In

The nummulitid foraminifer

Reproduction biology of

Growth of

Apart from quantification of growth (

Based on the published laboratory investigations, mean chamber building rates (CBR) were estimated to study time-dependence (

For studying population dynamics of larger benthic foraminifera, factors like the timing of reproduction, maximum life expectancy and growth rates are important to investigate the effects of seasonal and instantaneous environmental fluctuations on cell growth. As stated by

For the study of reproduction timing, growth and life expectancy of LBF under natural conditions, the ‘natural laboratory’ (

In this study, the ‘natural laboratory’ approach will be applied on

The sample sites for this study were located in the Northwest and South of Sesoko-Jima, Okinawa, Japan (

Location of stations where samples were taken between April 23, 2014 and August 14, 2015.

Main grain size and sample weight were not taken, since specimens were picked from reef rubble. Because

A. | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Sample | Date | Longitude | Latitude | Depth | Temperature | Salinity | pH | Sediment | Number of individuals | |

Main grain size | Weight in g | Gamonts / schizonts | ||||||||

1 | 23.04.2014 | 127°51.388′ | 26°40.086′ | 56 | 22,7 | 33,2 | coarse sand | 714,6 | 0 | |

2 | 02.05.2014 | 127°52.243′ | 26°37.126′ | 46 | 22,3 | 28,6 | fine sand / silt | 381,8 | 5 | |

3 | 09.05.2014 | 127°51.331′ | 26°40.039′ | 50 | 21,8 | 30,5 | 7,9 | coarse sand | 1183 | 49 |

4 | 30.05.2014 | 127°51.5160′ | 26°40.220′ | 54 | 23,3 | 31,9 | 7,9 | coarse sand | 216,2 | 11 |

5 | 18.07.2014 | 127°51.5324′ | 26°40.4240′ | 57,5 | 23,6 | 33,4 | 8,0 | coarse sand | 999 | 0 |

6 | 19.08.2014 | 127°51.4673′ | 26°40.4231′ | 56 | 26,2 | 32,2 | coarse sand | 349,5 | 18 | |

7 | 10.09.2014 | 127°51.5281′ | 26°40.2410′ | 54 | 27,2 | 31,1 | coarse sand | 797,2 | 14 | |

8 | 03.10.2014 | 127°52.2624′ | 26°37.4250′ | 41 | 26,9 | 30,1 | fine sand / silt | 1376,8 | 8 | |

9 | 10.11.2014 | 127°51.4629′ | 26°37.3511′ | 41 | 24,7 | 30,4 | coarse sand | 1572,8 | 21 | |

10 | 11.12.2014 | 127°51.517′ | 26°40.218′ | 47 | 23,5 | 30,8 | coarse sand | 515,1 | 16 | |

11 | 16.01.2015 | 127°51.5101′ | 26°40.2142′ | 53,7 | 21,0 | 31,4 | coarse sand | 309,3 | 32 | |

12 | 13.02.2015 | 127°51.5076′ | 26°40.1711′ | 57 | 20,1 | 31,7 | coarse sand | 488,4 | 12 | |

13 | 04.03.2015 | 127°51.4727′ | 26°40.2670′ | 57 | 22,0 | 30,7 | coarse sand | 1055,4 | 6 | |

14 | 15.04.2015 | 127°51.4540′ | 26°40.2362′ | 58 | 23,5 | 30,8 | 8,3 | coarse sand | 505,6 | 32 |

15 | 18.05.2015 | 127°51.5099′ | 26°40.2756′ | 55 | 22,9 | 31,3 | 8,0 | coarse sand | 267,1 | 11 |

16 | 11.06.2015 | 127°51.6201′ | 26°40.3148′ | 56,5 | 24,0 | 30,6 | coarse sand | 573,5 | 16 | |

17 | 14.07.2015 | 127°51.5144′ | 26°40.1600′ | 50 | 27,4 | 29,9 | coarse sand | 229,1 | 42 |

B. | ||||||||
---|---|---|---|---|---|---|---|---|

Sample | Date | Longitude | Latitude | Depth | Temperature | Salinity | pH | Number of individuals |

