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Crop production, water productivity, and virtual waterA method to calculate the water needed for crops is the water footprint (WF). The WF has a color-based classification: green water (precipitation), blue water (ground and surface water), and grey water (water to dilute polluted water to accepted water quality standards). A manual on how to calculate WFs has been published12. Calculations of WFs integrate green and blue crop water use (evapotranspiration by crops) over the growing period of specific crops and express results per unit of yield (m3 kg−1). The difference between crop-water use and effective rainfall is applied as a proxy for blue WFs when no data on actual irrigation water supply are available. WFs of specific crops vary greatly among countries, and even within countries45. This means that water can be saved when crops are smartly traded. This may also be possible within a country if crops are grown where water productivity is the highest.Calculation of the water footprintWater footprints (WFs) are calculated as green and blue water footprints (WFgreen, WFblue, respectively) adopting the method from the WF manual12. This study assumes that the difference between crop water requirement and evapotranspiration of green water (ETGreen) in crops is equal to the evapotranspiration of blue water (ETblue); therefore, crop water requirements are met with irrigation water. The crop water requirements are estimated with the Food and Agriculture Organization’s CROPWAT model46. The selected methods for calculating the reference evapotranspiration (ET0) and effective precipitation (Peff) are the FAO Penman–Monteith method47,48 and the USDA’s SCS method48, respectively. Calculations were performed at the provincial scale for each crop. Equations (1) through (4) are applied to calculate WFgreen and WFblue for the crops included in this study:Actual crop evapotranspiration from reference evapotranspiration:$$ ET_{c} = sum_{t} {ET_{0} times K_{c} } $$
(1)
Reference evapotranspiration:$$ ET_{0} = frac{{0.408Delta left( {R_{n} – G} right) + gamma frac{900}{{T + 273}}U_{2} left( {e_{a} – e_{d} } right)}}{{Delta + gamma left( {1 + 0.34U_{2} } right)}} $$
(2)
$$ WF_{green} = 10 times frac{{min left[ {ET_{c} ,P_{eff} } right]}}{Y} $$
(3)
$$ WF_{blue} = 10 times frac{{max left[ {0,ET_{c} – P_{eff} } right]}}{Y} $$
(4)
where ETc denotes the actual crop evapotranspiration (mm) during the growth period (t), ET0 represents the reference evapotranspiration (mm day−1), and Kc denotes the crop coefficient based on crop type and development stages (initial, middle, and late stages). In Eq. (2) ea (kPa), ed (kPa), Δ (kPa °C−1), G (MJ m−2 day−1), T (°C), Rn (MJ m−2 day−1), U2 (m s−1), and γ (kPa °C−1) denote the saturation vapor pressure, the actual vapor pressure, the slope of the saturation-vapor pressure curve, the soil heat flux, the average air temperature, the net radiation on the crop surface, the wind speed measured at a height of 2 m above ground level, and the psychrometric constant, respectively. Equations (3) and (4) calculate the green and blue water footprints (m3 ton−1), in which Peff (mm), Y (ton ha−1), and 10, are represent effective precipitation, the crop yield, and a conversion factor from mm to m3 ha−1, respectively. WFgreen and WFblue occur in irrigated cultivation; however, there is only WFgreen in rainfed cultivation.Optimization of crop productionAll the steps of the methods used in this work were coded in MATLAB for use by decision-makers, planners, and interested organizations.Balancing the agricultural systemAn internal trade network was created to organize and remedy the weaknesses of the trade network. The lack of a comprehensive trade network has caused the crops to be exported regardless of the country’s demands, which eventually leads to the import of the same crops. The production and demand amounts of each crop in each province and their WFgreen and WFblue are determined with the following equations applied to N = 51 crops in J = 31 provinces:$$ {CP}_{(i,j)} = {ICP}_{(i,j)} + {RCP}_{(i,j)} $$
(5)
$$ {ICP}_{(i,j)} = left( {{BCY}_{(i,j)} times {ICA}_{(i,j)} } right) $$
