Introduction
Sexual dimorphism in fossils has the potential to explain the evolution of sex and sexual selection throughout geological time (Knell et al. Reference Knell, Naish, Tomkins and Hone2013). Information from fossils is very important for understanding this aspect of evolution, because sexual selection works on evolutionary timescales (more than 1 million generations; Lande Reference Lande1980). However, sexual dimorphism in fossils is not easily recognized (Knell et al. Reference Knell, Naish, Tomkins and Hone2013; Motani et al. Reference Motani, Jiang, Rieppel, Xue and Tintori2015). With the exceptions of very well preserved specimens (e.g., Matzke-Karasz et al. Reference Matzke-Karasz, Smith, Symonova, Miller and Tafforeau2009; Siveter et al. Reference Siveter, Tanaka, Farrell, Martin, Siveter and Briggs2014), most fossil specimens lack evidence for many types of sexual traits, such as the soft tissues of copulatory organs. In addition, they do not show direct evidence of sexual behaviors such as mating and breeding. Therefore, it is difficult to interpret the functions of traits in fossil specimens as sexual behavior. Identification of sexes is often difficult; in particular, an extinct taxon with extreme sexual dimorphism may often be misinterpreted as a completely different different taxon. For rare taxa such as megafossils, it is also difficult to collect sufficient specimens to obtain a statistically sufficient sample size (Padian and Horner Reference Padian and Horner2013). Therefore, the evolution of sex and sexual dimorphism has seldom been investigated using fossils (Knell et al. Reference Knell, Naish, Tomkins and Hone2013).
Fossil ostracodes show sexual dimorphism in the shape and size of their adult valves (e.g., Horne et al. Reference Horne, Cohen and Martens2002; Ozawa Reference Ozawa2013). Many taxa show obvious sexual dimorphism in adult valves, and some taxa display sexual dimorphism even in juvenile valves (e.g., Kamiya Reference Kamiya1988; Forel et al. Reference Forel, Crasquin, Chitnarin, Angiolini and Gaetani2015). Males generally have a more elongated valve shape than females. The allometry between valve length and height allows the assessment of the valve shape and the identification of the sex of living and fossil specimens (e.g., Ozawa Reference Ozawa2013). Females have valves with higher height/length ratios than males. This ratio is a critical element in determining allometry: the static allometric slope and intercept are different between the sexes (e.g., Ikeya and Ueda Reference Ikeya and Ueda1988). Via ontogenesis, ostracodes grow by molting six to eight times in their life. Their valve shape changes with increasing valve size (Baltanás et al. Reference Baltanás, Otero, Arqueros, Rossetti and Rossi2000; Danielopol et al. Reference Danielopol, Baltanás, Namiotko, Geiger, Pichler, Reina and Roidmayr2008). After the final molt, they become adults, rapidly develop sexual dimorphism in their valves, and change their allometry between the valve length and height.
Sexual dimorphism may result in sexual selection. Sexual dimorphism in ostracode valve shape is correlated with either mating activity (swimming activity, mating position, or copulatory organ accommodation) and/or brooding (Cohen and Morin Reference Cohen and Morin1990). Abe (Reference Abe1990), who reviewed sex ratios in ostracode populations, concluded that sexual dimorphism is enhanced by selection pressures on both females and males. Previous studies have proposed that the sexual dimorphism in valves may have been affected by selection pressures on both sexes. An alternative hypothesis for the static allometry suggests that valve shape may be stable on evolutionary timescales. In the allometry law, the relationship between the valve length (L) and the valve height (H) is expressed as follows: H=aL b , where the constants a and b are the allometric intercept and slope, respectively. Following the formula conversion of Bonduriansky and Day (Reference Bonduriansky and Day2003), the valve shape (i.e., the H/L ratio) can be determined from the relation H/L=aL b−1 . Because it is hypothesized that the static allometric slope b has low evolvability (e.g., Egset et al. Reference Egset, Hansen, Le Rouzic, Bolstad, Rosenqvist and Pélabon2012; Firmat et al. Reference Firmat, Lozano-Fernández, Agustí, Bolstad, Cuenca-Bescós, Hansen and Pélabon2014; Pélabon et al. Reference Pélabon, Firmat, Bolstad, Voje, Houle, Cassara, Le Rouzic and Hansen2014; Voje et al. Reference Voje, Hansen, Egset, Bolstad and Pélabon2014), H/L ratios have been stable on evolutionary timescales. The stability of the static allometric intercept a on million-year timescales is still a matter of debate (Voje et al. Reference Voje, Hansen, Egset, Bolstad and Pélabon2014). In general, sexual dimorphism is thought to have evolved in response to selection pressures that differ between males and females (e.g., Badyaev and Martin Reference Badyaev and Martin2000). Sexual dimorphism is also affected by a combination of sexually dimorphic growth patterns and selection on individuals during growth (e.g., Badyaev et al. Reference Badyaev, Whittingham and Hill2001). However, no previous studies have tested whether sexual differences in ostracode valves are correlated with selection pressure or have addressed the relationship between sexual shape dimorphism and juvenile shapes.
