# Investigating the Ability of Growth Models to Predict In Situ Vibrio spp. Abundances

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Literature Search and Model Synthesis

#### 2.2. Data Preparation

^{2}via the Manoa and Palolo streams, which merge to form the Manoa–Palolo Stream prior to entering the canal, and the Makiki Stream, all of which run through urban areas before reaching the canal. Consequently, the streams are contaminated with a variety of anthropogenic substances, and their convergence in the Ala Wai Canal has contributed to its pollution and eutrophication [57]. We classified datasets from this area as the urban estuary habitat type due to the strong anthropogenic influence. The dataset by Bullington et al. [56] was labeled as URB1 and the dataset by Steward et al. [57] was labeled as URB2.

`data_preparation`. Results of the dataset preparation are summarized in Table 5.

#### 2.3. Model Simulations

#### 2.4. Model Performance

## 3. Results

#### 3.1. Vibrio spp. Growth Models

- Baranyi and modified Gompertz are the most commonly used primary models for describing Vibrio spp. growth over time.
- Square root and Arrhenius-based models are the most frequently applied secondary models for Vibrio spp. growth in dynamic conditions.
- V. cholerae, V. parahaemolyticus, V. harveyi, and V. vulnificus are the species used most often as modeling organisms.
- Vibrio growth was monitored in/on various substrates (free water column, within organisms, in broth substrates, etc.), under different temperature, salinity, and pH conditions. This implies that the aquatic environments and organisms (marine and freshwater), as well as food and water health and safety, are the key areas of research and concern.
- Temperature was the prevailing environmental parameter used in secondary models, implying a strong effect of temperature on Vibrio spp. abundance. The effect of temperature on the primary model parameters (growth rate and lag time) was most often modeled by the square root or the Arrhenius-based model.

#### 3.2. Vibrio In Situ Datasets

#### 3.3. Model Performance

- All models except Model 6 (Baranyi with polinomial pH and salinity secondary models) were able to score above average at least in some habitats, i.e., capture those habitats. Incidentally, Model 6 was the only one not applying a temperature correction
- A total of 93% of models captured the coastal area habitat.
- A total of 93% of all models captured estuary habitat, but only 85% of those (i.e., 79% of all models) captured both estuary datasets; 26 models captured EST1, with 22 of them capturing EST2 as well.
- A total of 75% of models captured an urban habitat, but only two (Models 9 and 28) captured both urban habitat datasets; URB1 was captured by all 20 of them; only 3 models managed to capture URB2.
- Only the Baranyi-type model (Model 8, with temperature and salinity secondary models) captured the AQC1 aquaculture habitat.
- The model with the highest ${R}^{2}$ values (Model 28—net exponential, for urban estuary URB2) had low generality, as it captured datasets from only two out of four habitats.
- Of the models that performed well for at least one habitat type, Model 17 had lowest generality as it captured only one EST1 dataset.

- ≈A total of 72% of the analyzed models had an exceptional ability to capture datasets from the coastal area habitat.
- The ability of models to capture/perform well for estuarine habitats was severely diminished, with only 16/28 (57% of the models) capturing one of the two estuary datasets, and only 10 models (36%) capturing both.
- None of the models were able to capture for the aquaculture habitat datasets, and only three (Models 8, 9, and 28) captured the urban estuary habitat.
- Model 28 seemed even more specialized, as it captured a single urban estuary (URB2)
- Most prolific Baranyi models (Models 8 and 9) remained so by capturing datasets from three habitat types, albeit only a single dataset from each.

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Literature Search

## Appendix B. Data Analysis

**Table A1.**List of parameters used in primary model analysis. Parameter A is the maximum increase in microbial cell density, and ${Y}_{0}$ and ${Y}_{max}$ represent logarithm of initial and maximum bacterial counts, respectively. Parameter ${T}_{min}$ is the minimum temperature required for growth of the organism. We used the minimum value from dataset divided by 2 (Est ${Y}_{0}$) to estimate initial bacterial count whenever it was not provided by the authors. In cases where the maximum bacterial count was not provided, we used the estimate of the maximal bacterial count from each dataset (Est ${Y}_{max}$). Parameters used in secondary models are available in the provided code.

