Image-based methods for phenotyping growth dynamics and fitness in large plant populations

Abstract

Background With the development of next-generation sequencing technologies, high-throughput phenotyping has become the new bottleneck of quantitative genetics analyses. The model species Arabidopsis thaliana offers extensive resources to investigate intraspecific trait variability and the genetic bases of ecologically relevant traits, such as growth dynamics and reproductive allocation. However, reproducible and cost-effective methods need to be developed for the measurement of growth and especially fitness related traits in large populations. Here we describe image-based methods that can be adapted to a wide range of laboratory conditions, and enable the reliable estimation of biomass accumulation and fruit production in thousands of A. thaliana individuals.

Results We propose a semi-invasive approach, where part of a population is used to predict plant biomass from image analysis. The other part of the population is daily imaged during three weeks, then harvested at the end of the life cycle where rosette and inflorescence are separately imaged. We developed ImageJ macros and R codes for image segmentation, 2D skeletonization and subsequent statistical analysis. First, ontogenetic growth is modelled from estimated and measured dry mass for all individuals with non-linear regressions, from which the dynamics of absolute growth rate (GR) and relative growth rate (RGR) are calculated. Second, analysis of the 2D inflorescence skeleton allows the estimation of fruit production, an important component of plant fitness. Our method was evaluated across 451 natural accessions of A. thaliana. Cross-validation revealed that our image-based method allows predicting approximately 90% of biomass variation and 70% of fruit production. Furthermore, estimated traits - like measured traits - showed high heritabilities and inter-experiment reproducibility.

Conclusions We propose a flexible toolkit for the measurement of growth and fitness related traits in large plant populations. It is based on simple imaging, making the method reproducible at low cost in different facilities. However, as manual imaging of large plant populations can quickly become a limiting factor, we also describe an automated high-throughput imaging coupled with micro-computers that enables large phenotypic screening for genome-wide association studies and stress experiments.

Background

Plants become less efficient to accumulate biomass as they get larger and older, resulting in a decline of the relative growth rate (RGR) in the course of ontogeny [1–⇓3]. This is due to developmental constraints such as increasing allocation of biomass to supporting structures like stems, and self-shading due overlapping leaves in larger individuals. Strong variation of growth has been reported across plant species [1,4–⇓⇓⇓⇓⇓⇓11], which has been assumed to reflect the inherent diversity of plant strategies to cope with contrasting levels of resource availability [1,5,8,12,13]. For instance, species from resource-scarce environments generally show a reduced speed of biomass accumulation compared to species from resource-rich environments, even when they are placed in the same, non-limiting conditions [2,14]. The same observation has been made within species [5,15]. However, the genetic bases of plant growth dynamics remain unclear, due to the complexity of the genetic architecture of underlying traits [16,17], and thus, to the necessity of phenotyping very large plant populations.

To compare growth dynamics between genotypes or treatments, several methods have been proposed to compute RGR from a small numbers of observations [7,18,19]. These methods are valuable to investigate changes in growth over a short period of time, for instance in response to environmental stress. However, sequential harvesting of many individuals during ontogeny is space and time consuming. Furthermore, it is problematic for evaluating standard deviation and measurement error across genotypes, as the same individual is not followed during ontogeny. Ecophysiological and ecological studies ultimately seek to compare individual variation of growth dynamics with fitness components like fruit and seed production. The model species A. thaliana is a valuable tool to make such comparison [20]. Because of its selfing mating system and its small size, numerous individuals can be grown in relatively small facilities, and experiments are reproducible indefinitely on the same genotypes [21]. In 2016, the genetic resources available for this species have reached a milestone with the complete sequencing of 1,135 natural accessions with publicly available seeds to conduct comparative analysis (http://1001genomes.org/) [22].