Gamonts / Schizonts | ||||||||

1 | 02.05.2014 | 26°37.2000′ | 127°51.6350′ | 21 | 22,3 | 35,2 | 41 | |

2 | 09.05.2014 | 26°39.7060′ | 127°52.2930′ | 25 | 21,9 | 35,1 | 36 | |

3 | 30.05.2014 | 26°39.9089′ | 127°52.1564′ | 21 | 23,0 | 35,2 | 7,9 | 21 |

4 | 18.07.2014 | 26°39.9362′ | 127°52.1641′ | 25 | 26,0 | 31,1 | 8,1 | 21 |

5 | 19.08.2014 | 26°39.9351′ | 127°52.1659′ | 26 | 28,0 | 30,9 | 7,9 | 41 |

6 | 10.09.2014 | 26°39.9091′ | 127°52.1580′ | 27 | 28,2 | 30,4 | 8,1 | 37 |

7 | 20.10.2014 | 26°39.9080′ | 127°52.1612′ | 23,5 | 25,6 | 30,3 | 8,1 | 55 |

8 | 10.11.2014 | 26°37.4079′ | 127°51.5399′ | 22,7 | 24,8 | 30,5 | 11 | |

9 | 11.12.2014 | 26°39.9008′ | 127°52.1523′ | 21,5 | 23,3 | 30,7 | 36 | |

10 | 16.01.2014 | 26°37.4598′ | 127°51.8458′ | 22 | 20,9 | 31,4 | 7 | |

11 | 13.02.2015 | 26°37.4445 | 127°51.8420 | 21,7 | 20,1 | 31,4 | 15 | |

12 | 04.03.2015 | 26°37.4597′ | 127°51.8360′ | 23 | 21,8 | 30,6 | 52 | |

13 | 15.04.2015 | 26°37.4950′ | 127°51.8422′ | 21 | 23,3 | 30,7 | 16 | |

14 | 18.05.2015 | 26°39.9471′ | 127°52.1600′ | 27 | 23,2 | 31,1 | 15 | |

15 | 11.06.2015 | 26°39.9430′ | 127°52.1642′ | 25,3 | 25,5 | 30,3 | 47 | |

16 | 14.07.2015 | 26°39.9160′ | 127°52.1652′ | 21 | 27,8 | 29,5 | 52 |

Samples, including environmental parameters (temperature and salinity) were taken between April 23, 2014 and July 17, 2015 in seventeen consecutive monthly samplings following the methods of

Four samples at each sampling depth (20 and 50 m) were scooped from the uppermost centimetres of sediment using plastic boxes. Fine sediment (silt and mud) was decanted from 50 m samples and the coarser fractions containing the living LBF were moved into shallow boxes. Samples from 20 m mainly contained coral rubble. Here, easily visible specimens were picked using feather steel forceps. The remaining foraminifera were brushed from the rubble into shallow boxes using a soft brush. All samples rested for a period of 24 h, after which living specimens are easily recognizable by their coloured protoplasm due to the symbionts spread into the final chambers. A small part of the picked living specimens were selected for growth investigations under laboratory conditions. The tests of the remaining population, as well as sediment samples, were washed with fresh water and dried. For a more detailed description of sampling and sample processing refer to

All specimens of

In this study, only megalopsheres (gamonts and schizonts) have been investigated because microspheres didn’t occur frequently enough to analyse their growth by frequency distributions. To infer the chamber building rate (CBR) and test diameter increase rate (DIR) from the sampled populations, the ‘natural laboratory’ approach (

The chamber number (NoC) is counted including nepiont (proloculus and deuteroloculus), while the maximal test diameter (TD) is measured through the centre of the proloculus. NoCs are processed as natural numbers, while TDs are transformed using the natural logarithm due to the nonlinear (logarithmic) test growth.

Chamber number and test diameter of the seventeen samples were illustrated as frequency diagrams using identical intervals along the abscissa. The illustration using densities (frequency per sediment weight) for 50 m samples as done in

Since distribution parameters mean (

Initially, the frequency distribution of each sample has been checked for normality by Chi-square goodness-of-fit test. If samples significantly deviate from normal distributions, they have been decomposed into normally distributed components using nonlinear regression based on numerical mathematics (IBM SPSS 22).