Sexual shape dimorphism is a phenotypic trait that responds to environmental changes. Temporal changes in phenotypic traits are very important for understanding selection and trait responses to selection, because the overall magnitudes and directions of adaptive evolution result in selection on these traits (Siepielski et al. Reference Siepielski, DiBattista and Carlson2009). If sexual shape dimorphism is affected by selection pressures on evolutionary timescales, time-series data of shape traits will show temporal changes and indicate characteristic patterns. Only a few studies have portrayed temporal changes in ostracode valve shape on million-year timescales (Reyment Reference Reyment1963, Reference Reyment1985; Hunt Reference Hunt2007a, Reference Hunt2013). Using the fossil record, temporal changes in phenotypic traits and their patterns can be determined on evolutionary timescales (e.g., Hunt et al. Reference Hunt, Bell and Travis2008; Firmat et al. Reference Firmat, Lozano-Fernández, Agustí, Bolstad, Cuenca-Bescós, Hansen and Pélabon2014; Saito-Kato et al. Reference Saito-Kato, Tanimura, Mori and Julius2015). In ostracode populations, the adult sex ratios (ASRs) indicate selection pressure on males. ASRs are reflective of male mortality rates (Kamiya Reference Kamiya1988; Abe Reference Abe1990; Rossi et al. Reference Rossi, Bartoli, Bellavere, Gandolfi, Salvador and Menozzi2004, Reference Rossi, Martorella and Menozzi2013; Martins et al. Reference Martins, Vandekerkhove, Mezquita, Schmit, Rueda, Namiotko and Rossetti2009; Rossi and Menozzi Reference Rossi and Menozzi2012). In the populations of previous studies, the sex ratios are female biased, that is, more females survive than males after the final molting. If the sexual shape dimorphism is enhanced by selection pressure on males, the valve-shape parameter can be correlated with the ASR. Temporal changes in traits result from responses to selection pressure during growth. If the sexual dimorphism traits were affected by selection pressures on growing individuals, the temporal changes in the traits of each sex could be correlated with changes in the juvenile traits.
The aims of this study are: (1) to investigate whether ostracode valve shape exhibits temporal changes on million-year timescales; (2) to test whether valve shape is correlated with female ratios, which are an indicator of selection pressure on males; (3) to examine whether adult shape is correlated with juvenile shape; and (4) to analyze temporal changes in static allometry between the valve shape and the valve length. For this study, we used Krithe dolichodeira s.l. from Paleocene sediments at the Integrated Ocean Drilling Program Site U1407 off Newfoundland in the northwestern Atlantic. This species shows clear sexual dimorphism (Coles et al. Reference Coles, Whatley and Moguilevsky1994; Ayress et al. Reference Ayress, Barrows, Passlow and Whatley1999) and is found in Cenozoic deep-sea sediments in the North Atlantic (Coles et al. Reference Coles, Whatley and Moguilevsky1994; Yamaguchi et al. Reference Yamaguchi, Matsui and Nishi2017a,Reference Yamaguchi, Matsui and Nishib). The sediments are continuous and well dated by means of planktic microfossil biostratigraphy (Norris et al. Reference Norris, Wilson and Blum2014; T. Yamaguchi, A. Bornemann, H. Matsui, and H. Nishi, unpublished observations). The ostracode specimens were obtained from successive discrete samples (Yamaguchi et al. Reference Yamaguchi, Matsui and Nishi2017a,Reference Yamaguchi, Matsui and Nishib).
Materials and Methods
Outline of the Methods
Specimens of Krithe dolichodeira were collected from Paleocene sediment samples. We measured the valve length (L) and height (H) of the specimens and calculated the valve area, ln(L×H). To examine the morphological variation of the specimens, we subjected a data set of ln(L×H) to the Gaussian mixture model (GMM) and Bayesian information criterion (BIC) and grouped the specimens into morphotypes (for details, see the subsection on GMM and BIC below). For sexual identification, we calculated the H/L ratios of the specimens and applied the ratios in each morphotype to the GMM and BIC. Male populations show isolated clusters of H/L ratios compared with female populations (e.g., Ikeya and Ueda Reference Ikeya and Ueda1988; Ozawa Reference Ozawa2013). In the genus Krithe, males show smaller H/L ratios than females (Athersuch et al. Reference Athersuch, Horne and Whittaker1989; Coles et al. Reference Coles, Whatley and Moguilevsky1994; Ayress et al. Reference Ayress, Barrows, Passlow and Whatley1999; Tanaka Reference Tanaka2016). If the BIC indicates two groups in the H/L ratios of a morphotype, the morphotype likely has sexual shape dimorphism in the H/L ratio. Dividing the time range of the sediment samples, we set time intervals. In each time interval, we calculated the sex ratios and the mean, variance, and standard deviation of the H/L ratios in each sex using GMM. To capture the allometric relationship between L and the H/L ratios, we subjected the parameters in each time interval to simple linear regression and calculated the allometric slope and intercept. Using Hunt’s (Reference Hunt2006) method, which uses model fitting and selection, we examined the pattern of temporal changes in the H/L ratios of females and males and in the allometric slope and intercept.
Sediment Samples
Yamaguchi et al. (Reference Yamaguchi, Matsui and Nishi2017a,Reference Yamaguchi, Matsui and Nishib) studied the taxonomy of ostracodes from Upper Cretaceous and Paleocene sediments at the Integrated Ocean Drilling Program Site U1407 (41°25′30″N, 49°48′28.8″W: Norris et al. Reference Norris, Wilson and Blum2014). Three cores were drilled into the seafloor of the Southeast Newfoundland Ridge at a present-day water depth of 3073 m. The core diameter was ~6.8 cm. The Upper Cretaceous and Paleocene sediments are pinkish-to-white nannofossil chalks (Norris et al. Reference Norris, Wilson and Blum2014). Between the core composite depth below sea floor (CCSF) of 214 m and 205 m, the sediments are a greenish color. At ~205 m CCSF, the lithology of the sediments is divided into two subunits: nannofossil chalks with radiolarians above ~205 m CCSF and nannofossil chalks below ~205 m CCSF. The seafloor is estimated to have been at a depth of 1800 m at 60 Ma (Norris et al. Reference Norris, Wilson and Blum2014). For this study, we used Krithe dolichodeira s.l. from 80 samples in the interval between 146.10 m CCSF and 211.83 m CCSF (the Paleocene). Samples with volumes of 10–30 cm2 were separated from the core sediments using fan-shaped plastic scoops. One scoop can seize a quarter-cylinder of sediment with an area of ~5 cm2 and a thickness of 1–2 cm. To obtain a single sediment sample, one or two plastic scoops were used. We discuss the fossil populations in a sediment volume of approximately 5–10 cm2.