Many high-throughput platforms have been developed in the last decades for plant phenotyping in crops [23–⇓⇓⇓27], and in A. thaliana [10,28–⇓⇓⇓⇓33]. However, most of them are (i) either commercial or require the purchase of expensive materials [23,25,27–⇓29,31] but see [34], (ii) not suitable for the analysis of growth phenotypes from germination to fitness parameters [30,32,34,35], or (iii) do not allow the quantification of complex traits like biomass accumulation and RGR [30,36]. Thus, we aimed at developing flexible and easily reproducible methods to measure individual growth dynamics and fruit production across large populations of A. thaliana. Our pipeline is based on manual or automated imaging, and subsequent analysis with ImageJ [37] and R [38]. The method was evaluated on a set of 451 worldwide accessions.

Results

Analysis of growth dynamics in large populations with simple imaging

Plant imaging and population sub-sampling

In our study, we used a hydroponic system where plants are cultivated in trays on inorganic solid media (rockwool cubes) and nutrients are daily provided through a solution [39] (Fig. 1a; Table S1). This system allows plants to have an unlimited source of nutrients for growth, as well as a highly controlled environment to avoid pests and herbivores. Furthermore, the hydroponic system also enables the measurement of the weight of the root system.

Figure 1. The hydroponic system for A. thaliana.

(a) Rockwool cube used in combination with small pot and black circle lid. (b) Example of tray image at 25 day old (top panel), individual pot at 25 day old in an early-flowering accession (bottom-left panel), and harvested adult plant with rosette and inflorescence (bottom-right panel).

The individual plant growth was followed using a code system: the genotype sowed in each pot was defined before the beginning of the experiment by the label of the tray (e.g., T01, T02, etc.) and the coordinate of the pot in each tray (e.g., A1, C5, D8, etc.). The label of the tray was placed at the top-left corner, which defined the coordinate of the first position (A1) on each tray (Fig. 1b). Four replicates of 480 genotypes were grown, with pots randomly distributed in 64 trays of 30 pots each (Fig. 1b). After germination at 23 °C, all plants, having two cotyledons, were vernalized at 4 °C during 41 days to maximize the flowering of all the different accessions. Due to mortality, only 451 accessions out of the 472 were completely phenotyped for growth and fitness. After shoot harvesting, rockwool cubes were dried at 65 °C and weighed to estimate root dry mass.

A growth chamber equipped with Raspberry Pi Automated Phenotyping Array (hereafter RAPA) was built at the Max Planck Institute (MPI) of Tübingen for large-scale phenotyping. 192 micro-cameras (two per tray) were mounted between fluorescent light tubes to simultaneously take top-view pictures of all plants (Fig. 2). The recording and storage of tray pictures were managed through embedded computers (Raspberry Pi rev. 1.2, Raspberry Pi Foundation, UK). All trays were daily imaged until fruit ripening with the automatic RAPA system. In addition, all trays were daily imaged with a manual setup (left side on Fig. 2a) during the first 25 days after vernalization. To show the general applicability of the method, here we used only images taken manually from the regular camera.

Figure 2. The RAPA facility.

(a) Entrance view of the growth chamber with a zoom on the camera installed between light tubes (top-left panel). On the right is the setup to water the plants and take manual tray picture. (b) Segmentation of tray image with the macro. (c) Examples of individual rosette images saved with the ImageJ macro, from which rosette area, perimeter and shape descriptors were extracted.

For modelling growth, we partitioned the whole population into two sub-populations: replicates 1 and 2 of every genotype represent the focal population on which growth dynamics and fruit production were measured. They were harvested at the end of reproduction when the first fruits (siliques) were yellowing (stage 8.00 according to Boyes et al. [40]). Inflorescences and rosettes were separated and both photographed with a high-resolution camera (Fig. 1b). Replicates 3 and 4 represent the training population. They were harvested at 16 days after the end of vernalization for building a predictive model of rosette biomass from images.