Derived Model | A | ${\mathit{Y}}_{0}$ | ${\mathit{Y}}_{\mathbf{max}}$ | ${\mathit{T}}_{\mathbf{min}}$ (${}^{\circ}$C) |
---|---|---|---|---|

Model 1 [26] | 4 | / | / | 6.4 °C |

Model 2 [26] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 6.4 |

Model 3 [32] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 15 |

Model 4 [33] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 8.3 |

Model 5 [35] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 10.0 |

Model 6 [36] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | / |

Model 7 [34] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 8.0 |

Model 8 [37] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 12.9 |

Model 9 [37] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 12.9 |

Model 10 [31] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 15.0 |

Model 11 [37] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 12.9 |

Model 12 [37] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 12.9 |

Model 13 [38] | / | Est ${Y}_{0}$ | Est ${Y}_{max}$ | 8.0 |

Model 14 [31] | / | Est ${Y}_{0}$ | / | 15.0 |

Model 15 [40] | 4 | Est ${Y}_{0}$ | / | 13.0 |

Model 16 [40] | 4 | Est ${Y}_{0}$ | / | 13.0 |

Model 17 [40] | 4 | Est ${Y}_{0}$ | / | 13.0 |

Model 18 [40] | 4 | Est ${Y}_{0}$ | / | 13.0 |

Model 19 [40] | 4 | Est ${Y}_{0}$ | / | 13.0 |

Model 20 [42] | 6 | Est ${Y}_{0}$ | / | 10.0 |

Model 21 [42] | 6 | Est ${Y}_{0}$ | / | 10.0 |

Model 22 [42] | 6 | Est ${Y}_{0}$ | / | 10.0 |

Model 23 [42] | 6 | Est ${Y}_{0}$ | / | 10.0 |

Model 24 [41] | 4 | Est ${Y}_{0}$ | / | 12.1 |

Model 25 [45] | / | Est ${Y}_{0}$ | 9.28 | 12.1 |

Model 26 [47] | / | Est ${Y}_{0}$ | 7.64 | 10.8 |

Model 27 [47] | / | Est ${Y}_{0}$ | 7.70 | 10.5 |

Model 28 [49] | / | Est ${Y}_{0}$ | / | / |

## Appendix C. Additional Results

#### Appendix C.1. Methods Used for Determining Vibrio spp. Abundance

**Figure A2.**Optimal run time for the simulation duration that produces the best match between the model prediction and the observation (data point of a dataset) based on R

^{2}median value. Models based on Table 4 are specified on the x axis. Primary models are labeled as follows: ML—modified logistic, Baranyi, Gompertz, modified Gompertz, TPL—three-phase linear, HPM—Huang primary, NL—no-lag, and NE—net exponential. Star (*) signifies models that had an evaluation issue with some of the data points in some of the datasets (details in Appendix D).

**Table A2.**Results of robust ANOVA one-way test from the package WRS2 [61].

Function: | t1way (formula = max_r2~Habitat, data = as) |

Test statistic: | F = 75.561 |

Degrees of freedom 1: | 3 |

Degrees of freedom 2: | 49.90 |

p-value: | 0 |

Explanatory measure of effect size: | 0.77 |

Bootstrap CI: | [0.68; 0.84] |

**Table A3.**Results of post hoc lincon test from the package WRS2 [61].

Formula: | lincon (max_r2~Habitat, data = as) | |||

Habitat type | psihat | ci.lower | ci. upper | p-value |

Aquaculture vs. Urban Estuary | −0.03910 | −0.08237 | 0.00417 | 0.01688 |

Aquaculture vs. Estuary | −0.14203 | −0.17331 | −0.11075 | 0.00000 |

Aquaculture vs. Coastal Area | −0.21525 | −0.27062 | −0.15989 | 0.00000 |

Urban Estuary vs. Estuary | −0.10293 | −0.14925 | −0.05662 | 0.00000 |

Urban Estuary vs. Coastal Area | −0.17616 | −0.23977 | −0.11254 | 0.00000 |

Estuary vs. Coastal Area | −0.07322 | −0.13069 | −0.01575 | 0.00263 |

## Appendix D. Model Evaluation Issues

Model | Issue | Impacts % of Dataset | Dataset |
---|---|---|---|

Model 3 | Negative specific growth rate | 26/99 = 26.26% | AQC1 [54] |

16/81 = 19.75% | AQC2 [55] | ||

52/223 = 23.32% | EST1 [58] | ||

30/127 = 23.62% | EST2 [59] | ||

4/72 = 5.56% | COAST [60] | ||

Model 8 | High values of specific growth rate which generate Inf values | / | / |