Age Model of the Core Sediments
The timescale used here follows the Geological Time Scale 2012 (Gradstein et al. Reference Gradstein, Ogg, Schmitz and Ogg2012). The core sediments are dated as latest Cretaceous and Paleocene using calcareous nannofossil biostratigraphy and carbon stable isotopes of the bulk sediments (T. Yamaguchi, A. Bornemann, H. Matsui, and H. Nishi, unpublished observations). We determined the geological ages of the sediment samples in the interval of 146.10–211.83 m CCSF using five datum events of calcareous nannofossil biostratigraphy (Supplementary Table 1). The geological ages of the sediment samples range from 62.60 to 56.87 Ma (Supplementary Table 2).
Measurements
We measured the L and H of 187 adult and 76 juvenile specimens of Krithe dolichodeira s.l. from 80 Paleocene samples (Supplementary Table 2). Adult specimens can be discriminated from juvenile specimens via the presence of a broad anterior marginal zone and multiple marginal pore canals (e.g., Coles et al. Reference Coles, Whatley and Moguilevsky1994; Horne et al. Reference Horne, Cohen and Martens2002; Fig. 1). For the measurements, we used a digital microscope, VHX-2000 (Keyence), at the Center for Advanced Marine Core Research at Kochi University (Supplementary Table 2). The measurements were carried out at a magnification of 300×. The precision (1σ) of the measurements was ±0.645 μm as estimated from 90 repeated measurements obtained using a Zeiss stage micrometer (length: 1 mm).
Figure 1 Light microscopy images of Krithe dolichodeira s.l. viewed inside the valves. Scale bar, 100 µm. A–E, K. dolichodeira s.l.: A, morphotype B, right valve, adult (342-U1407A-21X-4W, 74-76); B, morphotype B, right valve, adult (342-U1407A-21X-4W, 74-76); C, morphotype B, right valve, adult (342-U1407C-17X-6W, 110-112.5); D, morphotype S, right valve, adult (342-U1407C-14X-4W, 34-36.5); and E, right valve, juvenile (342-U1407C-16X-2W, 73-75). The measurements of the specimens are provided in Supplementary Table 2. An arrow indicates the truncation in the posterior margin.
GMM and BIC
The GMM assumes that the measurements of individuals are normally distributed. Given a sample of measurements, the goals of the method are to choose the model with the number of groups that best fit the data and to provide a full distributional description, for example, the mean and variance for each subcomponent (Hand et al. Reference Hand, Mannila and 2001; Hunt and Chapman Reference Hunt and Chapman2001). For model selection, BIC (Schwarz Reference Schwarz1978) is widely used. In the example in Figure 2, the highest BIC indicates that the model with two subcomponents provides the best fit of the hypothetical candidate models. Using GMM clustering, Hunt and Chapman (Reference Hunt and Chapman2001) recognized clusters of eight growth stages in a trilobite population. We used GMM clustering to recognize the morphotypes and the sexual dimorphism. First, to recognize the number of morphotypes in K. dolichodeira we entered the data set of the valve area, ln(L×H), into the GMM clustering. Next, to identify sex in each morphotype, we applied the same method to data sets of the H/L ratio in each morphotype.
Figure 2 A, Histogram of the sagittal length of the Permian brachiopod Dielasma. The GMM generated density curves for the candidate models. The BIC score was calculated for each model. B, The density curve of the bimodal distribution was selected as the best-fit model because it had the lowest BIC score. The data were sourced from Hammer et al. (Reference Hammer, Harper and Ryan2001).
In the GMM in this study, the general form of a mixture distribution for a value x, ln(L×H), or the H/L ratio is defined as
$$f\left( x \right){\equals} \mathop \sum\nolimits_{k{\equals}1}^K w_{k} f_{k} (x\!\mid\!{\rm \Theta }_{k} ),$$
where w k is the mixing proportion or weight of the kth subcomponent, K is the number of subcomponents, f k (x) is the density distribution, and Θ k is a set of parameters included in the distributional model. The mixing proportions (w k ) must lie between 0 and 1 and sum to 1.
The Gaussian distribution for a density distribution, f k (x) is defined as
$$f\left( {x{\rm \mid\!\Theta }_{k} } \right){\equals} {1 \over {\sqrt {2{\rm \pi \sigma }_{k}^{2} } }}{\rm exp}\{ {\minus}{{(x{\minus} {\rm \mu }_{k} )^{2} } \over {2{\rm \sigma }_{k}^{2} }}\} ,$$
where σk 2 is the variance of the variable x, µ k is the mean of the x values, and Θ k =(σk 2 , µ k ). w k s and Θ k are determined using the expectation and maximization approach (Dempster et al. Reference Dempster, Laird and Rubin1977). This approach enables the parameter set of w k and Θ k in the Gaussian density distribution to be calculated. The parameters are determined to maximize the likelihood score function defined by
$${\rm \Lambda }{\equals} \mathop \sum\nolimits_{i{\equals}1}^n \ln {\bigg\{} { \mathop \sum\nolimits_{k{\equals}1}^K w_{k} f_{k} (x_{i} \!\mid\!{\rm \mu }_{k} ,{\rm \sigma }_{k}^{2} ){\bigg\}} .$$
The parameter estimation consists of two steps, an E step and an M step. The initial values of the mean, µ k , and the other parameters, w k and σ k 2 , are given appropriately. In the E step, given an estimate of the subcomponent means, μ k , variances, σk 2 , and mixing proportions, w k , the conditional probability that a data point x i belongs to the jth subcomponent is calculated:
$$P_{{ij}} {\equals}{{w_{j} f_{j} (x_{i} \!\mid\!{\rm \mu }_{i} , {\rm \sigma }_{i}^{2} )} \over {\sum_{k{\equals}1}^K w_{k} f_{k} (x_{i} \!\mid\!{\rm \mu }_{k} , {\rm \sigma }_{k}^{2} )}}.$$
In the M step, the parameters are estimated from the data, given the conditional probabilities P ij (e.g., Celeux and Govaert Reference Celeux and Govaert1995). The E and M steps are iterated until convergence, after which an observation can be assigned to the subcomponent or cluster corresponding to the highest conditional or posterior probability.