The maximum NoC or TD at time

The normalized standard deviation

By illustrating the components as a function of time within the time interval of 15 months (May 2014 to July 2015), four megalospheric generations, maximum two per year, were identified. These two generations increase continuously through the investigation period with the same growth trend but with different onsets. The onset of one generation is the temporal interval before the date of the components with the lowest estimated maximum _{j}. This onset is characterized by chamber numbers of _{j1} = 2 and _{j2} = 3 as observed by _{j1} = 293.7 µm and _{j2} = 346.5 µm for 20 meters’ populations and _{j1} = 296.4 µm and _{j2} = 347.6 µm for 50 meters’ population.

Subsequent, the CBR was estimated using

where _{jmax} represents the growth asymptote (e.g., maximal possible chamber number or test diameter) and _{j} the _{jmax}∕2 is reached.

where _{j} and _{j} are function constants, _{j0} the nepiontic diameter and _{jmax} the maximal diameter. The duration of the onset for the CBR has been estimated using an iterative process, where the onset has been initially fitted with 10 days and increased up to 70 days in 5-day steps. Adjacent, the fit of the estimated function calculated using _{j}-values was tested by a reduced Chi-square goodness-of-fit test. The interval with the best Chi-square scores has been again tested with day-wise steps to find the exact length of onset. The onset with the best fit to the experimental data has been used to estimate the parameters of the Michaelis–Menten function _{jmax} and _{j,}which are used in the succeeding analysis. The same length of onset time has been applied for the DIR.

Parameters _{j}_{max} and _{j} of the first generation, which exhibits the higher _{jmax} values have been used to estimate the birthdate _{0} of each specimen _{j} defines the birthdate estimated by

Birthdates of all analyzed specimens are illustrated as frequency diagrams with monthly intervals. For samples from 50 m water depth simple counts of densities (count = 1) are biased by differing sample size of. Hence, a transformation of counts of densities (count*) per specimen

No volume measurements of reef rubble were acquired for samples from 20 m, therefore simple counts had to be used for frequency distributions.

Lomb periodograms (

The estimation of longevity have not been calculated in accordance to

More complex statistical investigations (e.g., numerical mathematical decomposition and/or fitting of the Michaelis–Menten functions) have been done using IBM SPSS Statistics 22 and Past 3.02 (

The 422 megalospheric specimens of ^{2}

On the contrary, the 377 megalospheric specimens sampled at ∼50 m water depth, which mostly consist of gamonts, show highly significant correlation between NoC and TD with relatively high ^{2}

Correlation between chamber number and the logarithm of the test diameter at the sampling sites used for the ‘natural laboratory’ at 20 m tested for significance (high correlation is present in sample 19.08.2014, 10.09.2014, 11.12.2014, 14.07.2014) and testing normal distribution of chamber number and the logarithm of test diameter by chi-square tests.

20 m | |||||||
---|---|---|---|---|---|---|---|

Date | Correlation | Chamber number | Test diameter | ||||

^{2} |
^{2} |
^{2} |
|||||

02.05.2014 | 41 | 0,06 | 0,111 | 39,90 | 3,30E–06 | 1318,73 | 1,38E–278 |

30.05.2014 | 25 | 0,02 | 0,524 | 57,20 | 2,04E–09 | 13,90 | 0,036 |

18.07.2014 | 21 | 0,00 | 0,822 | 21,53 | 0,004 | 33,85 | 3,82E–05 |

19.08.2014 | 41 | 0,45 | 1,43E–06 | 147,03 | 1,73E–27 | 26,86 | 0,001 |

10.09.2014 | 37 | 0,14 | 0,021 | 23,23 | 0,002 | 11,89 | 0,058 |

20.10.2014 | 55 | 0,05 | 0,117 | 19,38 | 0,008 | 21,42 | 0,004 |

11.12.2014 | 36 | 0,23 | 0,003 | 18,89 | 0,009 | 23,16 | 0,002 |

13.02.2015 | 15 | 0,19 | 0,100 | 132,54 | 1,69E–24 | 20,10 | 0,006 |

03.03.2015 | 52 | 0,00 | 0,860 | 16,66 | 0,017 | 48,48 | 8,94E–08 |

11.06.2015 | 47 | 0,08 | 0,054 | 48,77 | 7,91E–08 | 11,82 | 0,058 |

14.07.2014 | 52 | 0,74 | 2,59E–16 | 25,00 | 0,001 | 16,72 | 0,017 |

F | p(same slope) | ||||||

13,39 | 2,62E–20 |

Correlation between chamber number and the logarithm of the test diameter at the used for the ‘natural laboratory’ at 50% m sampling sites tested for significance (high correlation is present in sample 9.05.2015) and testing normal distribution of chamber number and the logarithm of test diameter by chi-square tests.