Model 9 | High values of specific growth rate which generate Inf values | 1/81 = 1.23% | AQC2 [55] |

6/223 = 2.69% | EST1 [58] | ||

4/127 = 3.15% | EST2 [59] | ||

Model 13 | Salinity, i.e., water activity >0.998 | 80/223 = 35.87% | EST1 [58] |

18/240 = 7.50% | URB2 [57] | ||

Model 27 | Temperature 10.5 °C | 2/81 = 2.47% | AQC2 [55] |

29/223 = 13.00% | EST1 [58] | ||

16/127 = 12.60% | EST2 [59] | ||

1/72 = 1.39% | COAST [60] |

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**Figure 1.**The methodological approach to model analysis. We performed a literature search to find all Vibrio spp. growth models and all available datasets suitable for comparison. We found five published datasets, and included two of our own collected through projects AqADAPT and AQUAHEALTH of the Croatian Science Foundation (HRZZ).

**Figure 2.**R

^{2}calculated for all models and for each dataset. Horizontal line depicts the median ${R}^{2}=0.13$ used to evaluate model performance. Primary models are labeled as follows: ML—modified logistic, Baranyi, Gompertz, modified Gompertz, TPL—three-phase linear, HPM—Huang primary, NL—no-lag and NE—net exponential. Star (*) signifies models that had an evaluation issue with some of the data points in some of the datasets (details in Appendix D).

**Figure 3.**Boxplot of model performance measured as ${R}^{2}$ in different habitat types (as classified in Table 5). Model performance significantly differed between habitat types (robust ANOVA, F(3,75.561) = 49.9, p < 0.001, effect size $\xi $ = 0.77, confidence interval CI($\xi $) = [0.68, 0.84]; Table A2). Significance codes are as follows: $p\le 0$ ‘****’, $p<0.01$ ‘**’, and $p<0.5$ ‘*’.

**Figure 4.**Model generality. Stacked bar chart used for graphical representation of model’s applicability on the dataset from a specific habitat: colors represent habitats (see the legend), and stars (*) denote models that exhibit the evaluation issue with some of the data points in some of the datasets (details in Appendix D). Values on y axis denote the frequency of occurrence of a particular model whose R

^{2}value is above the median (${R}^{2}>0.13$; Panel

**A**), and in the first quartile (${R}^{2}>0.22$; Panel

**B**). Primary models are labeled as follows: ML—modified logistic, Baranyi, Gompertz, modified Gompertz, TPL—three-phase linear, HPM—Huang primary, NL—no-lag and NE—net exponential. Star (*) signifies models that had an evaluation issue with some of the data points in some of the datasets (details in Appendix D). Note that there is only one coastal area dataset, while other habitats have two datasets each. Hence, scoring a single occurrence of the coastal area habitat represents a 100% success rate, while scoring the same in any other habitat represents a success rate of 50%.

**Figure 5.**Relationships between growth rate and environmental variables as predicted by secondary models. The models in panel (

**A**) include only a temperature correction. Panel (

**B**) shows dependence of growth rate on temperature for three salinity levels. Panel (

**C**) shows dependence of growth rate on salinity for three temperatures. A pH value of 8.1 was assumed for Model 6. Model 28 had a flat temperature response because it used the default parameter value [49] that minimized temperature correction, $\theta =1$; increasing $\theta $ would increase the temperature dependence.

**Table 1.**Systematized equations for Vibrio spp. primary growth models. Of the 12 models listed in this table, one (new logistic model) did not have parameters listed, so only the remaining 11 were used in further analysis. The reference in the column “Model” is the original paper containing the equation. The column “Article” lists all published articles that used the given primary models.

