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Journal of Thermal Biology

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Discovering divergence in the thermal physiology of intertidal crabs alonglatitudinal gradients using an integrated approach with machine learningSebastian J.A. Osoresa, Gonzalo A. Ruza,c, Tania Opitza, Marco A. Lardiesb,⁎

a Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chileb Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Santiago, Chilec Center of Applied Ecology and Sustainability (CAPES-UC), Santiago, Chile

A B S T R A C T

In intertidal marine crustaceans, phenotypic variation in physiological and life-history traits is pervasive along latitudinal clines. However, organisms have complexphenotypes, and their traits do not vary independently but rather interact differentially between them, effect that is caused by genetic and/or environmental forces.We evaluated the geographic variation in phenotypic integration of three marine crab species that inhabit different vertical thermal microhabitats of the intertidalzone. We studied seven populations of each species along a latitudinal gradient that spans more than 3000 km of the Chilean coast. Specifically we measured ninephysiological traits that are highly related to thermal physiology. Of the nine traits, we selected four that contributed significantly to the observed geographicalvariation among populations; this variation was then evaluated using mixed linear models and an integrative approach employing machine learning. The resultsindicate that patterns of physiological variation depend on species vertical microhabitat, which may be subject to chronic or acute environmental variation. Thespecies that inhabit the high- intertidal sites (i.e., exposed to chronic variation) better tolerated thermal stress compared with populations that inhabit the lowerintertidal. While those in the low-intertidal only face conditions of acute thermal variation, using to a greater extent the plasticity to face these events. Our mainresults reflect that (1) species that inhabit the high-intertidal maintain a greater integration between their physiological traits and present lower plasticity than thosethat inhabit the low-intertidal. (2) Inverse relationship that exists between phenotypic plasticity and phenotypic integration of the physiological traits identified,which could help optimize energy resources. In general, the study of multiple physiological traits provides a more accurate picture of how the thermal traits oforganisms vary along temperature gradients especially when exposed to conditions close to tolerance limits.

1. Introduction

Physiological patterns that characterize different populations arestrongly defined by environmental conditions (Hoffmann and Parsons,1989; Somero, 2002; Khaliq et al., 2014) that, among others, determinedistribution ranges, tolerance capacities, and ultimately organismalfitness. One of the main abiotic factors that affects physiologicalchanges in ectotherm organisms is temperature (Johnston and Bennett,2008; Castañeda et al., 2005; Mora and Maya, 2006; Angilletta, 2009;Lardies et al., 2011). Specifically, temperature has been shown to in-fluence basic organismal functions, biochemical rates, locomotion,growth and reproduction (Kingsolver and Huey, 2008; Somero, 2010;Gaitán-Espitia et al., 2013a, 2013b, 2014). Therefore, temperatureplays a fundamental role in species distribution patterns (Somero, 2005;Deutsch et al., 2008; Calosi et al., 2008). Latitudinal gradients alongwith intertidal gradients provide natural variation that can be used toinvestigate how temperature affects thermal physiology (Stillman andSomero, 2000; Helmuth et al., 2006). Coastal areas can be considered asnatural laboratories where resident organisms may differ in terms oflocal adaptation and/or phenotypic plasticity, both mechanisms that

allow populations to maximize fitness in response to environmentalheterogeneity (Gardiner et al., 2010; Yampolsky et al., 2014).

Variations in physiological traits along environmental gradients arecauses and consequences of phenotypic divergence in natural popula-tions (Torres Dowdall et al., 2012), conferring local fitness advantages(Kawecki and Ebert, 2004). In general, these evaluations of phenotypicdifferentiation have been often correlated usually with latitude(Lindgren and Laurila, 2009; Zippay and Hofmann, 2010). Overall, Theproblem is that the statistics are limited due to the lack of flexibility byincorporating only univariate and linearity for estimations (Naya et al.,2011; Sunday et al., 2014; Weber et al., 2015) with a limited capacity ofdata interpretation. Others have shown that environmental variationaffects integrated phenotypes involving several co-dependent traits(see, Salazar-Ciudad, 2007; Armbruster et al., 2014). Furthermore,phenotypic integration provides an explanation for how phenotypes aresustained by relationships between traits (Pigliucci and Preston, 2004).Because physiological traits play an important role in fitness (Ricklefsand Wikelski, 2002), the environmental characterization plays an im-portant role in the local adaptation for the effectiveness in the survivaland reproduction of the populations (McLean et al., 2014). In this sense,

https://doi.org/10.1016/j.jtherbio.2018.09.016Received 29 December 2017; Received in revised form 14 September 2018; Accepted 21 September 2018

⁎ Correspondence to: Universidad Adolfo Ibañez, Diagonal Las Torres 2640, Peñalolen, Santiago, Chile.E-mail address: marco.lardies@uai.cl (M.A. Lardies).

