# A Law of Word Meaning in Dolphin Whistle Types

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^{2}

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## Abstract

**:**

## 1. Introduction

^{−α}

## 2. Do Dolphin Whistle Types Have “Meaning”?

No. | Description |
---|---|

1 | Vocalizer aggresses or is aggressed by another adult dolphin |

2 | Vocalizer disciplines or is disciplined by another dolphin |

3 | Vocalizer affiliates with another dolphin, often rubbing or contact position |

4 | Vocalizer involved in sociosexual behavior with another dolphin involving genitals, intromission attempts, etc. |

5 | Vocalizer socially plays with another dolphin (e.g., play chases, etc.) |

6 | Vocalizer approaches or is approached by a dolphin other than its mother or infant |

7 | Vocalizer approaches or is approached by its mother |

8 | Vocalizer departs or is departed by a dolphin other than its mother or infant |

9 | Vocalizer departs or is departed by its mother |

10 | Vocalizer swimming with a dolphin other than its mother or infant (no apparent affiliation or aggression) |

11 | Vocalizer is swimming with its mother |

12 | Vocalizer swims alone |

13 | Vocalizer plays with an object (e.g., fish, toy) |

14 | Vocalizer orients to hydrophone |

15 | Vocalizer orients to orcas in another pool separated by a gate |

**Table 2.**Summary of correlations and anticorrelations between whistle types and behavioral contexts at the three levels, i.e., all individuals, age group and individual, at a significance level of 0.05. ID is the tag identifying an individual dolphin. Within the main column “Number of type-context pairs”, the column “All” is the number of possible type-context pairs (i.e., the product between the values of column “Whistle types” and “Contexts”). “All” is the sum of the values in the columns “Positively correlated”, “Negatively correlated” and “Uncorrelated”. The values in the column “Positively correlated” cannot exceed the corresponding values in column “Occurring at least once”.

Number of type-context pairs | ||||||||
---|---|---|---|---|---|---|---|---|

Level | ID | Whistle types | Contexts | All | Positively correlated | Negatively correlated | Uncorrelated | Occurring at least once |

All | - | 116 | 15 | 1,740 | 51 | 7 | 1,682 | 260 |

Adults | - | 26 | 15 | 390 | 17 | 2 | 371 | 91 |

BAY | 10 | 4 | 40 | 4 | 0 | 36 | 15 | |

CHE | 11 | 8 | 88 | 3 | 2 | 83 | 26 | |

CIR | 2 | 1 | 2 | 0 | 0 | 2 | 2 | |

GOR | 6 | 1 | 6 | 0 | 0 | 6 | 6 | |

SAD | 12 | 8 | 96 | 7 | 2 | 88 | 29 | |

SCH | 4 | 4 | 16 | 1 | 1 | 14 | 6 | |

STO | 11 | 9 | 99 | 5 | 0 | 94 | 27 | |

TER | 7 | 3 | 21 | 0 | 0 | 21 | 8 | |

Infants | - | 98 | 13 | 1,274 | 38 | 9 | 1,227 | 198 |

DEL | 15 | 10 | 150 | 3 | 1 | 146 | 33 | |

DES | 3 | 1 | 3 | 0 | 0 | 3 | 3 | |

ECB | 5 | 1 | 5 | 0 | 0 | 5 | 5 | |

LIB | 31 | 1 | 341 | 18 | 2 | 321 | 65 | |

NEP | 9 | 5 | 45 | 2 | 0 | 43 | 21 | |

NOR | 39 | 13 | 507 | 12 | 3 | 492 | 76 | |

PAN | 39 | 10 | 390 | 13 | 3 | 374 | 67 | |

SAM | 4 | 2 | 8 | 0 | 0 | 8 | 6 | |

TAS | 9 | 4 | 36 | 1 | 0 | 35 | 14 |

- Positive correlation: a whistle type tending to appear more often in certain behavioral contexts.
- Negative correlation (or anticorrelation): a whistle type tending to not appear in certain other contexts.

- Significantly high (positive correlation).
- Significantly low (negative correlation or anticorrelation).

- Individual (a single dolphin).
- Individuals from the same age group (infant or adult).
- All individuals (both infant and adult dolphins).

## 3. Consistency on the Context of Use of Whistle Types

**Table 3.**Frequency table of the support of positively correlated type-context pairs within each level at a significance level of 0.05. The units of support are individuals and the units of frequency are positively correlated type-context pairs. The p-value is the estimated probability of obtaining the same value of “Frequency” by “selecting” type-context pairs at random and independently from other dolphins.

Positively correlated type-context pairs | ||||||
---|---|---|---|---|---|---|

All | Adults | Infants | ||||

Support | Frequency | p-value | Frequency | p-value | Frequency | p-value |

1 | 59 | 0.99 | 20 | 0.68 | 42 | 0.99 |

2 | 3 | 0.097 | 0 | 1 | 2 | 0.14 |

3 | 0 | 1 | 0 | 1 | 1 | 0.0042 |

4 | 1 | 6.9 × 10^{-5} | 0 | 1 | 0 | 1 |

**Table 4.**Frequency table of the support of negatively correlated type-context pairs within each level at a significance level of 0.05. The units of support are individuals and the units of frequency are negatively correlated type-context pairs. The p-value is the estimated probability of obtaining the same value of “Frequency” by “selecting” type-context pairs at random and independently from other dolphins (see the Materials & Methods section).