(6)
$$ {RCP}_{(i,j)} = left( {{GCY}_{(i,j)} times {RCA}_{(i,j)} } right) $$
(7)
$$ {CD}_{(i,j)} = left( {{PCD}_{i} times {POP}_{J} } right) $$
(8)
$$ {TWF}_{blue(i,j)} = {ICP}_{(i,j)} times {WF}_{blue(i,j)} $$
(9)
$$ {TWF}_{green(i,j)} = {ICP}_{(i,j)} times {WF}_{green(i,j)} $$
(10)
where (i=1, 2,ldots , N;j=1, 2, ldots, J,) CP(i,j) (ton), ICP(i,j) (ton), RCP(i,j) (ton), BCY(i,j) (ton.ha−1), GCY(i,j) (ton.ha−1), ICA(i,j) (ha), RCA(i,j) (ha), CD(i,j) (ton), PCDi (ton.person−1), POPj (person), TWFblue(i,j) (m3), and TWFgreen(i,j) (m3) denote the production of crop i in province j, crop production of irrigated land, crop production in rainfed cultivation, irrigated crop yield, rainfed crop yield, irrigated acreage, rainfed areas acreage, demand for crop i in province j, per capita diet, population of province j, the blue WF of crop i in province j corresponding to irrigated cultivation, and the green WFs of crop i in province j corresponding to irrigated cultivation, respectively.TWFblue(i,j) equals zero in rainfed cultivation, and TWFgreen(i,j) is calculated with Eq. (10) based on RCP(i,j). The deficit or surplus over the demand of the provinces were determined by comparing CP(i,j) and CD(i,j) for each crop in each province. Equation (11) implies that CS(i,j) is the amount of crop i supplied in province j (ton), which involves the export and import of crops:$$ {CS}_{(i,j)} = {CP}_{(i,j)} – {CD}_{(i,j)} $$
(11)
where (i=1, 2,ldots , N;j=1, 2, ldots, J) .The internal trade network is formed once the deficit and surplus for each crop in the provinces is determined, and crops are traded based on the shortest distance between the provinces. The developed trade network would improve the country’s agricultural system and reduce transportation costs between the provinces. Each province adds to or subtracts Ti,j (ton) from its crop amounts, where imports imply an addition and exports a subtraction of crop amounts. The internal exports and imports of WFs and the net water footprints trade (NWFT) in each province are calculated as follows:$$ {WFT}_{(x,r,i)} = T_{(x,r,i)} times left( {{WF}_{green} + {WF}_{blue} } right)_{(x,i)} $$
(12)
$$EW{F}_{(x)}={sum }_{r,i}WF{T}_{(x,r,i)}$$
(13)
$$ IWF_{(r)} = sumlimits_{x,i} {WFT_{(x,r,i)} } $$
(14)
$$ {NWFT}_{(j)} = IWF_{(j)} – EWF_{(j)} $$
(15)
where (i=1, 2,ldots , N;j, x=1, 2, ldots, J, r=x-1), WFT(x,r,i) (m3), T(x,r,i) (ton), (WFgreen + WFblue)(x,i) (m3 ton−1), EWF(x) (m3), IWF(r) (m3), and NWFT(j) (m3) denote the WFs traded for crop i from exporting province x to importing province r, the amount of crop i exported from province x to province r, the blue and green WFs related to crop i in exporting province x, the WFs exported from province x by the trade of crops, the WFs imported into province r by the trade of crops, and the net water footprints trade in province j, respectively.The positive and negative values ​​of NWFT(j) represent the import and export of WFs to province j, respectively. The calculation of the internal trade between provinces with Eq. (11) permits determining the deficits and surpluses for each crop in the provinces nationally. At this juncture the provinces may resort to international trade to cope with deficits and surpluses. However, from this work’s premise of improving food security and self-sufficiency the cropping patterns of surplus crops in the provinces are modified as described in the next section.Modifying exports to optimize the cropping patternThe multi-objective optimization approach to increase food security and self-sufficiency redirects the resources to be used to cultivate export crops to the cultivation of crops that are in deficit (i.e., whose production is less than demand). This modification of cropping patterns in the provinces is based on their traditional cropping patterns. For this purpose, the internal trade network is linked to the optimization method to manage cropping patterns of the regions based on the output of the trade network, and on the goals of achieving food security and preventing water crisis. These two goals are pertinent in many countries where water scarcity is a limiting factor