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understanding how environmental gradients (for example, tempera-ture) have effects on physiological traits is desirable to understand howthe increase in global temperature can affect different populations(Magozzi and Calosi, 2015). In general, measuring physiological traitsin a population reflects the costs and benefits associated with somaticmaintenance in thermal environments (Heusner, 1985; Clarke andJohnston, 1999; Watson et al., 2014). Metabolic rate is the mainparameter used to measure subsistence energy costs being directly re-lated thermal sensitivities (Ruel and Ayres, 1999; Kovac et al., 2014)and thermal safety (see Sunday et al., 2011). Recovery time after cri-tical thermal events also provides an index of how sensitive species areto climate (Castañeda et al., 2004, 2005). Also, morphometric char-acteristics have been shown to follow some biogeographic patterns,mainly latitudinal patterns (Angilletta et al., 2004; Bidau and Martí,2007; Zamora‐Camacho et al., 2014).

Analyses involving computational intelligence could provide anunderstanding of the patterns that emerge from the interaction betweenorganismal traits and how these interactions can be modified by theenvironment (Park and Chon, 2007). In most cases, these interactionsbetween traits are often too complex and do not meet the assumptionsof conventional statistical procedures (Recknagel, 2001; Kampichleret al., 2010). Machine learning has many applications (see Olden et al.,2008; Thessen, 2016), but notably it has been shown to be useful whendisentangling associated variables to gain a deeper understanding ofmultiple interactions (Peters et al., 2014). In this sense, the phenotypicdivergence in an integrated phenotype has been related to the relativelylow amounts of phenotypic covariance in closely related populations(Game and Caley, 2006; Renaud et al., 2006) and other studies haveshown otherwise (Arnold and Phillips, 1999), generally adjustingmultivariate linear models. Therefore, more studies comparing the re-lationships between the traits are clearly necessary to understand thelink in the divergence between populations. The number of methodsused for integration in machine learning has grown steadily (Acevedoet al., 2009; Valletta et al., 2017). Therefore, there are multiple modelsthat differ in the technique of integrating the variables. Overall, inorder to better understand associations between multiple associatedvariables, a reduction in dimensionality is a key factor in the simplifi-cation of analysis (Kasun et al., 2016). Machine learning methods, ingeneral can fall into two categories: (1) unsupervised learning (i.e.,clustering), that identifies patterns in a heuristic way (Sathya andAbraham, 2013) and (2) supervised learning (i.e., classification) whichcan be used to infer a function from labeled training data. Due to theexistence of many methods that perform similar machine learningfunctions, it is pertinent to compare different algorithms, since theperformance of each algorithm differs given the clustering/classifica-tion problem (Caruana and Niculescu-Mizil, 2006; Übeyli, 2007), inorder to unmask the patterns of association between the traits thatemerge from the population divergence.

Using three crab species, which are distributed along a small ver-tical intertidal gradient (i.e. intertidal zone), we analyzed variation inthermal exposure at different spatial/temporal scales. Specifically,crabs in the lower intertidal experience acute thermal variation becausethey are exposed to periods of greater thermal changes only in periodsof extremely low tides, while those in the high intertidal experiencechronic thermal variation determined by daily tidal cycles. In addition,different populations of these species are distributed along a latitudinal-environmental gradient that covers more than 3000 km and is markedby gradual thermal variation (Barría et al., 2014; Gaitán-Espitia et al.,2014). We performed trait integration using machine learning, whichallowed us to unravel differences that exist in the degree of associationamong physiological traits of crabs and their relation with phenotypicplasticity (see Gianoli and Palacio‐López, 2009). To investigate thephysiological divergence among these closely related organisms thatinhabit different habitats, we determined the variation in the pheno-typic matrix. Finally using both conventional statistics and machinelearning methods, we investigated the thermal geographic variation of

physiological traits in intertidal crabs to determine the variation in acomplex phenotype along the latitudinal and intertidal gradients.