Estimation of rosette biomass from image analysis and modelling in the training population

We developed an ImageJ [37] macro to extract rosette morphological traits of all growing individuals from a tray image (Fig. 2b, c; Additional File 1). After automatic segmentation of the tray image (Fig. 2b), the macro returns individual rosette area and perimeter values in pixels, which can be then converted into cm² and cm, respectively, by measuring the area and perimeter (in pixels) of a 4 cm² calibrator present on trays. Three other morphological traits were also automatically measured with the macro: the rosette circularity , the aspect ratio , and the rosette roundness .

The macro automatically processes images when plants are young and do not overlap with each other. When they get bigger (i.e. 20-25 days after vernalization), the macro offers the possibility to manually separate plants. We estimated that, on a regular computer, the macro takes approximately 20-25 s per tray (30 individuals) when running on automatic mode, and between one and two minutes in manual mode (depending on the number of corrections to make). All individual rosette images extracted after segmentation are saved in. jpg format (Fig. 2c), called with the corresponding date, tray label and pot coordinates (for instance “20150509_Tray12_C5.jpg”). The ImageJ code of the macro is available in Additional File 1, with an example of tray image in Fig. S1.

We then developed a predictive model of rosette dry mass from the five traits extracted from rosette images with ImageJ. Generalized linear models (glm) were evaluated with a cross-validation approach on the training population (Additional File 2). Prediction accuracy was measured as the coefficient of correlation (r²) between measured and predicted rosette dry mass. Results showed that we can explain ca. 90% (P < 0.001) of rosette dry mass with the model that included rosette area, perimeter, circularity, aspect ratio and roundness. However, as removing rosette circularity, aspect ratio and roundness did not impact the prediction accuracy (r² = 0.91 when replicate 3 is used to train the model, Fig. 3a; and r² = 0.90 when replicate 4 is used to train the model, Fig. 3b), these traits were therefore removed in subsequent analyses. Thus, the final equation we used to estimate rosette dry mass from rosette pictures, in the 25 first days following vernalization, is given by Eq. 1 of Table 1, where the three coefficients (given in Table S2) were all significant (P = 0.03 for the intercept, P < 10⁻⁴ for both the coefficients of rosette area and rosette perimeter).

Figure 3. Cross-validation of the predictive model of rosette dry mass from rosette image.

Rosettes harvested at 16 days after vernalization. (a) First cross-validation performed with replicate 3 used as training dataset and replicate 4 as testing dataset. (b) Second cross-validation performed with replicate 4 used as training dataset and replicate 3 as testing dataset. r² measured from Pearson’s coefficient of correlation.

Table 1.

Equations of the models used in the study.

Fitting non-linear model of individual growth dynamics in the focal population

Since some plants germinated during or, for a few, after vernalization, we considered the first day of growth (t₀) for each individual of the focal population (replicates 1 and 2) as the day at which it had a minimum size. For convenience, we used the size of the biggest measured plant across all individuals at the first day of growth following vernalization. This corresponded to a plant with first true leaves just emerged (2-3 mm each, Additional File 2). This procedure allowed for normalization of growth trajectories from the same starting point between individuals that differ in germination speed. We used the predictive model established above on the training population to estimate rosette dry mass on the focal population during the 25 first days following vernalization (Fig. 4).

Figure 4. Logistic growth fitting and subsequent estimation of absolute growth rate and RGR.

Top panels: example of growth fitting on a single individual (from left to right: logistic fit of rosette dry mass M, absolute growth rate GR as the derivative of the logistic function, and RGR as the GR/M at every time points). Bottom panels: Representation of the logistic fits of M, GR and RGR across the 451 accessions, colored by growth duration (days after vernalization).