50 m | |||||||
---|---|---|---|---|---|---|---|

Date | Correlation | Chamber number | Test diameter | ||||

^{2} |
^{2} |
^{2} |
|||||

09.05.2014 | 49 | 0,13 | 0,019 | 125,87 | 3,96E–23 | 27,68 | 4,13E–04 |

30.05.2014 | 11 | 0,73 | 0,008 | 51,64 | 2,30E–08 | 33,01 | 5,34E–05 |

19.08.2014 | 18 | 0,83 | 1,63E–07 | 26,74 | 3,10E–04 | 243,38 | 1,21E–47 |

10.09.2014 | 14 | 0,62 | 0,001 | 52,15 | 1,85E–08 | 30,26 | 1,55E–04 |

10.11.2014 | 21 | 0,68 | 3,72E–06 | 50,00 | 4,66E–08 | 287,13 | 6,82E–57 |

11.12.2014 | 16 | 0,62 | 3,08E–04 | 41,18 | 1,94E–06 | 287,13 | 6,82E–57 |

16.01.2015 | 32 | 0,88 | 1,57E–15 | 28,37 | 3,19E–04 | 35,80 | 1,76E–05 |

13.02.2015 | 12 | 0,77 | 1,60E–04 | 29,24 | 2,30E–04 | 38,54 | 5,77E–06 |

15.04.2015 | 32 | 0,68 | 8,15E–09 | 49,74 | 5,21E–08 | 48,83 | 7,71E–08 |

18.05.2015 | 11 | 0,61 | 0,004 | 30,19 | 1,60E–04 | 5,20 | 0,091 |

11.06.2015 | 16 | 0,82 | 1,18E–06 | 43,34 | 7,89E–07 | 40,12 | 3,02E–06 |

14.07.2014 | 42 | 0,83 | 4,39E–17 | 23,66 | 0,002 | 24,02 | 0,002 |

F | p(same slope) | ||||||

2,2 | 0,014 |

Samples with a specimen number less than 10 have not been included in the ‘natural laboratory’.

Within the frequency distributions of the investigated months up to three components can be differentiated (_{j} (standard deviation) and

Decomposition of frequency distributions into normal-distributed components based on chamber number at 20 m water depth. Histograms are standardized to 50 specimens. (A) Sample May 2014; (B) Sample June 2014; (C) Sample July 2014; (D) Sample August 2014; (E) Sample September 2014; (F) Sample October 2014; (G) Sample December 2014; (H) Sample February 2015; (I) Sample March 2015; (J) Sample June 2015; (K) Sample July 2015.

Decomposition of frequency distributions into normal-distributed components based on test diameter at 20 m water depth. Histograms are standardized to 50 specimens. (A) Sample May 2014; (B) Sample June 2014; (C) Sample July 2014; (D) Sample August 2014; (E) Sample September 2014; (F) Sample October 2014; (G) Sample December 2014; (H) Sample February 2015; (I) Sample March 2015; (J) Sample June 2015; (K) Sample July 2015.

Decomposition of frequency distributions into normal-distributed components based on chamber number at 20 m water depth. Histograms are standardized to 50 specimens. (A) Sample May 2014; (B) Sample June 2014; (C) Sample August 2014; (D) Sample September 2014; (E) Sample November 2014; (F) Sample December 2014; (G) Sample January 2015; (H) Sample February 2015; (I) Sample April 2015; (J) Sample May 2015; (K) Sample June 2015; (L) Sample July 2015.

Four different generations of megalospheric

Fitting _{jt} (

Decomposition of frequency distributions into normal-distributed components based on test diameter at 20 m water depth. Histograms are standardized to 50 specimens. (A) Sample May 2014; (B) Sample June 2014; (C) Sample August 2014; (D) Sample September 2014; (E) Sample November 2014; (F) Sample December 2014; (G) Sample January 2015; (H) Sample February 2015; (I) Sample April 2015; (J) Sample May 2015; (K) Sample June 2015; (L) Sample July 2015.

Component parameters density, mean and standard deviation related to the sampling time during the investigation period for NoC and TD at 20 m.

