### Abstract

Synchrony, synchronistic occurrence, has been studied in population dynamics, health science and in phenology. Moran (1953) first introduced the concept of synchrony between population dynamics and concomitant weather conditions using Canadian lynx data showing that the degree of synchrony decreases with increasing distance and since then, it has been studied in various areas of research. Although spatial synchrony, which considers similarity across locations and species, has been studied widely, temporal synchrony, which considers timing of events, has been studied mostly in phenology. In a recent study, Naylor et al. (2007) suggested the possible use of variations in the ratios of oxygen and carbon isotopes to determine age, growth and reproductive patterns in shells of Haliotis iris. They suggested that oxygen isotope profiles within shells reflected ambient water temperature at the time of shell precipitation, and that these (δ^{18}O and δ^{13}C) profiles could be used to determine age and growth patterns. Naylor et al. (2007) used two temperature series, ambient water temperature and isotopic temperature from shells. Their preliminary work indicated that two types of growth model, the von-Berterlanffy (VB) or the Gompertz (G) growth model were equally good in "mirroring" isotopic temperature. However, the G model was preferred to the VB model as it fitted better to tagging information data (Naylor et al. 2007).In this study, we look at the tracking indices of two temperature series, ambient water temperature and isotopic temperature of Naylor et al. (2007) to measure synchronicity. We show that temperature estimated from abalone shells using oxygen isotope profiles statistically track and/or synchronize with ambient water temperature. In terms of fitting isotopic temperature with ambient water temperature, one growth model, namely the von Berterlanffy (VB), fits significantly better than the G model. This is established using a block bootstrapping method to calculate the confidence interval of so the so-called tracking indices, that mirror synchrony. This work represents an improvement because the VB model and the G model, by their definition, give different biomass estimation for the future in terms of time and amount. The VB model will estimate smaller biomass than the G model, although the G model will take longer to build the available biomass, since it reaches the minimum legal size 2-6 years later than the VB model. By choosing the VB model over the G model, we are selecting a model where in a shell reaches the minimum legal size faster, although the biomass of the shell is not as heavy as the amount calculated via the G model. The impact on total biomass, in the future, via the VB and the G models was not examined in this study, and is future work. Tracking indices between two temperature series (isotopic - estimated shell temperature and ambient water temperature) were obtained for four shells: (a) between the two temperature series as they are, (b) between ambient water temperature and the kernel smoothed isotopic temperature; and (c) on the moving block bootstrapped series of isotopic temperature and ambient water temperature. The local bandwidth choice in Kernel regression showed the largest bandwidth of shell 3, which can be related to the smallest asymptotic length (L_{∞}=136.32 with VB) and slower growth rate (large K, K=0.38 with VB) and the smallest bandwidth of shell 2, which can be related to the largest asymptotic length (L_{∞}=181.84 with VB) and its fast growth rate to the minimum legal size (Naylor et al. 2007). At the minimum legal size, shell 3 will be 6.6 years old whereas shell 2 will only be 4.4 years old. Tracking indices showed that the shell and water temperature series are synchronizing and parallel; and that the VB growth model synchronizes significantly better for shells 1, 3, and 4. The G growth model synchronizes significantly better for shell 2 only. (Figure Presented).

Language | English |
---|---|

Title of host publication | MODSIM07 - Land, Water and Environmental Management |

Subtitle of host publication | Integrated Systems for Sustainability, Proceedings |

Pages | 511-517 |

Number of pages | 7 |

Publication status | Published - 1 Dec 2007 |

Event | International Congress on Modelling and Simulation - Land, Water and Environmental Management: Integrated Systems for Sustainability, MODSIM07 - Christchurch, New Zealand Duration: 10 Dec 2007 → 13 Dec 2007 |

### Other

Other | International Congress on Modelling and Simulation - Land, Water and Environmental Management: Integrated Systems for Sustainability, MODSIM07 |
---|---|