2. Materials and methods

2.1. Model species and intertidal variability

Samples of three species of intertidal crustaceans (i.e., Cyclograpsuscinereus, Petrolisthes violaceus, and Petrolisthes tuberculosus) were usedfor this study. Specifically, samples were collected at three differentlevels within the intertidal zone: High (0.6–1.0m), Middle (0.3–0.5m)and Low (0.1–0.2m). The high intertidal is characterized by chronicenvironmental variability, the low intertidal experiences acute varia-bility, and the middle intertidal can be considered as a transition zone.The species used here have broad latitudinal distributions: C. cinereus(from Ancon, Peru to Calbuco, Chile), P. violaceus (Callao, Peru toPeninsula de Taitao, Chile) and P. tuberculosus (Callao, Peru to Chiloe,Chile) (Zagal and Hermosilla, 2007). The samples were collected fromseven locations along the coast of Chile: Iquique (20° 19′ 07.5′′), An-tofagasta (23° 46′ 30.8′′), Talcaruca (30° 29′ 32.9′′), El Tabo (33° 27′23.8′′), Lenga (36° 45′ 36.6′′), Playa Rosada (39° 49′ 46.4′′), and PlayaBrava (41° 52′ 00.4′′) (see SM1; Fig. 1). The sampled locations coveralmost the complete geographic range of these species in Chile(3000 km). It should be noted that within the wide latitudinal rangethat covered our study, two barrier with strong environmental changescould be identified: 1) biogeographic break at 30°S has been identifiedwithin the latitudinal range sampled. Specifically, the composition andabundance of biota differ on either side of this break (Navarrete andWieters, 2000; Navarrete et al., 2014). 2) Environmental barrier oflower intensity at 36°S has also been documented in coastal zones (seeFig. 1) and has been attributed to the Neogene development of ashallow oxygen minimum zone (OMZ) (Martinez-Pardo, 1990) andwind-induced coastal upwelling. In each sample site, we monitored thetemperature of the intertidal continuously using high-resolution loggers(Tidbit®, Onset Computer Corp., MA, USA). The thermal loggers usedtrack both sea surface temperature as well as air temperature duringextreme tides; thus, we recorded the environmental temperature fluc-tuations characterizing these sites every 30min during three years.

The crabs were collected during spring of 2012–2013 (see SM1),and to remove possible effects of sex, only male crabs were collectedand used in the physiological measurements. Covered with icepacksand placed in a cooler, sampled individuals were transported to thelaboratory of evolutionary ecology at the University Adolfo Ibáñez,Santiago, Chile. Crabs were acclimated for three weeks to the followingconditions: artificial seawater at 33 psu (Instant Ocean®), temperatureof 14 °C, photoperiod of 12:12 light/darkness, aeration and constantfeeding (Instant Algae, Shellfish Diet® and TetraFin Food Flakes®).

2.2. Physiological traits

2.2.1. Metabolic Rate 14 °C (MR14) and 20 °C (MR20)The metabolic rate was calculated based on the oxygen consump-

tion during a period of time (Gaitán-Espitia et al., 2014, 2017). Afteracclimation, each crab was incubated in artificial seawater at 14 °C andplaced in 113ml respirometric chambers. The oxygen concentrationwithin the chamber was quantified every 15 s for a maximum of 2 h anoptical sensor connected to an Oxygen register MINI-OXY-4 (PreSens,GmbH, Germany), If the concentration is reduced below 75% of theinitial oxygen concentration, the incubation is over. The sensor wascalibrated with synthetic seawater (saturated: 100%) and a sodiumsulfite solution (0%). We determine the metabolic rates of the crab at14 °C (mean temperature of the coast of Chile; see Gaitán-Espitía et al.,2017). Then, we acclimated the crabs to 20 °C for a period of threeweeks to estimate the metabolic rate at that temperature. The 6 °C ofthermal increase in our experimental treatments are consistent with thetrend of the increase in the average ambient temperature expected for

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the year 2100 under the business-as-usual scenario (Gatusso et al.,2015) In both cases, we used four respirometric chambers simulta-neously, of which three chambers contained animals and one chamberwas used as a blank. We used for metabolic rate estimations at least 30individuals by each population.

2.2.2. Thermal traitsTo examine the responses of the different populations to thermal

shock, the thermal performance of the animals was analyzed by mea-suring the righting response or rollover speed (i.e., the speed at whichan individual changed from an inverse position to an upright position)(see Lutterschmidt and Hutchison, 1997; Castañeda et al., 2004). Crabswere exposed to thermal shock in individual acrylic chambers(160×110×40mm) with six subdivisions (50× 50×40mm). Thechambers were placed within a thermoregulatory bath (© Lab. Com-panion RW-2025 ± 0.5 °C), which was manipulated to increase ordecrease the temperature. The crab roll-over speed was measured every1 °C changing the temperature of water bath every 30min from 9 °C to0 °C to search the critical thermal minimum (CTmin), and from 25 °C to40 °C for critical thermal maximum (CTmax). If after 10min of evalua-tion, the crab was not able to roll-over into a vertical position, then theminimum and maximum temperature when such an event occurred wasconsidered as CTmin and CTmax, respectively (Castañeda et al., 2004).The difference between CTmax and CTmin was the thermal range inwhich organisms were able to maintain their normal motor functions.