to achieve food security49. Therefore, concerning available agricultural water it is imperative to pay attention to the type of water (green or blue) used. Specifically, WFblue can be used in several areas of consumption; however, WFgreen is not controllable in the same manner. The usage of WFgreen by crops depends on the growing season, and the maximum use can be achieved by choosing the optimal crops. Therefore, this work treats WFgreen and WFblue as indicators of water crisis and food security, which were chosen as objective functions. In other words, controlling and managing WFs prevent its waste (thus reducing the water deficit and crisis). Selecting optimal crops based on WFs will increase production and food security. The water crisis and food security serve as the benchmark for comparison between the reference situation (without optimization) and the results of this new method. The reference situation refers to the initial state of food security and water crisis, which occurs before optimizing the cropping patterns.The food-security objective function is expressed as follows:$$F{S}_{i}=frac{{sum }_{j=1}^{J}C{P}_{(i,j)}}{{sum }_{j=1}^{J}C{D}_{(i,j)}}$$
(16)
The water-crisis objective function is written as follows:$${WC}_{j}=frac{sum_{i=1}^{N}{TWF}_{blue(i,j)}}{{RWR}_{j}}$$
(17)
where (i=1, 2,ldots, N=51;j=1, 2, ldots, J=31,) FSi, CP(i,j) (ton), CD(i,j) (ton), WCj, TWFblue(i,j) (m3), and RWRj (m3) denote the food security for crop i, production of crop i in province j, the demand of crop i in province j, the water crisis in province j, the blue WFs of crop i in province j, and the renewable water resources in province j, respectively.Maximizing the FS index and minimizing the WC index represent the ideal situation. The maximizing function was converted to a minimization function for the purpose of multiobjective optimization. The final form of the objective functions i given by the following equations:$$Min({Z}_{1})=frac{1}{N}{sum }_{i=1}^{N}(1-F{S}_{i})begin{array}{cc},& where,, F{S}_{i}end{array}=Minleft(frac{{sum }_{j=1}^{J}C{P}_{(i,j)}}{{sum }_{j=1}^{J}C{D}_{(i,j)}},1right)$$
(18)
$$Min({Z}_{2})=frac{1}{J}{sum }_{j=1}^{J}W{C}_{j}$$
(19)
where (i=1, 2,ldots , N=51;j=1, 2, ldots, J=31.) The objective function Z1 is calculated based on the food security index expressed as an average for all crops, and the objective function Z2 is calculated as the average of the water crisis indexes in the 31 provinces. Both objective functions are affected by cropping patterns and cultivation areas. The water and land used must be calculated prior to modifying the cropping patterns. The amounts of surplus crops in the provinces and their equivalent water and land are calculated using the following equations:$$ {SCP}_{(i,j)} = Max({CP}_{(i,j)} – {CD}_{(i,j)} + T_{(i,j)} ,0) $$
(20)
$$ {BCY}_{(i,j)} times (X_{1(i,j)} times ICA_{(i,j)} ) + {GCY}_{(i,j)} times (X_{2(i,j)} times RCA_{(i,j)} ) = {SCP}_{(i,j)} $$
(21)
where (i=1, 2,ldots, N;j=1, 2, ldots, J,) SCP(i,j), (X_{1(i,j)}), (X_{2(i,j)}) denote the surplus crop i in province j (ton) determined based on demand and trade in the province, and the percentage of crop i in province j that must be removed from irrigated and rainfed cultivation, respectively. The amount of water and land available for new cultivation are calculated as follows:$$ ICA_{j}^{free} = sumlimits_{i = 1}^{51} {X_{1(i,j)} times ICA_{(i,j)} } $$
(22)
$$ RCA_{j}^{free} = sumlimits_{i = 1}^{51} {X_{2(i,j)} times RCA_{(i,j)} } $$
(23)
$$ TWF_{blue,j}^{free} = sumlimits_{i = 1}^{51} {{WF}_{blue(i,j)} times BCY_{(i,j)} } times ICA_{j}^{free} $$
(24)
where (i=1, 2,ldots , N;j=1, 2, ldots, J,) ICAjfree and RCAjfree denote the total available area of ​​irrigated and rainfed cultivation (ha) in province j, respectively, and TWFblue,jfree represents the total amount of blue WFs available in province j (m3). It is noteworthy that the water and land available in irrigated cultivation can be altered. On the other hand, only the available land is controllable under rainfed cultivation.The objective functions of the proposed method [Eqs. (18) and (19)] were subjected to a set of constraints introduced next.