We used the BIC to subtract a term from the maximizing values of the likelihood. The formula for calculating the BIC is
$${\rm BIC}{\equals} {\minus}2\ln L\left( {\rm \theta } \right){\plus} d_{k} \ln N,$$
where, for a mixture model with K subcomponents, lnL(θ) is the maximizing value of the positive log-likelihood and d K is the number of free parameters to be estimated. N indicates the number of specimens. Both the number of subcomponents K, and the set {w k , µ k , σ k 2 |k=1, 2, …K} with the lowest BIC value are selected as parts of the most optimized model. For this calculation, we used R software (R Core Team 2015) and its ‘mclust’ packages (Fraley et al. Reference Fraley, Raftery, Murphy and Scrucca2012).
Sex Identification and Sex Ratio
As mentioned earlier, males form an isolated cluster with respect to females in plots of L versus H (e.g., Ikeya and Ueda Reference Ikeya and Ueda1988; Horne et al. Reference Horne, Cohen and Martens2002; Ozawa Reference Ozawa2013; Forel et al. Reference Forel, Crasquin, Chitnarin, Angiolini and Gaetani2015). In the Krithe species, males have smaller H/L ratios than females (Athersuch et al. Reference Athersuch, Horne and Whittaker1989; Coles et al. Reference Coles, Whatley and Moguilevsky1994; Ayress et al. Reference Ayress, Barrows, Passlow and Whatley1999; Tanaka Reference Tanaka2016). When a taxon has an obvious sexual shape dimorphism, the optimal distribution of the H/L ratios is bimodal. The sex ratio is defined as the proportion of females to the total number of adult individuals. This is the ASR, which is also called the tertiary sex ratio. We consider each valve specimen to be an individual.
Time Intervals
We divided the period of 62.6–56.8 Ma into 11 overlapping intervals (Fig. 3). First, we created six intervals: 58.93–56.8 Ma, 59.3–58.93 Ma, 59.6–59.3 Ma, 60.5–59.6 Ma, and 62.6–60.5 Ma. These intervals were designed to have 19–22 adult specimens. Next, linking the middle of one interval with that of the next interval, we created five additional intervals: 58.465–57.4 Ma, 58.465–58.115 Ma, 59.45–59.115 Ma, 60.05–59.45 Ma, and 61.55–60.05 Ma. The former six intervals overlap the latter five intervals. The durations of each interval range from 0.3 to 2.1 Myr. Each time interval has specimens of 105–106 generations, because ostracode longevity is several months to 1 yr (Cohen and Morin Reference Cohen and Morin1990). The variety in the duration of the intervals may affect the phenotypic variation (i.e., the variances of the H/L ratios) in the fossil record (Hunt Reference Hunt2004a). Hunt (Reference Hunt2004a,Reference Huntb) demonstrated the relationship between the phenotypic variation of fossils and the durations of the samples containing the fossils; time averaging inflates the variation by less than approximately 5%. Therefore, the bias in phenotypic variation resulting from time averaging is sufficiently small and can be ignored.
Figure 3 Time intervals and the temporal distribution of the sediment samples.
Correlation Analysis
Using Pearson’s correlation and Student’s t test, we examined the correlations between the proportion of females and the H/L ratios of both sexes and juveniles.
Allometry between L and the H/L Ratio
Using a simple linear regression, we attempted to calculate the allometry equation between L and the H/L ratio in both sexes at each time interval:
$$\log _{{10}} \left( {{H \over L}} \right){\equals} \log _{{10}} \left( a \right){\plus}b\log _{{10}} (L).$$
When a significant correlation was recognized at the 0.05 level or less in the equation, the intercept, log10(a), and the slope, b, were estimated.