Component 1 | Component 2 | |||||
---|---|---|---|---|---|---|

Density | Mean | s.d. | Density | Mean | s.d. | |

02.05.2014 | 8 | 54.6 | 9.79 | 2 | 33.2 | 2.54 |

30.05.2014 | 7 | 56.3 | 7.85 | 1 | 39.5 | 3.25 |

18.07.2014 | 7 | 52.4 | 4.53 | 4 | 37.3 | 4.64 |

19.08.2014 | 4 | 52.0 | 8.91 | 11 | 40.8 | 7.38 |

10.09.2014 | 7 | 50.8 | 5.35 | 11 | 36.6 | 6.07 |

20.10.2014 | 13 | 31.0 | 3.86 | 11 | 50.8 | 3.32 |

11.12.2014 | 8 | 30.6 | 3.82 | 11 | 45.4 | 3.35 |

13.02.2015 | 5 | 46.5 | 5.79 | 1 | 54.1 | 6.02 |

03.03.2015 | 7 | 40.9 | 5.09 | 13 | 53.4 | 6.17 |

11.06.2015 | 11 | 48.5 | 6.05 | 7 | 29.1 | 6.46 |

14.07.2015 | 11 | 48.0 | 5.98 | 8 | 30.3 | 6.46 |

02.05.2014 | 9 | 1049.7 | 43.14 | 16 | 2697.8 | 519.57 |

30.05.2014 | 6 | 1683.8 | 52.77 | 5 | 2801.8 | 782.35 |

18.07.2014 | 10 | 1466.9 | 91.93 | 8 | 2567.0 | 306.56 |

19.08.2014 | 13 | 1772.3 | 403.07 | 4 | 3354.0 | 374.11 |

10.09.2014 | 6 | 1330.9 | 322.40 | 8 | 2456.5 | 429.63 |

20.10.2014 | 3 | 997.2 | 54.20 | 8 | 2043.2 | 693.81 |

11.12.2014 | 5 | 1312.4 | 67.16 | 8 | 2203.2 | 612.81 |

13.02.2015 | 2 | 1504.2 | 282.67 | 4 | 2385.7 | 487.16 |

03.03.2015 | 8 | 1479.8 | 91.28 | 18 | 2669.2 | 503.46 |

11.06.2015 | 8 | 1009.7 | 71.64 | 9 | 1919.5 | 638.80 |

14.07.2015 | 8 | 1010.9 | 210.80 | 10 | 1976.7 | 424.92 |

Component parameters density, mean and standard deviation related to the sampling time during the investigation period for NoC and TD at 50 m.

Component 1 | Component 2 | Component 3 | |||||||
---|---|---|---|---|---|---|---|---|---|

