# Long-Term Changes in Four Populations of the Spiny Toad, Bufo spinosus, in Western France; Data from Road Mortalities

## Abstract

**:**

_{e}) transforms of annual counts as dependent variables against year as the independent variables. All coefficients showed no significant departure from the 0 hypothetical coefficients, indicative of population stability. This was supported by jackknife analysis, which showed good agreement of the pseudo-regression coefficients with the true equations. Stepwise regression of potential climate impacts on toad numbers suggested rainfall levels in October adjusted to 2- and 3-year lags were involved in driving population change. Road mortality counts were also made during 2020 and 2021 when human movement restrictions were in place due to the COVID-19 pandemic. To estimate the potential impact on this disturbance in the methodology, the Poisson distribution was used to estimate potential differences between what would have been expected counts and the observed counts. The results indicate that the observed mortalities were significantly lower than expected in all four populations.

## 1. Introduction

- (1)
- What are the general long-term population trends in the study area?
- (2)
- Are there differences in long-term numbers between populations?—here defined as subpopulations migrating to different breeding ponds.
- (3)
- To what extent do the populations fluctuate on an annual basis?
- (4)
- (5)
- What impact did the restrictions on human movement due to the COVID-19 pandemic have on road mortalities during 2020 and 2021?

## 2. Methods

#### 2.1. Study Area

#### 2.2. Protocol

#### 2.3. Statistical Analysis

_{e}) and years as the independent variable. This gives,

_{e}N = b + m × x ± ε

_{e}N represents road mortalities, x the year (2005 to 2019), m the regression coefficient and b the y-intercept with ε white noise error, which incorporates measurement error and random variation [24]. Due to a zero count for D25 in 2008, the dependent variable was treated as log

_{e}(N + 1). The null hypothesis is that log

_{e}N (or log

_{e}(N + 1)) is stable when m = 0; significant departures from m indicate population change with positive or negative regression coefficients representing population increase or decrease, respectively. Departures from the 0 regression coefficients were evaluated using t-tests at n-2 d.f. Tests for normality of the log

_{e}transformed annual counts were made using Anderson–Darling a

^{2}tests. This gave results from a

^{2}= 0.18 to 0.39 and P values from 0.33 to 0.89; hence, all data were normalised before analysis. The Pearson product moment correlation coefficient was used to compare for similarities in monthly counts.

^{2}

_{1}… = … δ

^{2}

_{k}. ANOVA was then used to test for differences in mean SVLs between populations, with the null hypothesis the means are homogenous. Post hoc tests were conducted with Tukey HSD. Leven’s test was also used to test for monthly presence with a null hypothesis of equality of months. Long-term interpopulation correlation of trends between species were assessed with the Pearson correlation coefficient at α = 0.05. To compare the presence of large (≥80 mm SVL) mortalities during the main migration months of October, November and December with their frequencies during January to September, a two-tail z-proportion test was applied at α = 0.05.

_{bufo}= b + m

_{1}x

_{1}+ m

_{2}x

_{2}+ m

_{3}x

_{3}……

_{1}, m

_{2}and m

_{3}… are regression coefficients and x

_{1}, x

_{2}and x

_{3}… the variables that had a significant influence on changes in N

_{bufo}. Independent variable selection is arbitrary, but the method is practical when the number of candidate variables is not large [24].

^{x}× e

^{−λ}/x!

## 3. Results

#### 3.1. Total and Regional Counts

#### 3.2. Monthly Counts

^{2}goodness-of-fit test with a null hypothesis of equality of month presence (expected = 102.1 toads) versus observed monthly numbers indicated a significant departure from the null model, χ

^{2}= 922.6 and P < 0.0001. The Pearson correlation coefficient showed strong monthly correlations between populations, r-values from 0.84 to 0.99 and p-values from 0.001 to 0.0001.

#### 3.3. Frequency of Large Females

#### 3.4. Annual Differences in SVL between Populations

#### 3.5. Long-Term Annual Counts

#### 3.6. Rainfall, Temperature and Annual Counts

_{bufo}= 207 − 5.66 × rain Oct

_{lag2}− 12.3 × rain Oct

_{lag3}

_{bufo}is B. spinosus annual counts. These results suggest that rainfall during October lagged to two and three years previous that from the year of annual counts, which is the beginning of the main migratory movement to breeding sites and may be involved as a key population driver.

#### 3.7. Mortalities during 2020 and 2021

## 4. Discussion

#### 4.1. General Considerations

#### 4.2. Comparisons with Sympatric Amphibians

#### 4.3. Rainfall and Temperature

#### 4.4. Impact of Lockdown Restrictions

#### 4.5. Concluding Remarks

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Map of the general study area with ponds shown in Figure 3 identified.

**Figure 3.**Examples of toad breeding ponds in the study area labelled with road numbers where mortalities from crossings were found.