Country | New Zealand |

City | Christchurch |

Period | 10/12/07 → 13/12/07 |

### Keywords

- Bootstrapping
- Growth
- Kernel smoothing
- Synchrony
- Tracking index

### ASJC Scopus subject areas

- Renewable Energy, Sustainability and the Environment
- Water Science and Technology

### Cite this

*MODSIM07 - Land, Water and Environmental Management: Integrated Systems for Sustainability, Proceedings*(pp. 511-517)

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*MODSIM07 - Land, Water and Environmental Management: Integrated Systems for Sustainability, Proceedings.*pp. 511-517, International Congress on Modelling and Simulation - Land, Water and Environmental Management: Integrated Systems for Sustainability, MODSIM07, Christchurch, New Zealand, 10/12/07.

**Tracking indices as measures of synchronization of isotopic temperature of NZ abalone shells with ambient water temperature.** / Kim, Susan; Hudson, I. L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Tracking indices as measures of synchronization of isotopic temperature of NZ abalone shells with ambient water temperature

AU - Kim, Susan

AU - Hudson, I. L.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - Synchrony, synchronistic occurrence, has been studied in population dynamics, health science and in phenology. Moran (1953) first introduced the concept of synchrony between population dynamics and concomitant weather conditions using Canadian lynx data showing that the degree of synchrony decreases with increasing distance and since then, it has been studied in various areas of research. Although spatial synchrony, which considers similarity across locations and species, has been studied widely, temporal synchrony, which considers timing of events, has been studied mostly in phenology. In a recent study, Naylor et al. (2007) suggested the possible use of variations in the ratios of oxygen and carbon isotopes to determine age, growth and reproductive patterns in shells of Haliotis iris. They suggested that oxygen isotope profiles within shells reflected ambient water temperature at the time of shell precipitation, and that these (δ18O and δ13C) profiles could be used to determine age and growth patterns. Naylor et al. (2007) used two temperature series, ambient water temperature and isotopic temperature from shells. Their preliminary work indicated that two types of growth model, the von-Berterlanffy (VB) or the Gompertz (G) growth model were equally good in "mirroring" isotopic temperature. However, the G model was preferred to the VB model as it fitted better to tagging information data (Naylor et al. 2007).In this study, we look at the tracking indices of two temperature series, ambient water temperature and isotopic temperature of Naylor et al. (2007) to measure synchronicity. We show that temperature estimated from abalone shells using oxygen isotope profiles statistically track and/or synchronize with ambient water temperature. In terms of fitting isotopic temperature with ambient water temperature, one growth model, namely the von Berterlanffy (VB), fits significantly better than the G model. This is established using a block bootstrapping method to calculate the confidence interval of so the so-called tracking indices, that mirror synchrony. This work represents an improvement because the VB model and the G model, by their definition, give different biomass estimation for the future in terms of time and amount. The VB model will estimate smaller biomass than the G model, although the G model will take longer to build the available biomass, since it reaches the minimum legal size 2-6 years later than the VB model. By choosing the VB model over the G model, we are selecting a model where in a shell reaches the minimum legal size faster, although the biomass of the shell is not as heavy as the amount calculated via the G model. The impact on total biomass, in the future, via the VB and the G models was not examined in this study, and is future work. Tracking indices between two temperature series (isotopic - estimated shell temperature and ambient water temperature) were obtained for four shells: (a) between the two temperature series as they are, (b) between ambient water temperature and the kernel smoothed isotopic temperature; and (c) on the moving block bootstrapped series of isotopic temperature and ambient water temperature. The local bandwidth choice in Kernel regression showed the largest bandwidth of shell 3, which can be related to the smallest asymptotic length (L∞=136.32 with VB) and slower growth rate (large K, K=0.38 with VB) and the smallest bandwidth of shell 2, which can be related to the largest asymptotic length (L∞=181.84 with VB) and its fast growth rate to the minimum legal size (Naylor et al. 2007). At the minimum legal size, shell 3 will be 6.6 years old whereas shell 2 will only be 4.4 years old. Tracking indices showed that the shell and water temperature series are synchronizing and parallel; and that the VB growth model synchronizes significantly better for shells 1, 3, and 4. The G growth model synchronizes significantly better for shell 2 only. (Figure Presented).