Model | Equation | Article |
---|---|---|

Modified logistic [25] |
$$Y\left(t\right)=\frac{A}{\left\{1+\mathrm{exp}\left[\frac{4\xb7{\mu}_{\mathrm{max}}}{A}\left(\lambda -t\right)+2\right]\right\}}$$
| [26,27,28,29] |

Baranyi [30] |
$$\left\{\begin{array}{c}Y\left(t\right)={Y}_{0}+{\mu}_{max}\mathrm{A}\left(\mathrm{t}\right)-ln[1+\frac{exp\left({\mu}_{max}\mathrm{A}\left(t\right)\right)-1}{exp({Y}_{max}-{Y}_{0})}]\\ \mathrm{A}\left(\mathrm{t}\right)=t+\frac{1}{{\mu}_{max}}ln\left[exp\left(-{\mu}_{max}t\right)+exp\left(-{\mu}_{max}\lambda \right)-exp\left(-{\mu}_{max}t-{\mu}_{max}\lambda \right)\right]\end{array}\right.$$
| [26,28,29,31,32,33,34,35,36,37] |

Gompertz [25] |
$$Y\left(t\right)={Y}_{0}+A\left({e}^{\left(-{e}^{-B\left(t-D\right)}\right)}\right)$$
| [37,38,39] |

Modified Gompertz [25] |
$$\phantom{\rule{1.em}{0ex}}Y\left(t\right)={Y}_{0}+Aexp\left\{-exp\left[\frac{{\mu}_{max}\xb7e}{A}\left(\lambda -t\right)+1\right]\right\}$$
| [28,29,31,40,41,42] |

Weibull [43] |
$$Y\left(t\right)={Y}_{0}-{\left(\frac{t}{\delta}\right)}^{p}$$
| [28,41] |

Three-phase linear [44] |
$$\left\{\begin{array}{c}Y\left(t\right)={Y}_{0},t\le \lambda \\ Y\left(t\right)={Y}_{0}+{\mu}_{max}\left(t-\lambda \right),\lambda <t<{t}_{s}\\ Y\left(t\right)={Y}_{max},\phantom{\rule{1.em}{0ex}}t\ge {t}_{s}\end{array}\right.$$
| [29,45] |

Huang [46] |
$$\left\{\begin{array}{c}Y\left(t\right)={Y}_{0}+{Y}_{max}-ln\left\{exp\left({Y}_{0}\right)+\left[exp\left({Y}_{max}\right)-exp\left({Y}_{0}\right)\right]exp\left(-{\mu}_{max}\mathrm{B}\left(\mathrm{t}\right)\right)\right\}\\ \mathrm{B}\left(\mathrm{t}\right)=t+\frac{1}{4}ln\frac{1+exp\left[-4\left(t-\lambda \right)\right]}{1-exp\left(4\lambda \right)}\end{array}\right.$$
| [29,47] |

No-lag phase [48] |
$$\phantom{\rule{1.em}{0ex}}Y\left(t\right)={Y}_{0}+{Y}_{max}-ln\left\{exp\left({Y}_{0}\right)+\left[exp\left({Y}_{max}\right)-exp\left({Y}_{0}\right)\right]exp\left(-{\mu}_{max}t\right)\right\}$$
| [47] |

Net exponential |
$$Y\left(t\right)={Y}_{0}\xb7{e}^{\mu t}$$
| [49] |

Modified Richards [25] |
$$Y\left(t\right)=A{\left\{1+\nu \xb7exp\left(1+\nu \right)\xb7exp\left[\frac{{\mu}_{max}}{A}\left(1+\nu \right)\left(1+\frac{1}{\nu}\right)\xb7\left(\lambda -t\right)\right]\right\}}^{\left(-\frac{1}{\nu}\right)}$$
| [29] |

Modified Schnute [25] |
$$Y\left(t\right)=\left({\mu}_{max}\frac{\left(1-b\right)}{a}\right){\left[\frac{1-b\xb7exp\left(a\xb7\lambda +1-b-at\right)}{1-b}\right]}^{\frac{1}{b}}$$
| [29] |

New logistic [50] |
$$\frac{\mathrm{d}Y}{\mathrm{d}t}={\mu}_{max}Y\left\{1-{\left(\frac{Y}{{Y}_{max}}\right)}^{m}\right\}\left\{1-{\left(\frac{{Y}_{min}}{Y}\right)}^{n}\right\}$$
| [51] |

**Table 2.**Systematized equations for Vibrio spp. secondary growth models. These models modify specific growth rate and lag time in primary models to capture effects of environmental conditions such as temperature, salinity, and pH.