**Figure 4.**Monthly counts for all populations. Black bars indicate D949/ D764 area, grey D60, forward hatched D25 area and backward hatched D44/D127. The broken line indicates expected frequencies under a null hypothesis of equality of monthly counts. See text for other details.

**Figure 5.**Box plots of SVL distributions of the four populations. Gray boxes indicate central 50% of the samples, the horizontal line and triangle within the box indicate the medians and means, respectively. The bottom of the boxes are situated at the first quartile (Q1) and the top the third quartile (Q3). The vertical lines are the normal ranges and the circles are outliers, unusually large or small values. See text for further details.

**Figure 6.**(

**A**) Histograms showing mortality counts from 2005 to 2021 for all four areas. Solid bars represent large females (≥80 mm SVL), gray bars smaller individuals (either sex) and scaled bars represent estimates derived from the Poisson distribution for 2021 and 2022. Note differences of scale between the y-axes. (

**B**) Pooled histograms from all four regions. Black bars represent D949/D764, backward cross-hatched bars D44/D127, gray bars D60 and forward-hatched bars D25. Dotted lines were calculated from the regression equations for each population given in Table 2. See text for further details.

D949/D746 | D44/D127 | D60 | D25 | |
---|---|---|---|---|

Means | 83.7 ± 20.2 | 71.3 ± 73.8 | 66.9 ± 22.2 | 77.3 ± 23.1 |

Skewness | −0.07 | 0.24 | 0.47 | −0.08 |

n | 187 | 347 | 386 | 359 |

**Table 2.**Regression coefficients (m) relating annual mortalities between 2005 and 2019 along with results of the Jackknife analysis (mJK). For m, the ±values are standard errors of the coefficients and the t-tests against the 0 regression coefficients. When m was positive, numbers were generally increasing; when m was negative, numbers were decreasing. The latter was only found for D949/D764, but the result was not significant. For the Jackknife results, means and standard errors are the mean values of the 15-year pseudoregression coefficients with their standard deviation. Right column identifies years when influence functions were detected, indicating unexpected low (L) or high numbers (H) given current trends at the time. All t-tests were set at n − 2 years (15 − 2 = 13 years). See text for further details.

Area | m | ±SE | t | P | Mean JK m | Mean JK Std Error | P | Influence Function |
---|---|---|---|---|---|---|---|---|

D949/D764 | −0.07 | 0.04 | 1.58 | 0.14 | −0.07 | 0.046 | 0.14 | 2007 (L) |

D44/D127 | 0.05 | 0.04 | 1.41 | 0.18 | 0.03 | 0.055 | 0.20 | 2015 (L) |

D60 | 0.15 | 0.03 | 4.84 | <0.0001 | 0.15 | 0.031 | <0.0001 | 2010 (H) |

D25 | 0.23 | 0.04 | 6.20 | <0.0001 | 0.22 | 0.039 | <0.0001 | 2008 (L) |

**Table 3.**Poisson probabilities that road mortality counts during 2020 and 2021 are a true measure of expected mortalities P (λ = x). The rate parameters (λ) are derived from the mean values of the long-term annual counts (15 years) and the random variable x from the observed numbers in each area during 2020 and 2021. The likelihood that the true counts were greater than the rate parameters (x > λ) ranged from 84–100% during 2020 and greater than 99% for 2021.

2 | λRate Parameter | xRandom Variable | P (λ = x) | P (x > λ) |

D949/764 | 12 | 1 | <1% | >99.9% |

D44/127 | 15 | 5 | <1% | >99.9% |

D60 | 24 | 8 | <1% | >99.9% |

D25 | 22 | 15 | 0.03% | 92.3% |

2020 total n | 29 | |||

λRate Parameter | xRandom Variable | P (λ = x) | P (x > λ) | |

D949/764 | 12 | 1 | <1% | >99.9% |

D44/127 | 15 | 4 | <1% | >99.9% |

D60 | 24 | 5 | <1% | >99.9% |

D25 | 22 | 11 | 0.004% | >99.9% |

2021 total n | 21 |

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**MDPI and ACS Style**

Meek, R.
Long-Term Changes in Four Populations of the Spiny Toad, *Bufo spinosus*, in Western France; Data from Road Mortalities. *Conservation* **2022**, *2*, 248-261.
https://doi.org/10.3390/conservation2020017

**AMA Style**

Meek R.
Long-Term Changes in Four Populations of the Spiny Toad, *Bufo spinosus*, in Western France; Data from Road Mortalities. *Conservation*. 2022; 2(2):248-261.
https://doi.org/10.3390/conservation2020017

**Chicago/Turabian Style**

Meek, Roger.
2022. "Long-Term Changes in Four Populations of the Spiny Toad, *Bufo spinosus*, in Western France; Data from Road Mortalities" *Conservation* 2, no. 2: 248-261.
https://doi.org/10.3390/conservation2020017