AB - Synchrony, synchronistic occurrence, has been studied in population dynamics, health science and in phenology. Moran (1953) first introduced the concept of synchrony between population dynamics and concomitant weather conditions using Canadian lynx data showing that the degree of synchrony decreases with increasing distance and since then, it has been studied in various areas of research. Although spatial synchrony, which considers similarity across locations and species, has been studied widely, temporal synchrony, which considers timing of events, has been studied mostly in phenology. In a recent study, Naylor et al. (2007) suggested the possible use of variations in the ratios of oxygen and carbon isotopes to determine age, growth and reproductive patterns in shells of Haliotis iris. They suggested that oxygen isotope profiles within shells reflected ambient water temperature at the time of shell precipitation, and that these (δ18O and δ13C) profiles could be used to determine age and growth patterns. Naylor et al. (2007) used two temperature series, ambient water temperature and isotopic temperature from shells. Their preliminary work indicated that two types of growth model, the von-Berterlanffy (VB) or the Gompertz (G) growth model were equally good in "mirroring" isotopic temperature. However, the G model was preferred to the VB model as it fitted better to tagging information data (Naylor et al. 2007).In this study, we look at the tracking indices of two temperature series, ambient water temperature and isotopic temperature of Naylor et al. (2007) to measure synchronicity. We show that temperature estimated from abalone shells using oxygen isotope profiles statistically track and/or synchronize with ambient water temperature. In terms of fitting isotopic temperature with ambient water temperature, one growth model, namely the von Berterlanffy (VB), fits significantly better than the G model. This is established using a block bootstrapping method to calculate the confidence interval of so the so-called tracking indices, that mirror synchrony. This work represents an improvement because the VB model and the G model, by their definition, give different biomass estimation for the future in terms of time and amount. The VB model will estimate smaller biomass than the G model, although the G model will take longer to build the available biomass, since it reaches the minimum legal size 2-6 years later than the VB model. By choosing the VB model over the G model, we are selecting a model where in a shell reaches the minimum legal size faster, although the biomass of the shell is not as heavy as the amount calculated via the G model. The impact on total biomass, in the future, via the VB and the G models was not examined in this study, and is future work. Tracking indices between two temperature series (isotopic - estimated shell temperature and ambient water temperature) were obtained for four shells: (a) between the two temperature series as they are, (b) between ambient water temperature and the kernel smoothed isotopic temperature; and (c) on the moving block bootstrapped series of isotopic temperature and ambient water temperature. The local bandwidth choice in Kernel regression showed the largest bandwidth of shell 3, which can be related to the smallest asymptotic length (L∞=136.32 with VB) and slower growth rate (large K, K=0.38 with VB) and the smallest bandwidth of shell 2, which can be related to the largest asymptotic length (L∞=181.84 with VB) and its fast growth rate to the minimum legal size (Naylor et al. 2007). At the minimum legal size, shell 3 will be 6.6 years old whereas shell 2 will only be 4.4 years old. Tracking indices showed that the shell and water temperature series are synchronizing and parallel; and that the VB growth model synchronizes significantly better for shells 1, 3, and 4. The G growth model synchronizes significantly better for shell 2 only. (Figure Presented).

KW - Bootstrapping

KW - Growth

KW - Kernel smoothing

KW - Synchrony

KW - Tracking index

UR - http://www.scopus.com/inward/record.url?scp=80052939931&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780975840047

SP - 511

EP - 517

BT - MODSIM07 - Land, Water and Environmental Management

ER -