Model | Equation | Article |
---|---|---|

Square root [52] |
$${\mu}_{max}={\left[a\left(T-{T}_{min}\right)\right]}^{2}$$
| [26,33,35,40,41,45] |

Polynomial model |
$$\lambda \phantom{\rule{0.222222em}{0ex}}or\phantom{\rule{0.222222em}{0ex}}{\mu}_{max}=a+{a}_{1}T+{a}_{2}{T}^{2}+\dots +{a}_{n}{T}^{n}$$
| [32,34,36,51] |

Response surface [37] |
$$\begin{array}{c}{\mu}_{max}\phantom{\rule{0.222222em}{0ex}}or\phantom{\rule{0.222222em}{0ex}}1/\lambda =exp({C}_{0}+{C}_{1}\xb7T+{C}_{2}\xb7{a}_{w}\\ +{C}_{3}\xb7T\xb7{a}_{w}+{C}_{4}\xb7{T}^{2}+{C}_{5}\xb7{a}_{w}^{2})\end{array}$$
| [37] |

Arrhenius-based [23] |
$${\mu}_{max}=\mathrm{exp}\left({C}_{0}+\frac{{C}_{1}}{T}+\frac{{C}_{2}}{{T}^{2}}+{C}_{3}{a}_{w}+{C}_{4}{a}_{w}^{2}\right)$$
| [31,37,40,42] |

Modified Ratkovsky [22] |
$${\mu}_{max}=b{\left(T-{T}_{min}\right)}^{2}\left\{1-exp\left[c\left(T-{T}_{max}\right)\right]\right\}$$
| [31] |

Suboptimal Huang square root [53] |
$${\mu}_{max}={\left[a{\left(T-{T}_{min}\right)}^{0.75}\right]}^{2}$$
| [47] |

Four-parameter square root and water activity [38] |
$$\begin{array}{c}{\mu}_{max}={\left(b\left(T-{T}_{min}\right)\left\{1-exp\left[c\left(T-{T}_{max}\right)\right]\right\}\right)}^{2}\phantom{\rule{4pt}{0ex}}\\ \xb7\left({a}_{w}-{a}_{wmin}\right)\left\{1-exp\left[d\left({a}_{w}-{a}_{wmax}\right)\right]\right\}\end{array}$$
| [38] |

Net Vibrio growth rate [49] |
$$\begin{array}{c}{\mu}_{\nu}=[{\mu}_{max}\ast \mathrm{fn}(S,{S}_{\mathrm{opt}},{S}_{\mathrm{width}})-{k}_{d}]\ast {\theta}^{T-20},\mathrm{with}\hfill \\ \phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}\mathrm{fn}(S,\phantom{\rule{4pt}{0ex}}{S}_{\mathrm{opt}},{S}_{\mathrm{width}})=\frac{-{\left(S-{S}_{\mathrm{opt}}\right)}^{2}}{{e}^{2}{\left({S}_{\mathrm{width}}\right)}^{2}},\mathrm{if}\hfill \\ \phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}S<{S}_{\mathrm{opt}}-0.5\xb7{S}_{\mathrm{width}},\mathrm{or}\hfill \\ \phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}S>{S}_{\mathrm{opt}}-0.5\xb7{S}_{\mathrm{width}}\hfill \end{array}$$
| [49] |

**Table 3.**Parameters used in Vibrio spp. primary and secondary models. Last column lists models using the particular parameter.

Parameter | Description | Used in Model |
---|---|---|

$Y\left(t\right)$ ${Y}_{0}$ ${Y}_{max}$ | Logarithm of real-time initial and maximum bacterial counts | All primary models |

${\mu}_{max}$ | Maximum specific growth rate | All primary models except Weibull and New logistic All secondary models except Net Vibrio growth rate |

${\mu}_{\nu}$ | Net Vibrio growth rate | Net Vibrio growth rate |

$\lambda $ | Lag time | All primary models except Gompertz, Weibull and New logistic |

t | Time | All models |

${t}_{s}$ | Time to reach stationary growth phase | Three-phase linear |

A | Maximum increase in microbial cell density | Modified logistic Gompertz Modified Gompertz Modified Richards Modified Schnute |

B, D | Maximum relative growth rate and time at which the absolute growth rate is maximum | Gompertz |