Previous studies have shown that leaf and whole-plant growth follow a sigmoid curve in A. thaliana [41–⇓43]. We thus used a three-order logistic function f of rosette dry mass (M) in the course of time t (Eq. 2 in Table 1) [3] as: where A, B and t_i are the parameters characterizing the shape of the curve, which are expected to differ between individuals depending on genotypes and/or environmental conditions. A is the upper asymptote of the sigmoid curve, which was measured as rosette dry mass (mg) at maturity (Fig. 4). B controls the steepness of the curve, as the inverse of the exponential growth coefficient r (r = 1/B). t_i is the inflection point that, by definition, corresponds to the time point where the rosette is at 50% of its final dry mass, and where the absolute growth rate (GR, mg d⁻¹) is maximal [3]. Both B and t_i were estimated by fitting a logistic growth function on every individual in R (Table S2; Additional File 2). We then estimated several dynamical variables from the fitted parameters (Fig. 4; Table 1; Table S2), such as absolute growth rate (GR(t), the derivative of the logistic growth function, mg d⁻¹; Eq. 3 in Table 1) and RGR(t) (GR(t) / M (t), mg d⁻¹ g⁻¹; Eq. 4 in Table 1).

Image-based estimation of fruit production

Fruits (siliques) were manually counted on the pictures of the inflorescence of 352 out of the 856 plants harvested in the focal population. In addition, we analysed the inflorescence features of all the 856 harvested plants with ImageJ [37] to automatically estimate the number of siliques through image segmentation and 2D skeletonization with a dedicated macro (code in Additional File 3, and example of inflorescence image in Fig. S2). The analysis of the inflorescence 2D skeletons with ImageJ (Fig. 5) returned seven vectors of variables for each plant, which were automatically saved in a. csv file by the macro. These skeleton variables are: number of branches (sk₁), junctions (sk₂), end-point voxels (sk₃), junction voxels (sk₄), slab voxels (sk₅), triple points (sk₆), and maximum branch length (sk₇). These seven vectors were averaged per individual, giving a set of seven variables with unique value that were used as predictors of silique number.

Figure 5. Estimation of the number of siliques from inflorescence images.

(a) From left to right: raw inflorescence image, segmented image and skeletonized image processed with the macro. (b) Cross-validation performed on a subset of the data with Pearson’s coefficient of correlation (r²) between estimated and measured number of siliques on 352 test plants.

Using the same approach as for estimating rosette dry mass from images, we estimated silique number from a cross-validation approach with glm performed on the 352 plants for which we had both manual measurements and skeleton parameters (detailed R code in Additional File 4). The cross-validation was tested across 1000 permutations of a random training dataset of 264 individuals, i.e. 75% of the 352 individuals. It showed that the predicted and measured silique number had a high correlation with r² close to 0.7 (Fig. 5b and Additional File 4). We then used all the 352 plants as training dataset to predict the number of siliques in all harvested individuals of the focal population. The parameters of the equation to estimate the number of siliques (S) from ImageJ-processed inflorescence images (Eq. 5 in Table 1) are given in Table S2.

Robustness of the method and reproducibility of trait measurement

Our analysis of trait variation focuses on eight phenotypic traits: five were measured (growth duration, final rosette and root dry mass, root and reproductive allocation), and three were estimated (GR and RGR at the inflection point, number of siliques). Trait values for all individuals are available in Table S3. They were all strongly variable across the 451 accessions (Fig. 6). The part of phenotypic variance accounted by genetic variation across individuals (broad-sense heritabilities, H²) for all traits were higher than 0.70, except for root allocation, a measured trait, with a H² of 0.40 (Table S4). Importantly, H² of the traits estimated with our method (GR and RGR at inflection, and number of siliques) were in the same range (0.91, 0.75 and 0.76, respectively) than for the heritabilities of the measured traits (0.89, 0.95, 0.71, 0.40 and 0.84 for growth duration, rosette final dry mass, root final dry mass, root and reproductive allocation, respectively; see Table S4).

Figure 6. Variation in eight traits measured across the population of 451 accessions.