Density | Mean | s.d. | Density | Mean | s.d. | Density | Mean | s.d. | |

09.05.2014 | 14 | 36.0 | 5.46 | 7 | 50.7 | 9.59 | |||

30.05.2014 | 3 | 38.6 | 2.87 | 4 | 56.3 | 5.80 | |||

19.08.2014 | 3 | 29.2 | 7.26 | 6 | 51.8 | 3.82 | |||

10.09.2014 | 5 | 38.2 | 5.14 | 3 | 59.1 | 4.81 | |||

10.11.2014 | 6 | 33.6 | 3.04 | 2 | 49.9 | 3.68 | |||

11.12.2014 | 3 | 30.4 | 3.28 | 3 | 51.8 | 7.80 | 5 | 64.7 | 6.84 |

16.01.2015 | 7 | 33.1 | 7.13 | 5 | 52.6 | 4.10 | |||

13.02.2015 | 3 | 38.0 | 6.06 | 3 | 55.1 | 3.29 | |||

15.04.2015 | 7 | 42.5 | 8.92 | 11 | 56.5 | 1.95 | |||

18.05.2015 | 3 | 40.0 | 7.03 | 11 | 56.5 | 3.95 | |||

11.06.2015 | 6 | 42.5 | 2.36 | 3 | 56.4 | 4.57 | 8 | 28.4 | 6.49 |

14.07.2015 | 9 | 46.0 | 7.66 | 3 | 61.9 | 2.70 | 4 | 29.6 | 4.19 |

09.05.2014 | 14 | 36.0 | 5.46 | 7 | 50.7 | 9.59 | |||

30.05.2014 | 3 | 38.6 | 2.87 | 4 | 56.3 | 5.80 | |||

19.08.2014 | 3 | 29.2 | 7.26 | 6 | 51.8 | 3.82 | |||

10.09.2014 | 5 | 38.2 | 5.14 | 3 | 59.1 | 4.81 | |||

10.11.2014 | 6 | 33.6 | 3.04 | 2 | 49.9 | 3.68 | 5 | 64.7 | 6.84 |

11.12.2014 | 3 | 30.4 | 3.28 | 3 | 51.8 | 7.80 | |||

16.01.2015 | 7 | 33.1 | 7.13 | 5 | 52.6 | 4.10 | |||

13.02.2015 | 3 | 38.0 | 6.06 | 3 | 55.1 | 3.29 | |||

15.04.2015 | 7 | 42.5 | 8.92 | 11 | 61.5 | 1.95 | |||

18.05.2015 | 3 | 40.0 | 7.03 | 3 | 61.4 | 3.57 | |||

11.06.2015 | 6 | 42.5 | 2.36 | 2 | 59.0 | 4.21 | 8 | 28.4 | 6.49 |

14.07.2015 | 9 | 46.0 | 7.66 | 3 | 61.9 | 4.70 | 4 | 29.6 | 4.19 |

20 m samples; Generation 2 (A) and Generation 3 (B) are more or less completely represented, similar at 50 meter’s samples’ Generation 2 (C). Only Generation 3 (D) is slightly truncated.

CBR; Generation 2 maximum (A), Generation 2 mean (B), Generation 3 maximum (C), Generation 3 mean (D). DIR; Generation 2 maximum (E), Generation 2 mean (F), Generation 3 maximum (G), Generation 3 mean (H).

CBR; Generation 2 maximum (A), Generation 2 mean (B), Generation 3 maximum (C), Generation 3 mean (D). DIR; Generation 2 maximum (E), Generation 2 mean (F), Generation 3 maximum (G), Generation 3 mean (H).

In comparison CBR and DIR are highly correlative, yet don’t exhibit a linear correlation. Deviations from a linear correlation can be especially well observed in the initial and later test parts. This pattern is stronger in specimens from 20 m water depth than those from the deeper samples, as seen in

For Generation 2 (A) and 3 (B) at 20 m and for Generation 2 (C) and 3 (D) at 50 m.

For further analyses, the parameters of CBRs and DIRs of Generation 2 have been used for samples from both water depths.

Birthdates for every sampled specimen were inferred based on a) the chamber building rate and b) on the diameter increase rate. Estimated birthdates of the 20 meters’ population are given as histograms with monthly intervals using simple counts (

By inversion of the CBR (A) and DIR (B) at 20 m. Density is given as simple counts.

By inversion of the CBR (A) and DIR (B) at 50 m. Density is weighted by sediment weight.

CBR’s histograms for 20 m clearly illustrate two major reproduction phases over the year, one in summer (July–August) and one in winter (February–March and November–December) with the summer reproduction being dominant.

At 50 m reproduction timing based on the CBR does not change between histograms using simple or standardized counts. Reproduction peaks occur around similar times, in summer (July–August) and winter (February–March and November–December). Reproduction events are more or less equally expressed, with slightly increased winter peaks.

Sinusoidal regression analysis on CBR’s and DIR’s histograms is acquired by the sum of sinusoids using the most significant periods of the Lomb periodogram, the Nyquist frequencies (ESM3) and the harmonic series. The best fit is gained using Nyquist frequencies and the Lomb periodogram, while harmonic series shows the worst fit. The sum-of-sinusoids is not identically repetitive over several years for Lomb periodogram and Nyquist frequencies and similar patterns continue if the cycles have convergent phases. Continuity over several years is only given by the harmonic series, hence they should be used if long-term trends are to be predicted.

Amplitudes of the sinusoidal functions based on CBR depicts the importance of oscillations. The population from 20 m exhibit, according to the Lomb periodogram, periods at 261.8 days, 137.1 days and 80 days with the corresponding amplitudes 10.10, 12.77 and 3.211. For the Nyquist frequencies the periods are at 258.7 days, 136.1 days and 51.92 days with the corresponding amplitudes 14.01, 10.20 and 5.22. The harmonic series gives periods at 365, 182.5 and 121.6 days with the corresponding amplitudes 9.82, 6.87 and 7.73.