$\nu $ | Shape parameter | Modified Richards |

a, b, c, m, n | Fitted coefficients | Modified Schnute and New logistic model |

${C}_{0},{C}_{1},{C}_{2}$ ${C}_{3},{C}_{4},{C}_{5}$ | Fitted coefficients | Response surface and Arrhenius-based |

T, ${T}_{min}$, ${T}_{max}$ | Temperature, minimum and maximum temperature required for growth of the organism | All secondary models |

$\delta $, p | Coefficients in the Weibull model | Weibull |

${a}_{w},{a}_{wmin},{a}_{wmax}$ | Optimal, the minimum, and maximum water activity | Four-parameter |

$S,{S}_{\mathrm{opt}},{S}_{\mathrm{width}}$ | Salinity, optimal salinity value, and salinity range for optimal growth | Net Vibrio growth rate |

**Table 4.**List of models used in the analysis. For each model, Vibrio spp. is specified along with the environment where the growth of the organism was observed. The primary model defines growth function and the secondary model describes functional dependencies accounting for environmental conditions (temperature, salinity, and pH). “Temp” stands for temperature, “Sal” for salinity represented in models as the concentration of NaCl (% NaCl), and “Sal (w.a.)” stands for water activity calculated from salinity. In simulations, salinity from datasets was converted to water activity when needed.

Derived Model | Vibrio spp. | Environment | Environmental Conditions | Primary Model | Secondary Model |
---|---|---|---|---|---|

Model 1 [26] | V. cholerae | Sea water | Temp | Modified logistic | Square root |

Model 2 [26] | V. cholerae | Sea water | Temp | Baranyi | Square root |

Model 3 [32] | V. parahaemolyticus | Soy sauce | Temp | Baranyi | Polynomial |

Model 4 [33] | V. parahaemolyticus | C. gigas | Temp | Baranyi | Square root |

Model 5 [35] | V. parahaemolyticus | C. virginica | Temp | Baranyi | Square root |

Model 6 [36] | V. cocktail ^{1} | Table Olives | pH and Sal | Baranyi | Polinomial |

Model 7 [34] | V. cholerae and V. vulnificus | O. minor | Temp | Baranyi | Polinomial |

Model 8 [37] | V. harveyi | TSYEB ^{2} | Temp and Sal (w.a.) | Baranyi | Response surface |

Model 9 [37] | V. harveyi | TSYEB ^{2} | Temp and Sal (w.a.) | Baranyi | Arrhenius-based |

Model 10 [31] | V. parahaemolyticus | L. vannamei | Temp | Baranyi | Modified Ratkowsky |

Model 11 [37] | V. harveyi | TSYEB ^{2} | Temp and Sal (w.a.) | Gompertz | Response surface |

Model 12 [37] | V. harveyi | TSYEB ^{2} | Temp and Sal (w.a.) | Gompertz | Arrhenius-based |

Model 13 [38] | V. parahaemolyticus | Model broth system | Temp and Sal (w.a.) | Gompertz | The four-parameter square root |

Model 14 [31] | V. parahaemolyticus | L. vannamei | Temp | Modified Gompertz | Modified Ratkowsky |

Model 15 [40] | V. parahaemolyticus | Broth | Temp | Modified Gompertz | Square root Arrhenius-based |

Model 16 [40] | V. vulnificus | Broth | Temp | Modified Gompertz | Square root Arrhenius-based |

Model 17 [40] | V. parahaemolyticus | Flounder sashimi | Temp | Modified Gompertz | Square root Arrhenius-based |

Model 18 [40] | V. parahaemolyticus | Salmon sashimi | Temp | Modified Gompertz | Square root Arrhenius-based |

Model 19 [40] | V. vulnificus | Oyster meat | Temp | Modified Gompertz | Square root Arrhenius-based |

Model 20 [42] | V. parahaemolyticus^{3} | C. gigas broth | Temp | Modified Gompertz | Square root Arrhenius-based |

Model 21 [42] | V. parahaemolyticus^{4} | C. gigas broth | Temp | Modified Gompertz | Square root Arrhenius-based |

Model 22 [42] | V. parahaemolyticus^{3} | C. gigas Oyster slurry | Temp | Modified Gompertz | Square root Arrhenius-based |

Model 23 [42] | V. parahaemolyticus^{4} | C. gigas Oyster slurry | Temp | Modified Gompertz | Square root Arrhenius-based |