Assessment of Temporal Changes in Traits
Following the method of Hunt (Reference Hunt2006), we tested the goodness of fit of the models for temporal changes in the H/L ratios and L of each sex and in the allometric slope and intercept. The method uses two assumptions: (1) genetic drift is not treated as a null model; and (2) adaptive evolution is equated with relentless directional selection. For the model fitting, we examined the five models defined by Hunt (Reference Hunt2006, Reference Hunt2008) and Hunt et al. (Reference Hunt, Bell and Travis2008, Reference Hunt, Hopkins and Lidgard2015): general random walk; unbiased random walk; stasis; strict stasis; and the Orstein–Uhlenbeck process. The general random walk model for directional evolution consists of a succession of random steps with a directional trend (Hunt Reference Hunt2006, Reference Hunt2008). The directional trend occurs when environmental or biotic factors that govern the position of phenotypic optimum peaks are stationary in the long term (Hansen Reference Hansen2012). The unbiased random walk for the random walk model lacks a directional trend. Stasis is an evolutionary trajectory with a constant mean; deviations around that mean are uncorrelated and normally distributed (Sheets and Mitchell Reference Sheets and Mitchell2001). A random walk can result from neutral genetic drift or from randomly varying natural selection (Hunt Reference Hunt2007b). The stasis mode is caused by genetic constraints or genetic drift among populations and by stabilized selection that fixes the adaptive peak or forces it to fluctuate around a steady mean (Hunt and Rabosky Reference Hunt and Rabosky2014). Strict stasis is the stasis with zero variance around the long-term mean. It represents no real change on evolutionary timescales (Hunt et al. Reference Hunt, Hopkins and Lidgard2015). The Orstein–Uhlenbeck process is natural selection with a combination of directional and stabilizing selection and is likely caused by the microevolution of a population in the vicinity of a fixed adaptive peak (Hunt et al. Reference Hunt, Bell and Travis2008). Calculating the bias-corrected Akaike information criterion and the Akaike weight in each model, the model with the highest Akaike weight value is selected as the best-fit model (e.g., Anderson et al. Reference Anderson, Burnham and Thompson2000). Hunt (Reference Hunt2008) proposed two methods for model parameterization: ancestor–descendant and joint parameterizations. Ancestor–descendant parameterization uses the morphological differences between each ancestor–descendant pair of populations, whereas joint parameterization considers the joint distribution of traits across all sampled populations. Here, we selected joint parameterization, because we address the temporal changes in the traits of a single species. The parameters for the model fitting, means, variances, and numbers of individuals were obtained. Multiplying the number of individuals by the female or male ratio, we calculated the numbers of females and males, respectively. For the age of each time interval, we used the mean geological ages of the sediment samples with adult specimens. For the model fitting and selection, we used R’s ‘paleoTS’ package (Hunt Reference Hunt2015).
Results
The Density Distribution of ln(L×H) and the Morphotypes
The BIC scores indicate two subcomponents in valve area, ln(L×H) (Table 1): one group with an ln(L×H) of 12.34–12.96 and another group with an ln(L×H) of 12.06–12.30 (Fig. 4). The large and small groups consist of 126 and 61 specimens, respectively. The two groups are found from 62.6 to 56.87 Ma (Fig. 4A). Both groups share the outline, vestibulum shape, and the shape and number of marginal pore canals with K. dolichodeira (Fig. 1). The Coles et al. (Reference Coles, Whatley and Moguilevsky1994) specimens of K. dolichodeira indicate an ln(L×H) of 12.03–12.76. Therefore, we treat the two groups as morphological variations of K. dolichodeira and call the large and the small groups morphotypes B and S, respectively.
Figure 4 A, Plot of the age versus the area, ln (L×H), of the valves. The dotted line indicates a ln(L×H) of 12.32. B, Histogram of ln(L×H) values in adult Krithe dolichodeira. The curve is the density estimation of the Gaussian mixture model with two subcomponents.
Table 1 The Bayesian information criterion (BIC) scores and the number of subcomponents in the Gaussian mixture model for ln(L×H). The degree of freedom (d K ), the log-likelihood (lnΛ), and number of subcomponents (K) are given. Bold type indicates the lowest BIC value.
The Density Distribution of the H/L Ratio
The BIC scores indicate a bimodal distribution in morphotype B and a trimodal distribution in morphotype S (Fig. 5A,B, Table 2). Morphotype B likely appears due to sexual dimorphism in the adult valve shape, while morphotype S does not exhibit sexual dimorphism. Morphotypes B and S comprise 126 and 61 specimens, respectively. We chose to investigate morphotype B. Juveniles of the species are difficult to tell apart from juveniles of the Krithe sp. of Yamaguchi et al. (Reference Yamaguchi, Matsui and Nishi2017b). We measured juvenile specimens from samples that contained only adult morphotype B. In the juveniles, the BIC scores indicate a unimodal distribution (Fig. 5C, Table 2). The morphotype B data set constitutes measurements of a mixture of left and right valves. Right valves do not differ significantly from left valves in their mean H/L ratios (Supplementary Fig. 1). Welch’s t-test failed to reject the null hypothesis that the means of the H/L ratios are equivalent between the left and right valves at a 0.05 significance level (t=1.5646, df=114.7, two-tailed p=0.12). In the bimodal model of morphotype B, the means and standard deviations (1σ) are as follows: 0.423±0.0142 and 0.492±0.0164, with 51 and 75 specimens, respectively. We consider the groups with the smallest mean and with the largest mean to be the males and females, respectively. The identification of the sex is discussed in the next section. The GMM indicates a bimodal population for all the adults and a unimodal population for all the juveniles (Fig. 5C).
Figure 5 A, Plot of L and H in morphotype B. B, Histogram of the H/L ratios in morphotype B. The curve is the density estimation of the GMM with two components. C, Plot of L and H in morphotype S. D, Histogram of the H/L ratios in morphotype S. The curve is a density estimation of the GMM with three components. E, Plot of L and H in juveniles. F, The histogram of the H/L ratios in juveniles. The curve is the density estimation of the GMM with one component.
Table 2 The Bayesian information criterion (BIC) scores and the number of subcomponents in the Gaussian mixture model for the H/L ratios. The degrees of freedom (d K ), the log-likelihood (lnΛ), and number of subcomponents (K) are given. Bold type indicates the lowest BIC value.
Correlation Analyses
We calculated the proportion of females (i.e., the ASRs) and the means, variances, and standard deviations of the H/L ratios in each time interval. In the correlation between these calculated values, we recognized a significant correlation in the H/L ratios between the females and juveniles (Fig. 6, Table 3).