In each barplot, accessions (n = 2) are ranked by increasing growth duration. M: final rosette dry mass, GR: absolute growth rate, RGR: relative growth rate, Root alloc.: ratio of final root dry mass over total plant dry mass (including root, rosette and inflorescence). Repro. Alloc: ratio of inflorescence dry mass over total plant dry mass. Error bars represent standard errors.

To evaluate the reproducibility of trait value estimated across genotypes with our method, we repeated a second experiment on 18 accessions selected for their highly contrasted phenotypes (Fig. S3). We used nine phenotypic groups, each containing two accessions, spanning the range of growth duration and RGR variation (three groups of growth duration and three groups of RGR, see Table S5 and Fig. S3). These 18 accessions were grown using the same protocol (n = 8). Three replicates were harvested at the estimated inflection point of the growth trajectory of each genotype, and five replicates were harvested at the end of reproduction. Using the inflection point of the growth trajectory (i.e. when the rosette is estimated to be 50% of its final dry mass) had two goals: (i) test whether predicted rosette dry mass at later vegetative growth is consistent with measurement, and (ii) test whether the genotypic trait values are correlated between two independent experiments. In additions, the number of siliques was manually counted on the plants at the end of reproduction (stage 8.00 [40]).

Results showed a good correlation between the rosette dry mass at the inflection point estimated in the first experiment and the dry mass measured in the second experiment (r² = 0.67; Fig. 7a). This suggests that (i) the method is suitable for estimating rosette dry mass in the course of the of the whole life cycle, and (ii) model predictions are conserved across experiments. Furthermore, the number of siliques estimated from image analysis in the first experiment was well correlated with the number of siliques manually counted in the second experiment (r² = 0.70; Fig. 7b).

Figure 7. Reproducibility of rosette dry mass and silique number estimation.

Measured across 18 contrasted accessions following the same protocol. (a) Pearson’s coefficient of correlation (r²) between rosette dry mass M estimated at the inflection point t_i in the first experiment and rosette dry mass M measured at t in the second experiment. (b) Pearson’s coefficient of correlation (r²) between the number of siliques estimated in the first experiment and the number of siliques measured in the second experiment.

Discussion

Biomass accumulation is a key physiological parameter related to individual performance and stress response [1,44]. Here, we have developed a set of methods based on high-throughput image analysis for a rapid and accurate estimation of growth variation, including plant size, growth rate and RGR. The method uses low-cost techniques robustly applicable in any facilities (e.g., growth chambers, greenhouses). Our method developed for A. thaliana has the advantage of being cost-effective and flexible to any facilities. From simple imaging, it allows a single experimenter to simultaneously measure rosette biomass accumulation, RGR and fruit production over thousands of plants. Importantly, all the growth parameters measured in this study varied strongly between individuals, notably between early and late flowering plants (Fig. 4, Table S3). A. thaliana is the favorite model in plant genetics and molecular biology, and it is also becoming a model in evolutionary biology and ecology [9,21,45]. Our approach therefore offers new avenues for dissecting the links between growth and fitness, and the genetic and evolutionary bases of phenotypic variation. The same method could be applicable to other species, but the 3D architecture in non-rosette species requires more sophisticated image analysis. A recent study in maize offers a nice example of high-throughput 3D reconstruction of plants and biomass prediction [25].

Technical considerations about high-throughput imaging and analysis

In this study, we took advantage of the RAPA system to collect plant images at high-throughput during growth. Additionally, we took pictures of the trays with a regular camera every day when we watered the plants. Measurements of rosette morphology (area, perimeter and shape descriptors) were the same on manual images and RAPA images. Thus, tray imaging can be done easily in any laboratory or facilities, and analyzed with the ImageJ macro developed in this study (Additional File 1). The time lapse and frequency of tray imaging is important for proper fitting of the growth curves. We used daily imaging during the 25 first days of growth after vernalization, but a logistic growth function could be fitted with only one picture every 2-3 days. Although less accurate, reducing the frequency of imaging would help the experimenter to save time during both image acquisition and analysis, notably if no automatic system like RAPA is available. Here we showed that our method is robust and reproducible across experiments as long as we grow the plants in the same environment. However, we recommend making a new predictive model of plant biomass with cross-validation for each experimental design, specifically if growth conditions change, as the relationship between rosette morphology and rosette biomass may differ depending on genotypes and environments.