(i)

Modification of the cropping patterns

The available land in each province is allocated to crops that feature a deficit in the country and are part of the traditional cropping patterns of the provinces. The set of cultivable crops is determined using the following equation:$$ P = left{ {pleft| {p in i,sum_{j = 1}^{31} {SCP_{(p,j)} < 0} } right.} right} $$ (25) where p denotes the set of crops with deficit conditions in the country and SCP(i,j) was defined above. Letting traditional irrigated and rainfed cropping patterns be denoted by Aj and Bj in province j, respectively, the set of irrigated and rainfed crops cultivable in province j was calculated as follows:$$ IC_{j} = P cap A_{j} begin{array}{*{20}c} {} & {(j = 1,2,3,ldots,31)} \ end{array} $$ (26) $$ RC_{j} = P cap B_{j} begin{array}{*{20}c} {} & {(j = 1,2,3,ldots,31)} \ end{array} $$ (27) where (j=1, 2, ldots, J), ICj and RCj denote the irrigated and rainfed crops cultivable in province j, respectively. (ii) Constraint on cultivation area A fraction of ICAjfree can be used in irrigated lands:$$ 0 le M times sumlimits_{i = 1}^{51} {{(X}_{1(i,j)} times ICA_{(i,j)} ) le ICA_{j}^{free} } begin{array}{*{20}c} , & {0 le M le 1} & {} \ end{array} $$ (28) where (j=1, 2, ldots, J), and M denotes the fraction of blue water available. (iii) Constraint on water use The amount of water used to modify the cropping pattern in the provinces is limited:$$ sumlimits_{i = 1}^{51} {TWF_{blue(i,j)}^{m} le RWR_{j} - sumlimits_{i = 1}^{51} {TWF_{blue(i,j)} + } } TWF_{blue,j}^{free} $$ (29) where (left(j=1,2,3,ldots,Jright),) TWFmblue(i,j) denotes the blue WFs used to modify the cultivation in province j, and TWFblue(i,j) represents the initial blue WFs consumed in province j to cultivate crops before changing the cropping pattern.Ideal solution and pareto optimalityThis work applied the multi-objective optimization Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The NSGA is based on the Genetic Evolutionary Algorithm and the Selection, Crossover, and Mutation operations50. The NSGA was introduced by Deb et al.51,Srinivas and Deb52, then improved to the NSGA-II51. The NSGA-II has been widely studied in water resources management53,54,55.The NSGA-II produces a Pareto front of solutions, in which, each point represents a management scenario. The decision-maker selects a scenario based on the objective functions and situational analysis. Multi-criteria decision-making methods (MCDM) can be applied to select an efficient point on the Pareto front curve56,57. This work implements the technique for order preference by similarity to ideal solution (TOPSIS) as the MCDM employed for that purpose. A description of the TOPSIS method is presented in the appendix.The NSGA-II parameters were determined based on a trial-and-error process. Multiple runs of the algorithm were used to adjust the parameters to reduce uncertainty. For this purpose, the population size and maximum iteration were set equal to 400 and 500, respectively, and the crossover and mutation rates were set equal to 0.8 and 0.1, respectively. The flowchart of the proposed approach is displayed in Fig. 1.Figure 1Flowchart of the methodology.Full size image More

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Culture maintenance and growthTwelve strains of Thalassiosira spp. were obtained from the Provasoli-Guillard National Centre of Marine Phytoplankton (NCMA, https://ncma.bigelow.org/), and one strain from the Australian National Culture Collection, representing 7 species in total (Supplementary Table 1). Cultures were maintained in polystyrene tissue culture flasks in artificial seawater with f/2 media [37] at 20 °C, with 60 µmolm−2s−1 of light on a 12:12 light cycle.Three strains originally identified as Thalassiosira sp. in the NCMA collection were further classified to the species level using sequencing of the ITS2 gene region (Supplementary Table 1): CCMP1055 as T. auguste-lineata (84.64% similarity; [38]) and CCMP2929 as T. weisflogii (98.37% similarity