Figure 6 Plots of shape ratios. A, Mean of female H/L ratio versus male H/L ratio; B, proportion of females versus mean of female H/L ratio; C, proportion of females versus mean of male H/L ratio; D, mean of juvenile H/L ratio versus mean of female H/L ratio; and E, mean of juvenile H/L ratio versus mean of male H/L ratio. r is the correlation coefficient. For detailed statistical results, see Table 3.
Table 3 Results of the linear regression analyses. The asterisk indicates significance at the 0.05 level; 95% CI and t 9 represent the 95% confidence interval and the t-value at nine degrees of freedom, respectively; R2 is the coefficient of determination.
Allometry
In six time intervals (58.0–56.8 Ma, 58.465–57.4 Ma, 58.93–58.0 Ma, 59.45–59.115 Ma, 59.6–59.3 Ma, and 60.05–59.45 Ma), the female H/L ratios correlate significantly with L (Fig. 7, Table 4). Conversely, the male H/L ratios have a significant correlation with L only in the interval of 59.115–58.465 Ma.
Figure 7 Plots of the mean of the H/L ratio versus L in: females (A) and males (B) in the time intervals of 58.0–56.8 Ma, 58.93–58.00 Ma, and 59.30–58.93 Ma; in females (C) and males (D) in the time intervals of 58.465–57.4 Ma, 59.115–58.465 Ma, and 59.450–59.115 Ma; in females (E) and males (F) in the time intervals of 59.6–59.3 Ma, 60.5–59.6 Ma, and 62.6–60.5 Ma; and in females (G) and males (H) in the time intervals of 60.50–59.45 and 61.55–60.05 Ma. In the plotted marks, B is the same as A, D is the same as C, F is the same as E, and H is the same as G. Lines were generated using a simple linear regression model. r is the correlation coefficient. Detailed statistical results are shown in Table 4.
Table 4 Result of linear regression analyses between H/L ratios and L in both sexes at each time interval. df, degrees of freedom; R2, coefficient of determination; * significance at 0.05 level; ** significance at 0.01 level.
Time-Series Data of ASRs, H/L Ratios, and Allometric Slope and Intercept
The ASRs range from 0.45 to 0.73 and decrease to less than 0.5 in the intervals of 58–56.8 and 59.30–58.93 Ma in the late Paleocene (Fig. 8A, Supplementary Table 3). The means of the female H/L ratios show a fluctuation between 0.484 and 0.499, while those of the male H/L ratios display a change from 0.417 to 0.428 (Fig. 8B, Supplementary Table 3). The juvenile H/L ratios exhibit means of 0.511–0.548. The female allometric slope and intercept change from −0.388 to −0.247 and from 0.406 to 0.812, respectively (Fig. 8C,D, Supplementary Table 4). In the interval of 59.115–58.465 Ma, we see a significant allometric relationship between the male L and H/L ratio (Table 4). The allometric slope and intercept are 0.58 and −2.06, respectively (Supplementary Table 4).
Figure 8 Temporal changes in (A) the proportion of females; (B) the mean H/L ratio; (C) b, the allometric slope; and (D) a, the allometric intercept. Vertical bars in B–D indicate ±1 standard deviation.
Temporal Changes in Valve-Shape Trait
The output of the model fitting is summarized in Table 5. For the H/L ratios of both sexes, the strict stasis model is supported more strongly than the other models. The relative support for the Orstein–Uhlenbeck model is negligible. For the slope and intercept in the female allometry equations, the strict stasis model is also accepted as the best-supported model, accounting for 86% of the Akaike weight (Table 5). Therefore, the H/L ratios of both sexes and the allometric slope and intercept exhibit no real evolution between 61 and 57 Ma (Fig. 8B–D).
Table 5 Results of the model fits for the time series of mean trait values in both sexes. Directional evolution was modeled as a general random walk. For each model fit, the log-likelihood (lnΛ), number of parameters (K), and bias-corrected Akaike information criterion (AICc) are given.
Discussion
Sexual Shape Dimorphism and Sex Identification
In the anatomy of living Krithe, specimens with male copulatory organs are more elongate than specimens without the organ (Tanaka Reference Tanaka2016). Krithe dolichodeira shows strong sexual dimorphism in adult valves (Coles et al. Reference Coles, Whatley and Moguilevsky1994). Males have slenderer valves than females. In the Coles et al. (Reference Coles, Whatley and Moguilevsky1994) specimens, the mean and standard deviation (1σ) of the H/L ratios are 0.48±0.024 in females and 0.43±0.0053 in males. Coles et al. (Reference Coles, Whatley and Moguilevsky1994) also noted that the male valves show more distinct truncation concavity in the posterior margin (Fig. 1B) than do the female valves. However, we recognized female specimens with distinct truncations in the specimens of Coles et al. (Reference Coles, Whatley and Moguilevsky1994: Text-fig. 3I, N) and Ayress et al. (Reference Ayress, Barrows, Passlow and Whatley1999: Fig. 3G) and a male specimen without truncation in the specimens of Coles et al. (Reference Coles, Whatley and Moguilevsky1994: Text-fig. 3Q). Therefore, we believe that the truncation is not a sexual dimorphic trait.
