged cumulative distribution function + (cdf) + + G(u)=i=1mwiFi(u) + where + + Fi() + is the cdf for the the + ith model and + + + wi + is the model weight as before. + + HĈx + is then obtained as the solution to + + u:G(u)=x + or, equivalently + + u:G(u)x=0 + for the proportion affected + + x. + Finding the solution to this last equation is referred to as + finding the root(s) of the function + + + G(u)x. + As of ssdtools v2, methods such as + ssd_hc() and ssd_hp() + now use the inversion principle by default when + multi_est = TRUE. To estimate the values + using the original weighted arithmetic mean set + multi_est = FALSE.

    +
    + + Confidence Intervals +

    ssdtools generates confidence intervals + for + + HCx + and + + HPu + values via bootstrapping. By default all versions of + ssdtools use parametric bootstrapping for + non-censored data as it has better coverage than the equivalent + non-parametric approach used in some other SSD modelling software + such as Burrlioz (see + Fox + et al., 2022). The first two versions of + ssdtools both calculated the model averaged + CI from the weighted arithmetic mean of the CIs of the individual + distributions. Unfortunately, this approach has recently been shown + to have poor coverage + (Fox + et al., 2024) and is inconsistent with the inversion + principle.

    +

    Consequently, v2 also offers a parametric bootstrap method for + non-censored data that uses the joint cdf to generate data before + refitting the original distribution set and solving for the newly + estimated joint cdf (see details in + Fox + et al., 2024). This so-called ‘multi’ method can be + implemented with + (ci_method = "multi_free") and + without (ci_method = "multi_fixed") + re-estimation of the model weights. In order to implement the + ‘multi’ method of bootstrapping described above, v2 also provides + the probability density (ssd_pmulti()), + cumulative distribution (ssd_qmulti()) and + random generation (ssd_rmulti()) functions + for multiple distributions.

    +

    However, although the ‘multi’ method has good coverage it is + computationally slow. To overcome this limitation, the default + method + (ci_method = "weighted_samples") + provided by the current update is a faster heuristic based on taking + bootstrap samples from the individual distributions proportional to + their weights + (Fox + et al., 2024).

    +
    + + Plotting +

    As well as fitting SSDs and providing methods for estimating + + + HCx + and + + HPu + values, from v1 ssdtools has extended the + ggplot2 R package + (Wickham, + 2016) by defining geom_ssdpoint(), + geom_ssdsegment(), + geom_hcintersect() and + geom_xribbon() geoms and a discrete + color-blind scale scale_color_sdd() for SSD + plots. The current version (v2) adds + scale_fill_ssd() for a discrete color-blind + fill scale and ssd_label_comma() and + ssd_label_comma_hc() for formatting of x-axis + labels.

    +
    +
    + + Example of use +

    The following code fits the six default distributions to the boron + example data set from ssddata + (Fisher + & Thorley, 2021) and prints the goodness of fit table + complete with information criteria:

    + library(ssdtools) +fits <- ssd_fit_dists(ssddata::ccme_boron) +ssd_gof(fits) + # A tibble: 6 × 9 + dist ad ks cvm aic aicc bic delta weight + <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> +1 gamma 0.440 0.117 0.0554 238. 238. 240. 0.005 0.357 +2 lgumbel 0.829 0.158 0.134 244. 245. 247. 6.56 0.013 +3 llogis 0.487 0.0994 0.0595 241. 241. 244. 3.39 0.066 +4 lnorm 0.507 0.107 0.0703 239. 240. 242. 1.40 0.177 +5 lnorm_lnorm 0.320 0.116 0.0414 240. 243. 247. 4.98 0.03 +6 weibull 0.434 0.117 0.0542 238. 238. 240. 0 0.357 +

    The model averaged + + HC5 + estimate with 95% CIs can then be obtained using:

    + ssd_hc(fits, ci = TRUE) + # A tibble: 1 × 11 + dist proportion est se lcl ucl wt method nboot pboot samples + <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <dbl> <dbl> <I<list>> +1 average 0.05 1.26 0.819 0.397 3.41 1 parametric 1000 1 <dbl [0]> +

    And all of the distributions plotted via:

    + autoplot(fits) + +

    Species sensitivity distributions for the six default + distributions with the Boron species concentration + data.

    + +
    +

    The model averaged cdf with 95% CIs (with the model averaged + + + HC10 + indicated by a dotted line) can be plotted using:

    + predictions <- ssdtools::predict(fits, ci = TRUE) +ssd_plot(ssddata::ccme_boron, predictions, + hc = 0.1, xlimits = c(NA, 3000), + shape = "Group", color = "Group", label = "Species", + xlab = "Concentration (mg/L)" +) + + scale_color_ssd() + +

    Model averaged species sensitivity distribution with 95% + CI based on the six default distributions with Boron species + concentration data. The + + HC10 + value is indicated by the dotted line.

    + +
    +
    + + Acknowledgements +

    We acknowledge contributions from Angeline Tillmanns, Seb Dalgarno, + Kathleen McTavish, Heather Thompson, Doug Spry, Rick van Dam, Graham + Batley, and Ali Azizisharzi. Development of + ssdtools was funded by the Ministry of + Environment and Climate Change Strategy, British Columbia and the + Department of Climate Change, Energy, the Environment and Water, + Australia.

    +
    + + + + + + + + NewmanMichael C. + OwnbyDavid R. + MézinLaurent C. A. + PowellDavid C. + ChristensenTyler R. 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