to Strain 1587 used in our study; [39]). Strain CCMP1059 was tentatively identified as Cyclotella striata (94.17% identity match to clone ZX28-3-40; [40]) also from order Thalassiosirales, but this assignment requires further investigation.Experimental set upExperimental cultures (200 mL) were grown in 250 mL polystyrene tissue culture flasks in triplicate, at a starting concentration of 2500 cells ml−1. All 13 strains were grown in a “standard” environment (identical to maintenance conditions) with 9 phenotypic traits measured to describe the initial trait-scape. Five strains (1010, 1059, 2929, 3264, and 3367) were grown in two additional environments in triplicate: a high temperature and light treatment (HT: 30 °C, 200 µmol photons m−2s−1 of light, 12:12 light:dark), and a low nutrient treatment (LN: f/400 media with an adjusted N:P ratio of 10:1 achieved by reducing the nitrate concentration from 4.4 to 1.8 µM, 60 µmol photons m−2s−1 of light, 12:12 light:dark). Cultures for the two additional treatments were inoculated with 10,000 cells ml−1 (LN) and 5,000 cells ml−1 (HT) in anticipation of limited growth.Growth was tracked daily using in vivo fluorescence as a proxy for cell density [41]. One mL aliquots of experimental cultures were measured for chlorophyll-a fluorescence using a plate reader (TECAN Infinite M1000 Pro, Männedorf, Switzerland) using 455/680 nm excitation/emission spectra. Phenotypic traits were measured at mid-late exponential phase, assessed by visually examining in vivo fluorescence growth curves. In the case of the low nutrient treatment, where growth was limited to 3–5 days, cultures were harvested in early stationary phase. Duration of growth for each experiment is summarised in Supplementary Table 2.Phenotypic trait measurement methodsPhenotypic traits were selected to capture different commonly measured base physiological functions, and to include traits that are used in biogeochemical models. We also selected traits that demonstrated independence and orthogonality (i.e., not all co-varying), based on pilot studies, in order to successfully define the multivariate trait-scape [42].Growth rateGrowth rates for each time step were calculated from the daily in vivo fluorescence measurements according to the calculation:$$mu = frac{{{{{{{{{mathrm{ln}}}}}}}}left( {F_2} right)-{{{{{{{mathrm{ln}}}}}}}}left( {F_1} right)}}{{t_2 – t_1}}$$Maximum growth rates were determined by the average growth over 2–4 consecutive steps depending on the duration of exponential growth.Flow cytometry traitsFor flow cytometry trait measures (growth rate, size, chlorophyll a content, lipid content), 1 mL aliquots of experimental culture were fixed with EM grade paraformaldehyde (0.8% final concentration, Electron Microscopy Sciences, Ft Washington, PA) in 1.6 mL cryopreservation tubes (CryoPure, Sarstedt), frozen in liquid nitrogen, then stored at −80 °C prior to analysis. All measures were performed using a Cytoflex LX (Beckman Coulter, CA, USA).Cell counts and sizeCell counts were done by gating the diatom population using chlorophyll a (488 nm excitation, 690/50 nm detector) and forward scatter channel thresholds. Cell size was estimated using forward scatter values calibrated against spherical beads (2, 4, 6, 10, 15 µM diameters; Invitrogen, CA). This resulted in a conversion equation of equivalent spherical diameter (ESD) = (FSC + 194636)/75775, which was used to assess relative changes in cell size [43].Chlorophyll a contentChlorophyll a (Chl-a) fluorescence of the gated diatom population was quantified using 488 nm excitation, 690/50 nm detection. A standard bead (Cytoflex Daily QC Fluorospheres; Beckman Coulter) was used to calibrate the performance of the instrument and ensure comparable measures across samples. Chlorophyll values were divided by ESD to account for cell size differences.Side scatter/granularitySide scatter is an indicator of the internal complexity of a cell or “granularity”. This trait is measured in tandem with other flow cytometry