The 50 meters’ population depicts similar periodic lengths in chamber number. The Lomb periodogram gives significant periods at 288 days, 130.9 days and 68.5 days with the corresponding amplitudes 7.39, 10.24 and 5.79. For Nyquist frequencies, the analysis resulted in period lengths of 130.5, 267.4 and 66.9 days with the amplitudes 10.37, 8.20 and 5.22. Here the harmonic series gives periods at 365, 182.5 and 121.6 days with the corresponding amplitudes 6.38, 3.52 and 11.34; note here the very low amplitude of the 180 days period.

Quite similar periodic lengths can be found based on the inversion of the DIR’s at both water depths, even though the longest period is extended in both populations. The population from 20 m exhibit, according to the Lomb periodogram, periods of 304 days, 125.2 days and 84.7 days with the corresponding amplitudes 12.25, 7.92 and 4.49. For Nyquist frequencies the periods are at 306.3 days, 136.8 days and 84.1 days with the corresponding amplitudes 13.2, 9.31 and 4.88. The harmonic series results in periods of 365, 182.5 and 121.6 days with the amplitudes 11.74, 9.22 and 8.02. This is illustrated in

Based on lomb periodogram (green; based on NoC (A), based on TD (B)), nyquist frequency (blue; based on NoC (C), based on TD (D)) and harmonic series (orange; based on NoC (E), based on TD (F)).

At 50 m water depth the Lomb periodogram gives significant periods at 320 days, 130.9 days and 64 days with corresponding amplitudes 2.99, 8.05 and 4.65. For Nyquist frequencies the analysis resulted in period lengths of 135.7, 86.26 and 362.2 days with amplitudes 8.64, 3.75 and 3.82. Here the harmonic series gives again periods at 365, 182.5, and 121.6 days length, with the amplitudes 4.52, 4.35 and 10.19. As it is illustrated in

Based on lomb periodogram (green; based on NoC (A), based on TD (B)), nyquist frequency (blue; based on NoC (C), based on TD (D)) and harmonic series (orange; based on NoC (E), based on TD (F)).

All these oscillations are comparable to those found in the volumetric growth of

Oscillation around ∼300 and ∼130 days periodic length exhibit amplitudes of similar magnitude at 20 and 50 meters’ populations. However, it can be observed that within the reproductive oscillations at 20 m the long-term cycle (∼300 days) exhibit a higher amplitude, while at 50 m the intermediate cycle (∼130 days) shows the higher amplitude. Oscillations with a periodic length around 180 days can only be found using the harmonic series. They are much more strongly expressed in 20 meter’s population, while at 50 m water depth expression is strongly reduced.

The same patterns with only slightly differences can be observed in the histograms for CBR’s and DIR’s. At 20 m population the reproduction peak in winter ‘14 is weaker and less distinctively expressed in the CBR than in the DIR. Reproduction peaks are equally distinct for CBR and DIR at 50 m, but the histogram for DIR shows a much stronger winter ‘14 peak.

The longevity of each specimen of

During main reproduction times up to three overlapping generations of

The first derivate of the MM indicates the continuously decreasing number of chambers built per day correlated with increasing lifetime. This is very similar for both water depths starting at 20 m with 1.82 chambers/day (Generation 2) and 1.90 chambers/day (Generation 3); at 50 m this is 1.84 chambers/day (Generation 2) and 1.84 chambers/day (Generation 3). Interestingly, the initial growth of

CBR building rates and chamber per day rates in daily interval for the first week and afterwards increasing time-intervals.