Reproducible and low-cost methods for genetic and ecophysiological studies

The semi-invasive approach based on statistical modelling and cross-validation to convert rosette morphology into biomass drastically reduces the number of replicates necessary to measure the dynamics of biomass accumulation. Here, we presented the analysis of eight growth trait across 451 accessions, for which we measured high heritabilities using only four replicates per genotype (Table S4). The reproducibility of our method is supported by the second experiment where 18 contrasted accessions were phenotyped in the same condition (Fig. 7). Importantly, we voluntarily chose 18 accessions that maximize differences in growth duration and RGR to reproduce the most extreme phenotypes (Fig. S3).

Importantly, our methods offer the possibility to evaluate the relationship between growth dynamics and fitness components on the same individuals. This enables high-throughput investigations about the mechanisms of plant acclimation to different conditions, as well as its genetic underpinnings (e.g. genotypes-by-environment interactions). Measuring growth dynamics and fitness components on large plant populations is a strong bottleneck for our understanding of the mechanisms of plant adaptation and evolution. The same approach we have developed here can easily be reproduced in any laboratory working with A. thaliana, and potentially with other species. Taking advantage of its flexibility, we hope that our method can help future studies to dissect the relationships between genetic diversity, environment and plant performance.

Methods

Plant material

472 natural accessions of A. thaliana were selected from the germplasm of the 1001 Genomes project [22] (http://1001genomes.org/: a list of the accessions used in this study is available in Table S4) for monitoring vegetative growth and fitness in the RAPA system at MPI-Tübingen. Seeds used in this study were obtained from parental plants propagated under similar conditions in greenhouse. All seeds were stored overnight at -80 °C and surface-sterilized with 100% ethanol before sowing.

Growth conditions

Plants were cultivated on a semi-hydroponic system. Seeds were sowed on 3.6 cm × 3.6 cm × 4 cm depth rockwool cubes (Grodan cubes, Rockwool International A/S, Denmark) fitted in 4.6 cm (diameter) × 5 cm (depth) circular pots (Pöppelmann GmbH and Co., Germany). The pots were covered with a black circle pierced in the centre (5-10 mm hole manually made with a puncher). Before sowing, the dry rockwool cubes were weighed with a microbalance. Then, they were watered by dipping them completely into 75% strength nutrient solution in order to achieve full humidification and fertilization. The chemical composition of the nutrient solution was obtained from Conn et al. [39] (also available in Table S2).

After sowing, trays were incubated for two days in the dark at 4 °C for seed stratification, and then transferred for six days to 23 °C for germination. After six days, when most seedlings had two cotyledons, trays were transferred to 4 °C for 41 days for vernalization. During germination and vernalization, all trays were watered once a week by putting them in 4-6 cm (ca. three-quarter of the pot height) of a 75% strength nutrient solution for 5-10 s. After 41 days of vernalization, when true leaves had emerged on most individuals, plants were thinned to one plant per pot, and trays were moved to the RAPA room, set to 16 °C with a temperature variability of close to ± 0.1 °C, air humidity at 65 %, and 12 h day length, with a PPFD of 125 to 175 μmol m⁻² s⁻¹ provided by a 1:1 mixture of Cool White and Gro-Lux Wide Spectrum fluorescent lights (Luxline plus F36W/840, Sylvania, Germany). Light, temperature, and humidity were continuously monitored online and logged data were stored in a Structured Query Language (SQL) database. All trays were randomly positioned in the room, and watered every day with 100% strength nutrient solution.