measures and was included as a phenotypic trait. The interpretation of this trait is not straight forward, but is independent of other flow cytometry traits measured and has been used in other flow cytometry studies of microalgae [44]. This trait was divided by ESD to account for cell size differences.Neutral lipidsRelative neutral lipid content was determined using the fluorescent stain BODIPY™ 505/515 (Thermo Fisher, MA, USA) which is commonly used to assess neutral lipid content in phytoplankton [45,46,47]. Background fluorescence (488 nm excitation, 525/40 nm detector) of PFA-fixed cells was measured in tandem with the size, chlorophyll a, and side scatter. After this, 10 µL of BODIPY stain (2 mg mL−1 in DMSO) was added to each sample, resulting in a final BODIPY concentration of 2 μg mL−1. Samples were incubated for 10 min in the dark before being read again on the flow cytometer. Neutral lipid content was defined as the difference in median fluorescence per cell between the pre- and post-stained sample. This value was then divided by the ESD size to account for size-related effects.Photophysiological traitsPhotophysiological measures were taken by conducting a rapid light curve [48] with a water PAM (Water-PAM; Walz GmbH, Effeltrich, Germany) using 1 mL of experimental culture diluted in artificial seawater. The rapid light curve protocol exposes the culture to 8 steps of increasing irradiance for 10 seconds each, measuring the photophysiological response at each step. Maximum electron transport rate (ETRmax), Ik (half saturation irradience), and alpha (the photosynthetic rate during the light-limited linear region) were calculated using the regression fit function in the PAM WinControl software. Photophysiology measurements were taken between 4–5 h after the start of the photoperiod.Reactive oxygen speciesThe development of reactive oxygen species (ROS) was measured using the fluorescent probe 2’,7’-dichlorodihydrofluorescein diacetate (H2DCFDA; Thermo Fisher, MA, USA) which has been used in a number of phytoplankton studies [49,50,51]. Two 1 mL aliquots of experimental culture were transferred to a 48 well tissue culture plate; 2 µL of stain (2.5 mg mL−1 H2DCFDA was made in DMSO) was added to one aliquot, with the other acting as a blank. The plates were sealed (Breathe-Easy, Diversified Biotech) and incubated in the dark at growth temperature (20 or 30 °C) for 2 h. Incubation was done in the dark because of the effects of light on the dye itself, therefore the effects of the excess light treatment were not captured in this trait. Fluorescence of H2DCFDA was read using a plate reader with 488 nm excitation 525 nm emission (TECAN Infinite M1000 Pro, Männedorf, Switzerland). ROS concentration was estimated as the difference in fluorescence units per cell between the stained and unstained aliquots of each culture. This metric was also divided by ESD size to account for size effects.Taxonomic confirmation of strainsDNA from stock cultures (10 mL) was extracted using a DNeasy PowerSoil kit (QIAGEN Inc., CA, USA) and checked for quality with a NanopDrop™ 2000 (ThermoFIsher Scientific, MA, USA), before amplification and sequencing at the Australian Genome Research Facility (AGRF, Sydney, Australia). PCR conditions and primers used were those developed by Chappell et al. [52] for the ITS region: forward primer: 5ʹ-RCGAAYTGCAGAACCTCG-3ʹ, reverse primer: 5ʹ-TACTYAATCTGAGATYCA-3ʹ.Bioinformatics processing was conducted using Geneious Prime (Version 2020.0.5; Biomatters Ltd.). Strain sequences were compared to GenBank using the BLAST function to confirm species identity. Nucleotide sequences were aligned using the MUSCLE alignment [53], followed by Bayesian inference analysis using MrBayes [54] to generate a phylogenetic tree. The out-group for the tree was a strain of Chaetoceros atlanticus isolate TPV2 1146 obtained from GenBank. Percentage similarity between strains according to the alignment was used as a metric of genetic relatedness.Statistical analysisWe