20 m | 50 m | |||
---|---|---|---|---|

Days | NoC | ch per day | NoC | ch per day |

1 | 2 | 1.8 | 2 | 1.8 |

2 | 4 | 1.7 | 4 | 1.8 |

3 | 6 | 1.7 | 5 | 1.7 |

4 | 7 | 1.6 | 7 | 1.6 |

5 | 9 | 1.5 | 9 | 1.5 |

6 | 10 | 1.4 | 10 | 1.5 |

7 | 12 | 1.4 | 12 | 1.4 |

10 | 16 | 1.2 | 15 | 1.2 |

15 | 21 | 1.0 | 21 | 1.0 |

30 | 33 | 0.6 | 33 | 0.6 |

60 | 45 | 0.3 | 47 | 0.3 |

90 | 52 | 0.2 | 54 | 0.2 |

120 | 56 | 0.1 | 59 | 0.1 |

150 | 58 | 0.1 | 62 | 0.1 |

180 | 60 | 0.1 | 64 | 0.1 |

210 | 62 | 0.0 | 66 | 0.1 |

240 | 63 | 0.0 | 67 | 0.0 |

270 | 64 | 0.0 | 68 | 0.0 |

300 | 65 | 0.0 | 69 | 0.0 |

330 | 65 | 0.0 | 70 | 0.0 |

360 | 66 | 0.0 | 71 | 0.0 |

Deeper living specimens have a stronger chambers size increase and take more time to build adult-stage chambers

Estimated CBRs gained by the natural laboratory approach exceeds the CBR rates expected from laboratory cultures (

Schizontic laboratory offspring from even shallower collected environments studied by _{1} (28.08.1969) reaches 2,184 µm after 253 days, while in the present study a mean test diameter estimated by the fitted function for 20 meter’s population results in 2,332 µm after that time. Final adult size is comparable due to the decreasing growth rate characteristic in adult specimens, therefore the DIR like the CBR becomes much flatter in culture. Cultured individuals only reach ∼1,500 µm after 150 days, while specimens from Sesoko-Jima are already ∼2,000 µm at that time interval. Laboratory cultures of gamonts from

Fitted by a Michaelis-Menten function (black) (A). Correlation between CBR for 50 m population and the CBR of the laboratory cultures (B), illustrating the stronger increase of the CBR gained from the natural laboratory in initial part of the function.

Even though slightly different frequency/density histograms exist using birth dates of specimens based on CBR and DIR, both indicate a continuous reproduction with two peaks throughout the year, which explains the presence of differently sized megalospheric generations within the studied monthly samples. The unequal distances between winter reproductions as seen in

Reproduction events in

The histogram of 20 meter’s population is given in simple counts (A). The histogram of 50 meter’s population is given in weighted frequencies (B). Both are fitted as sum-of-sinusoids illustrating the overall trend.

Within

Histogram of the monthly wet days (>1 mm precipitation) of the sampling area (Nago City, Okinawa) for the sampling year 2014.

In the 50 m population this strong dominance of summer reproduction is lost and the pattern is reversed. In the density histogram for CBRs (

Maximum longevity of

Based on population dynamic studies of megalospheric

Summarizing the reproduction of

The successful application of the ‘natural laboratory approach’ exemplifies that this methodology can be used for other larger foraminifera and shallow marine organism, where size can be quantified in monthly samples (e.g., scleractinians, molluscs and brachiopods).

Student’s t tests were used to check the coincidence in parameters for CBRs and DIRs for 20 m and 50 m samples.

Summarizing parameters and significance for all calculated cycles.

Chamber number and test diameter (µm) for each specimen for each sampling.

Chamber number and test diameter (µm) for each specimen for each sampling.

This work was was performed using the micro-CT Facility, which is part of the Department of Palaeontology at the University of Vienna, Austria. We especially would like to thank Kazuhiko Fujita and Yoshikazu Ohno (University of the Ryukyus) for providing equipment and helpful advice, as well as Harii Saki and Fred Saki-Sinniger (Tropical Biosphere Center) for their suggestions, help, and support during the field work at Sesoko Station. We would also like to express our gratitude to Carles Ferràndez-Cañadell (Barcelona) for aiding us in sampling and picking. For boat operation and technical knowledge, we thank Shohei Kadena and Yoshikatsu Nakano (Sesoko Station). Sampling would not have been possible without the professional diving experience of Takeshi Sugiura and the assistance of Claire Pasciarelli, Hector Solatges and Rian Prasetia. Thanks are due to Michael Stachowitsch (University of Vienna) for correcting the text as a professional copy editor.

The authors declare there are no competing interests.

The following information was supplied regarding data availability:

The raw data are provided in the

The primary data is available at: Wolfgang Eder, Julia Woeger, Shunichi Kinoshita, Johann Hohenegger, & Antonino Briguglio. (2018). Growth estimation of the larger foraminifer Heterostegina depressa by means of population dynamics (3D datasets)). Zenodo.