The second experiment for validating the method was performed on a set of 18 selected accessions (Table S6, Fig. S1), grown in the same conditions. Plants were harvested at the estimated inflection point for rosette dry mass measurement (inflection point estimated from the first experiment, n = 3), and six replicates were harvested at the end of the life cycle for manual silique counting (n = 5).

Plant imaging and harvesting

All plants were daily imaged with 192 micro-cameras (5 Megapixel, OmniVision OV5647), two per tray, mounted between fluorescent light tubes in the RAPA room at MPI Tübingen. The recording and storage of tray pictures were managed through embedded computers (Raspberry Pi rev. 1.2, Raspberry Pi Foundation, UK). In addition, all trays were manually imaged every day during watering with a high-resolution camera (16.6 Megapixels, Fig. 1; Canon EOS-1, Canon Inc., Japan).

For the focal population harvested at fruit ripening, inflorescences and rosettes were separated and both separately photographed with a high-resolution camera (16.6 Megapixels, Canon EOS-1). The duration of growth (days) was estimated as the time in days between t₀ and harvesting. The rosettes, inflorescences and rockwool cubes that contain the roots were dried for at least three days at 65 °C, and weighed separately with a microbalance (XA52/2X, A. Rauch GmbH, Graz, Austria). Root dry mass of each individual was estimated as the difference in the weight of the dry rockwool cube before and after plant growth. Root and reproductive allocation were measured as the ratio of root and inflorescence dry mass, respectively, over total (rosette + roots + inflorescence) plant dry mass. For the training population harvested at 16 days after vernalization, rosette were dried at 65 °C for three days, and separately weighed with a microbalance (XA52/2X).

Statistical analyses

All coefficients of correlation (r²) used to estimate the prediction accuracy of our cross-validation approaches were obtained from Pearson’s coefficients between estimated and measured data, using the cor.test function in R. Non-linear fitting of the logistic growth functions (Eq. 2 in Table 1) were performed on every individual with the nls function in R (detailed code in Additional File 2). Broad-sense heritabilities (H²) were calculated with a Bayesian approach implemented in a MCMCglmm model performed in R, considering the accession as a random factor, as: where y is any trait of interest after logarithmic transformation for the individual k of genotype i, G_i is the identifier of the accession i, and e_ik is the residual error associated with every individual. H² was calculated at the proportion of genotypic variance over total variance :

Declarations

List of abbreviations

• t₀: first day of growth used for logistic fitting, when plants have two leaves of 3 mm² (see Additional File 2)

• t_i: inflection point (in days) of the logistic growth curve (corresponds to the point where the rosette is half it final dry mass, and where absolute growth rate is maximum)

• A: upper asymptote of the logistic growth curve (et as the rosette dry mass measured at the end of reproduction)

• B: inverse of the exponential constant of the logistic growth curve

• M: rosette dry mass (in mg)

• GR: absolute growth rate (in mg d⁻¹) measured by deriving the logistic equation of growth (Eq. 1 in Table 1)

• RGR: relative growth rate (mg d⁻¹ g⁻¹) measured as the ratio between GR and M for each time point throughout ontogeny.

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Availability of data and material

The datasets supporting the conclusions of this article are included within the article and its additional files. Correspondence and requests for materials should be addressed to or .

Competing interests

The authors declare no competing financial interests.

Funding

This work was supported by an ERC grant (ERC-AdG-IMMUNEMESIS, DW), and the Max Planck Society (FV, MEA, GW, DW). JB was funded by Alexander von Humboldt Foundation.

Author Contributions

FV, GW, JB, RS and DW designed the study. FV, RS and GW performed the experiments and extracted the data. FV, GW and JB performed image and statistical analyses, and wrote codes. All authors interpreted the results and wrote the paper.

Acknowledgements

We thank Jane Devos for her help in performing the experiments, and Denis Vile, Dominik Grimm and Moises Exposito-Alonso for helpful comments about image analysis and statistical modelling.