In the plot of L and H (Fig. 5A), the lack of clear coeval clusters may have been caused by the variable sizes of the species. In fossil ostracode populations that result from the accumulation of valves over a long time, instar and adult clusters cannot be straightforwardly recognized (Danielopol et al. Reference Danielopol, Baltanás, Namiotko, Geiger, Pichler, Reina and Roidmayr2008). Ostracodes changed their valve size and growth pattern over geological time (e.g., Hunt and Roy Reference Hunt and Roy2006; Hunt et al. Reference Hunt, Wicaksono, Brown and MacLeod2010; Yamaguchi et al. Reference Yamaguchi, Norris and Bornemann2012; Forel et al. Reference Forel, Crasquin, Chitnarin, Angiolini and Gaetani2015). A continuous distribution of L and H may have resulted in changes in the valve size during the Paleocene. As mentioned earlier, the BIC scores for the H/L ratios in morphotype B indicate two Gaussian subcomponents (Fig. 5B, Table 2). We interpret these two subcomponents as representing sexual dimorphism, not two species. Both subcomponents occur together in the samples, indicating that they dwelled contemporaneously in the same environment. All the specimens of both subcomponents possess the diagnostic characters of Krithe dolichodeira s.l. (Yamaguchi et al. Reference Yamaguchi, Matsui and Nishi2017b), as indicated by the taxonomy of Coles et al. (Reference Coles, Whatley and Moguilevsky1994). The juvenile population does not exhibit dimorphism (Fig. 5F, Table 2), suggesting that the dimorphism appeared in the adult stage. The difference in the H/L ratios between the subcomponents is consistent with sexual dimorphism in adult valves of morphotype B. Therefore, the adult dimorphism is thought to indicate the sexes. The subcomponent with the smallest mean is observed in males, and the subcomponent with the largest mean is observed in females.
Growth and Sexual Shape Dimorphism
During growth from juvenile to adult, the valve shape becomes more elongated and the variation decreases. Both sexes show higher means of H/L ratios than do juveniles, indicating slenderer valve shapes. The standard deviation of the adult H/L ratio is obviously smaller than that of the juveniles, except for the data in the time interval of 58.0–56.8 Ma; therefore, maturation alters both valve shape and size in K. dolichodeira s.l. as in the Candona species, Cytherissa lacustris, and Eucypris virens of Danielopol et al. (Reference Danielopol, Baltanás, Namiotko, Geiger, Pichler, Reina and Roidmayr2008). The female H/L ratios have a significant correlation with the juvenile ratios (Fig. 6, Table 3), suggesting an effect of allometric constraints on the female shape. Conversely, the male H/L ratios do not have a significant correlation with the juvenile ratios. The effects of the allometric constraints differ between the sexes.
Ostracode ASR as Reflective of Selection Pressure on Males
Under the assumption of the preservation of all dead valves, fossil ASRs indicate the productivity of both sexes in the long term (Abe Reference Abe1990). Abe (Reference Abe1990) also assumed that (1) the valves would not be sorted by sexual shape dimorphism when dead valves are transported after the death of individuals; and (2) the predators for ostracodes would not favor one sex. A cohort with an even ASR would suffer from male-biased mortality. The living cohort would show a high ASR every month. The dead population, which is formed from the annual accumulation of dead specimens of the cohort, would exhibit an even ASR (Abe Reference Abe1983, Reference Abe1990). Under these assumptions, ASRs in dead populations would not show sex-biased mortality during seasons or in the short term, but would indicate the sex ratios at the maturation of the cohort. If the secondary sex ratios are even, skewed ASRs reflect sex-biased mortality just before maturation. The core sediments of the nannofossil ooze do not display stratigraphic changes in grain size (Norris et al. Reference Norris, Wilson and Blum2014), suggesting stable depositional environments without turbulence through the Paleocene. These stable environments allow us to assume that there was no transportation of dead valves. Székely et al. (Reference Székely, Liker, Freckleton, Fichtel and Kappeler2014) summarized four mutual factors that affect ASRs: (1) biased primary and secondary sex ratios; (2) sex-differential mortality; (3) different maturation rates in males and females; and (4) sex differences in dispersion pattern and habitats. In field observations of living populations, ostracode ASRs are not consistent with juvenile and offspring sex ratios. Abe (Reference Abe1990) summarized the proportion of females of seven brackish and marine taxa during the A − 1 and A stages. The A − 1 stage is the juvenile stage prior to the final molt, and the A stage is the adult stage. The ASRs are lower than the proportion of females in the A − 1 stage. Vandekerkhove et al. (Reference Vandekerkhove, Matzke-Karasz, Mezquita and Rossetti2007) examined offspring sex ratios in cultivated Eucypris virens populations having different ASRs. They found that the female-biased population was derived from an even, sex-unbiased population. Kamiya (Reference Kamiya1988), Abe (Reference Abe1990), and Rossi et al. (Reference Rossi, Martorella and Menozzi2013) postulated that increases in the proportion of females from the A − 1 stage to the A stage result from increases in male mortality after the final molt. Different maturation rates between the sexes in ostracodes have been reported. In female-biased populations, field observations and culture experiments on living ostracodes suggest that ASRs are influenced by sexual differences in mortality and life span more strongly than are juvenile sex ratios (Kamiya Reference Kamiya1988; Martins et al. Reference Martins, Vandekerkhove, Mezquita, Schmit, Rueda, Namiotko and Rossetti2009; Rossi and Menozzi Reference Rossi and Menozzi2012; Rossi et al. Reference Rossi, Martorella and Menozzi2013). Males grow more rapidly than females and die after copulation (Rossi et al. Reference Rossi, Martorella and Menozzi2013). In fossil specimens, differences in the maturation rate between the sexes cannot be observed; therefore, the effect of differences in maturation rates can be ruled out. Székely et al. (Reference Székely, Liker, Freckleton, Fichtel and Kappeler2014) believe that ASRs are variable between local communities but homogenous at the metapopulation level. We assume fossil ASRs at the metapopulation level. Consequently, we interpret the ASR as indicating the degree of selection pressure on adult males under the assumption of even secondary sex ratios and no taphonomic bias.