Negatively correlated type-context pairs | ||||||
---|---|---|---|---|---|---|

All | Adults | Infants | ||||

Support | Frequency | p-value | Frequency | p-value | Frequency | p-value |

1 | 10 | 0.99 | 5 | 0.979499 | 7 | 0.99 |

2 | 2 | 0.00074 | 0 | 1 | 1 | 0.023 |

## 4. Dolphin Whistle Types Obey a Law of Word Meaning

**Table 5.**Summary of the correlation between whistle type frequency and number of positively correlated behavioral contexts. ID is the tag identifying an individual dolphin and N is the number of points on which the Pearson correlation r was calculated.

Level | ID | N | Pearson r | p-value |
---|---|---|---|---|

All | - | 46 | 0.730 | 0.0015 |

Adult | - | 14 | 0.593 | 0.0055 |

SAD | 6 | 0.990 | <10^{-5} | |

Infant | - | 35 | 0.947 | <10^{-5} |

LIB | 16 | 0.996 | 0.0083 | |

NOR | 11 | 0.478 | 0.097 | |

PAN | 11 | 0.760 | 0.091 |

## 5. Discussion

_{1}, p

_{2},…p

_{n}is [23]:

_{i}, i.e., H = E[-log p

_{i}]. If according to standard information theory H is a measure of information [23], then it follows from H = E[-log p

_{i}] that H is indeed an average measure of information and –log p

_{i}is the information of the i-th symbol. In general, if a symbol has frequency p then its information is –log p. Thus, the information of a symbol decreases as its probability (or relative frequency) increases. Consistently, the higher the semantic or contextual degree of a certain item (e.g., a word or a whistle type), the less informative it is, i.e., the lower its information. Besides, this inverse relationship has implications for the scope of information theoretic models of Zipf’s law [24,25,26] departing from the assumption that the frequency of a signal (e.g., a word) is positively correlated with its number of semantic associations (e.g., its semantic degree of its contextual degree). Our findings indicate that this assumption is not only valid for human language but also for dolphins whistle types.

- 1.
- Whistle production depends on the context.
- 2.
- Coordination between individuals (dolphins share the context in which a certain whistle type tends to be or not be produced).
- 3.
- Agreement with a law of word meaning (the positive correlation between the frequency of a whistle type and its contextual degree).

- What are really the faces of the die?
- How a combination of faces yields a “distinctive” signal?
- Is it realistic that the faces are statistically independent?
- Why should they be statistically independent?
- …

## 6. Conclusions

## 7. Materials and Methods

^{4}in our case). This probability p is the p-value shown in Table 3 and Table 4.

^{8}uniformly distributed permutations. This kind of test has the benefit of preserving the distributions of the two variables involved. We chose the Pearson correlation statistic for simplicity. Notice that the use of a Monte Carlo technique frees us from the constraints the parametric Pearson correlation test [34]. Although a Spearman rank correlation test might be considered more convenient a priori (estimating p-values through permutations as in the Pearson correlation test), it was excluded because it gives less statistically significant correlations between frequency and contextual degree than the Pearson correlation test. Table 6 shows a comparison of the results obtained with the two statistics. In particular, the Spearman rank correlation fails to find a significant correlation for the dolphin SAD. The best statistic is the one that allows one to reject the null hypothesis that there is no positive correlation between frequency and contextual degree in as many cases as possible. For this reason, Table 5 shows only the results with the best statistic, i.e., Pearson correlation, between the two that we tried.

**Table 6.**Summary of the correlation between whistle type frequency and number of positively correlated behavioral contexts. ID is the tag identifying an individual dolphin and N is the number of points on which the Pearson correlation r and the Spearman ρ were calculated.

Level | ID | N | Pearson r | p-value | Spearman ρ | p-value |
---|---|---|---|---|---|---|

All | - | 46 | 0.730 | 0.0015 | 0.470 | 0.0016 |

Adult | - | 14 | 0.593 | 0.0055 | 0.651 | 0.0082 |

SAD | 6 | 0.990 | <10^{-5} | 0.655 | 0.17 | |

Infant | - | 35 | 0.947 | <10^{-5} | 0.426 | 0.00084 |

LIB | 16 | 0.996 | 0.0083 | 0.615 | <10^{-5} | |

NOR | 11 | 0.478 | 0.097 | 0.403 | 0.091 | |

PAN | 11 | 0.760 | 0.091 | 0.512 | 0.091 |

## Acknowledgements

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Ferrer-i-Cancho, R.; McCowan, B.
A Law of Word Meaning in Dolphin Whistle Types. *Entropy* **2009**, *11*, 688-701.
https://doi.org/10.3390/e11040688

**AMA Style**

Ferrer-i-Cancho R, McCowan B.
A Law of Word Meaning in Dolphin Whistle Types. *Entropy*. 2009; 11(4):688-701.
https://doi.org/10.3390/e11040688

**Chicago/Turabian Style**

Ferrer-i-Cancho, Ramon, and Brenda McCowan.
2009. "A Law of Word Meaning in Dolphin Whistle Types" *Entropy* 11, no. 4: 688-701.
https://doi.org/10.3390/e11040688