Model 24 [41] | V. parahaemolyticus | Oncorhynchus spp. | Temp | Modified Gompertz, Weibull | Square root |

Model 25 [45] | V. parahaemolyticus | L. vannamei | Temp | Three-phase linear | Square root |

Model 26 [47] | V. parahaemolyticus | L. vannamei | Temp | Huang primary | Suboptimal Huang square root |

Model 27 [47] | V. parahaemolyticus | L. vannamei | Temp | No-lag | Suboptimal Huang square root |

Model 28 [49] | Vibrio spp. | NR Estuary | Temp and Sal | Net exponential | Net Vibrio growth rate |

^{1}V. vulnificus, V. furnissii and V. fluvialis,

^{2}Tryptone Soybean Yeast Extract Broth,

^{3}pathogenic,

^{4}nonpathogenic.

**Table 5.**The seven datasets used for model validation. AQC1 and AQC2 were previously unpublished; the other datasets are publicly available and can be accessed through the provided reference. Information for each dataset contains reported values (i.e., the number of entries in a dataset), values used for validation (i.e., the number of observations after the missing values were removed from the dataset), temperature, salinity, and pH range. Seven datasets used for model validation were classified into four habitat types based on the characteristics of the collection sites. Methods used for determining Vibrio spp. abundance are listed in Appendix C.1.

Dataset | Reported Values | Values for validation | Temperature Range (°C) | Salinity Range (ppt) | pH | Habitat TYPE | Collection Site |
---|---|---|---|---|---|---|---|

AQC1 [54] | 108 | 99 | 11.1–27.5 | 33.5–39.3 | 8.10–8.61 | Aquaculture | Adriatic Sea, Croatia |

AQC2 [55] | 88 | 81 | 7.86–25.23 | 24.9–38.2 | 7.56–8.49 | Aquaculture | Adriatic Sea, Croatia |

URB1 [56] | 213 | 149 | 22.4–31 | 7.98–34.74 | 7.51–8.27 | Urban Estuary | Ala Wai Canal in Honolulu, Hawaii |

URB2 [57] | 243 | 240 | 19.2–31.8 | 1.0–36.0 | / | Urban Estuary | Ala Wai Canal in Honolulu, Hawaii |

EST1 [58] | 249 | 223 | 3.1–31.7 | 0.09–18.56 | 6.57–9.17 | Estuary | Neuse River Estuary, North Carolina (USA) |

EST2 [59] | 133 | 127 | 2.16–25.89 | 9.32–31.86 | 6.82–8.41 | Estuary | Great Bay Estuary, New Hampshire (USA) |

COAST [60] | 117 | 72 | 8.9–29.4 | 12.0–40.0 | / | Coastal Area | Eastern North Carolina coast (USA) |

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## Share and Cite

**MDPI and ACS Style**

Purgar, M.; Kapetanović, D.; Geček, S.; Marn, N.; Haberle, I.; Hackenberger, B.K.; Gavrilović, A.; Pečar Ilić, J.; Hackenberger, D.K.; Djerdj, T.; Ćaleta, B.; Klanjscek, T. Investigating the Ability of Growth Models to Predict In Situ *Vibrio* spp. Abundances. *Microorganisms* **2022**, *10*, 1765.
https://doi.org/10.3390/microorganisms10091765

**AMA Style**

Purgar M, Kapetanović D, Geček S, Marn N, Haberle I, Hackenberger BK, Gavrilović A, Pečar Ilić J, Hackenberger DK, Djerdj T, Ćaleta B, Klanjscek T. Investigating the Ability of Growth Models to Predict In Situ *Vibrio* spp. Abundances. *Microorganisms*. 2022; 10(9):1765.
https://doi.org/10.3390/microorganisms10091765

**Chicago/Turabian Style**

Purgar, Marija, Damir Kapetanović, Sunčana Geček, Nina Marn, Ines Haberle, Branimir K. Hackenberger, Ana Gavrilović, Jadranka Pečar Ilić, Domagoj K. Hackenberger, Tamara Djerdj, Bruno Ćaleta, and Tin Klanjscek. 2022. "Investigating the Ability of Growth Models to Predict In Situ *Vibrio* spp. Abundances" *Microorganisms* 10, no. 9: 1765.
https://doi.org/10.3390/microorganisms10091765