assessed the multivariate phenotypes for the Thalassiosira strains using principal component analysis (PCA). The input variables were the 9 independent trait measurements made on each replicate culture (n = 36, 3 biological replicates per strain). Trait data was standardized (mean = 0, SD = 1) for each trait prior to PCA analysis to account for differences in the units and scale of measurements. The resulting PCA plot was defined as the ‘trait-scape’.Hierarchical clustering analysis was performed on the 9-trait dataset used to assess similarity in multivariate phenotypes between each replicate for each strain (n = 3 per strain).To compare genetic vs. phenotypic similarity, percentage similarity between strains was correlated against the distance between strain centroids (multivariate means) within the trait-scape. Distances between multivariate means (centroids) were calculated using the equation:$${{{{{{{mathrm{distance}}}}}}}} = sqrt {left( {{{{{{{{mathrm{{Delta}}}}}}}PC}}1.{{{{{{{mathrm{a}}}}}}}}} right)^2,+,left( {{{{{{{{mathrm{{Delta}}}}}}}PC}}2.{{{{{{{mathrm{b}}}}}}}}} right)^2}$$ΔPC1 is the difference in PC1 co-ordinates between the two strains, a is the % variance explained by PC1, ΔPC2 is the difference in PC2 co-ordinates between the two strains, b is the % variance explained by PC2.To assess whether a trait-scape generated using fewer input traits (4 rather than 9) was representative of the full, 9-trait plot, we conducted PCA using 4 input traits, and then assessed whether the inter-strain distances (distances between centroids) within the plot were correlated using linear regression. This provided a quantitative assessment of whether the strains were in the same relative positions to each other within the trait-scape.Covariation of traitsTo compare the pairwise relationships between traits across the strains, correlation matrices were made using data collected in the standard environment, and for the HT and LN environments.Phenotypic plasticityThe change in phenotypes in the new environments were assessed firstly by conducting PCA on the full dataset, including trait data from the 13 strains grown in the standard environment, plus the 5 strains grown in the two additional environments. This generated an “expanded trait-scape”. In addition, correlation matrices were generated for the new environments’ trait dataset to assess differences in trait-trait relationships between the ‘standard’ and “expanded” datasets.Relative changes in trait values for each trait in the new environments were calculated as follows:$$ {{{{{{{mathrm{Relative}}}}}}}},{{{{{{{mathrm{change}}}}}}}} \ = frac{{{{{{{{{mathrm{trait}}}}}}}},{{{{{{{mathrm{value}}}}}}}},{{{{{{{mathrm{new}}}}}}}},{{{{{{{mathrm{environment}}}}}}}} – overline {{{{{{{mathrm{x}}}}}}}} ,,{{{{{{{mathrm{trait}}}}}}}},{{{{{{{mathrm{value}}}}}}}},{{{{{{{mathrm{standard}}}}}}}},{{{{{{{mathrm{environment}}}}}}}}}}{{overline {{{{{{{mathrm{x}}}}}}}} ,,{{{{{{{mathrm{trait}}}}}}}},{{{{{{{mathrm{value}}}}}}}},{{{{{{{mathrm{standard}}}}}}}},{{{{{{{mathrm{environment}}}}}}}}}}$$We used PCA to assess whether the relative changes in trait values were consistent between strains in the two different environments. i.e., was the relative change in whole phenotype consistent. If the changes were consistent across strains, we expected to see clustering in the PCA based on treatment.Statistical softwareStatistical analyses were performed in R [55], Matlab, and Microsoft Excel. Hierarchical clustering analysis with multiscale bootstrap resampling (1000 replicates) on trait values from biological replicates was done with the ‘pvclust’ package in R [56] using Euclidean distance and the average (UPGMA) method. Principal component analysis was used to generate the multivariate trait-scape was done using the “vegan package” in R [57]. The contributions of each trait to the PC axes (loadings) were extracted using the “factoextra” package in R [58]. Trait correlation matrices were generated using the “corrplot” package in R [59]. More