The time-series data of the ASRs indicate changes from female-biased to male-biased populations as well as changes in selection pressure on males on the million-year timescale (Fig. 8A). The fossil population shifted to male-biased during the late Paleocene. Our data indicate a shift in the sex bias of the population on evolutionary timescales, as Fisher (Reference Fisher1930) predicted, that is, that sex-biased populations must shift to nonbiased populations on evolutionary timescales. According to his idea, intrasex competition in a population changes the sex ratios and eventually makes the ratios reach an equilibrium of 0.5. Our result does not imply that the cause of the shift was competition. The fossil populations constitute 105–106 generations. The fossil ASRs do not correspond to the operational sex ratios of Emlen and Oring (Reference Emlen and Oring1977). Their temporal changes indicate an alternation of male mortality rates in the long term. Therefore, our data partially support Fisher’s (Reference Fisher1930) speculation that the sex-biased population could change its sex ratios on evolutionary timescales.
Durable Valve Shape for Selection Pressure on Males
Strict stasis is fitted to the temporal change in the H/L ratios of both sexes (Fig. 8B, Table 5). The ratios do not show real evolutionary changes from 63 to 57 Ma. The H/L ratios do not have a correlation with the ASRs, suggesting that the valve shape is insensitive to selection pressure on males (Fig. 6, Table 3). In both sexes, the ratios do not show a correlation. The female valve shape changed independently from the male valve shape, and the female trait was not under the same type of selection as the male trait. Therefore, we believe that the sexual shape dimorphism was not under sexual selection. Our data do not support Abe’s (Reference Abe1990) hypothesis on the evolution of sexual shape dimorphism driven by sexual selection.
Function as a Sexual Display Trait
Our data suggest that the sexual shape dimorphism did not serve as a sexual display trait. The female allometry equation with a slope of −0.388 to −0.247 indicates an inverse allometry (b<0) (Supplementary Table 3). The male allometry has the slope of 0.58, showing a negative allometry (0<b<1). The types of allometry disagree with the trend of allometry in sexual display. In general, sexual display traits show a positive allometry (b>1) (e.g., Green Reference Green1992; Petrie Reference Petrie1992; Bonduriansky and Day Reference Bonduriansky and Day2003; Bonduriansky Reference Bonduriansky2007). As mentioned earlier, the valve shape does not correspond to selection pressure on males. Therefore, we believe that the sexual shape dimorphism did not function as a sexual display.
Stability in Allometric Slope and Intercept
The temporal change in the slope and intercept of the female allometry equation fits the strict stasis model (Fig. 8C,D, Table 5) and supports the hypothesis of low evaluated allometry slope in the fossil record, as Firmat et al. (Reference Firmat, Lozano-Fernández, Agustí, Bolstad, Cuenca-Bescós, Hansen and Pélabon2014) reported. Firmat et al. (Reference Firmat, Lozano-Fernández, Agustí, Bolstad, Cuenca-Bescós, Hansen and Pélabon2014) investigated temporal changes in the allometry of the fossil arvicoline rodent species over the last 600 Kyr. Conversely, Voje et al. (Reference Voje, Hansen, Egset, Bolstad and Pélabon2014) analyzed more than 300 data sets of allometric relationships of animal morphology, which are generally considered to be spread over several millions of years. Voje et al. (Reference Voje, Hansen, Egset, Bolstad and Pélabon2014) predicted stability in the slope on million-year timescales, and the fossil ostracode data have demonstrated this. This stable slope indicates that the evolution of the Paleocene ostracode valve shape is constrained by static allometry.
Conclusions
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1. The sexual shape dimorphism in Krithe dolichodeira was durable during the Paleocene. It showed no real evolution, even though the selection pressure on males indicates changes. Our study does not support Abe’s (Reference Abe1990) hypothesis that a selection pressure on the sexes would drive the evolution of sexual shape dimorphism.
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2. The shape dimorphism was not functional for sexual display. It was not correlated with selection pressure on males. The allometry between the shape parameter and the valve length indicate inverse and negative allometry, in contrast to the positive allometry of sexual display traits.
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3. The temporal change in the ASRs indicates a shift from a female-biased to a male-biased population on a million-year timescale. Our observation demonstrates Fisher’s (Reference Fisher1930) speculation that a skewed sex ratio in a population can change on evolutionary timescales.
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4. As in Firmat et al. (Reference Firmat, Lozano-Fernández, Agustí, Bolstad, Cuenca-Bescós, Hansen and Pélabon2014), our result also indicates a stable allometric slope and intercept on million-year timescales. This stable slope suggests that the evolution of the Paleocene valve shape was constrained by static allometry.
Acknowledgments
This research used samples provided by the Integrated Ocean Drilling Program. We would like to express appreciation to Motomi Genkai-Kato and Gyo Itani (Kochi University) for their constructive advice and discussions on ecology; to Gene Hunt (Smithsonian Institution National Museum of Natural History) and an anonymous reviewer for their review of the manuscript, critical comments, and constructive suggestions; and to Catherine Badgley (University of Michigan) for her editing of the manuscript. This study was financially supported by the Integrated Ocean Drilling Program Expedition 342 After Cruise Research Program of the Japan Agency for Marine–Earth Science and Technology to T.Y., H.M., and H.N. and a scientific fund of the Fujiwara Natural History Public Interest Incorporated Foundation, Japan to T.Y. In addition, we would like to thank Enago (www.enago.jp) for the English-language review.
Supplementary Material
Data available from the Dryad Digital Repository: http://doi.org/10.5061/dryad.14j2m.3