2.2.3. Recovery time from CTmin (RTC)Once the CTmin for crabs was determined, the crabs were placed at

14 °C inside an aquarium with seawater (33 psu), and then we regis-tered the time it took them to recover their ability to move, i.e. theirRecovery time (see Castañeda et al., 2005).

2.2.4. Morphometric measurementsBefore and after the physiological measurements, the crabs were

placed on a paper towel to eliminate the excess of water and then thewet body mass (WW) was recorded using a 0.0001 precision analyticalbalance (Shimadzu AUX220®). In addition to recording the measure-ments of cephalothorax width (CW) and cephalororax length (CL) witha 0.1 mm precision caliper.

2.3. Trait selection, comparisons of physiological trait means andphenotypic plasticity index

Using the nine traits recorded we trained a classifier using LearningVector Quantization (LVQ); adjusting the model with each populationof the crabs studied, using these as class label. Using a greedy approach,traits were removed one by one and after each removal the effects onthe classification performance were measured. From this, we were ableto select the relevant traits using the absolute value of the t-statistic foreach parameter of the models; this was done using the varImp functionextracted from the CARET package (Kuhn, 2008). Also, we removedfeatures that were redundant, particularly those that were highly cor-related (i.e., absolute correlation coefficient> 0.85). Then, traits thatare eliminated in the subset of data are those traits that have a lowerranking depending on the pre-classification made, in other words ROCcurve analysis is conducted on each predictor. The sensitivity andspecificity are computed for each cutoff and the ROC curve is com-puted. The trapezoidal rule is used to compute the area under the ROCcurve. This area is used as the measure of variable importance.

Using a generalized linear mixed model (GLMM), we evaluated theeffect of latitude on the selected physiological traits, taking into ac-count the nested structure of our design (i.e., sample sites nested withinthe regions defined according to the two environmental barriers men-tioned above). Hence, we considered two zones with abrupt environ-mental differences along the latitudinal gradient: 1) biogeographicbreak located at 30°S near the Talcaruca site and 2) an environmentalbarrier at 36°S near the Lenga site. These breaks allow us to divide ourstudy area into northern, central, and southern regions (see Fig. 1A).

Fig. 1. Geographic and environmental gradient of the study area and thermal tolerances of the study organisms along the southern Pacific. (A) Study sites along theChilean coast. Mean (black points, mean ± standard deviation), maximum (red points) and minimum temperature registered (blue points) at the sampling sites.Critical temperatures of the different studied organisms; (B) Cyclograpsus cinereus; (C) Petrolisthes violaceus and (D) Petrolisthes tuberculosus. (blue line = CriticalThermal Minimum, red line = Critical Thermal Maximum, mean ± standard deviation). (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

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Field sampling included sites within different regions (i.e. north, centerand south). In the model, then these interzones were used as a structureof dependency as random factor and the sampling sites were included asfixed effects. Akaike's Information Criterion (AIC) was used to choosethe best model. Statistical analyses were performed using the lme4package (Bates et al., 2007) implemented in the R platform 2.15.0 (RDevelopment Core Team 2009).

We quantify the phenotypic plasticity, based on the phenotypicdistance between individuals of a given species, exposed to differentenvironments, which is summarized in a relative distance plasticityindex (Relative Distance Plasticity Index: RDPI), which translates asphenotypical Absolute Distances between individuals of the same gen-otype and different environments, divided by one of the two phenotypicvalues. The RDPI values range from 0 (no plasticity) to 1 (maximumplasticity) and can be obtained for each species as:

= +( )RDPI d x x n/( ) /ij i j i j ij

where n is the total number of distances, xij is a trait in a rectangularmatrix where i (rows) represents a given level of the environmentaltreatment, and j (column) refers to the individual number identificationlong a given row. Specifically, it is defined the distance among traitvalues dij i j for all pairs of individuals for which i is different from i asthe absolute value of difference x xi j ij when i i , and obtain relativedistances by dividing this difference by the sum +x x( )i j ij (for moredetails on the calculation of RDPI see Valladares et al., 2006; Grasseinet al., 2010; Ameztegui, 2017).

2.4. Phenotypic integration with machine learning

Multivariate analyses were performed to identify physiological

patterns and to evaluate how they vary biogeographically along theChilean coast. For this, unsupervised and supervised machine learningalgorithms were employed and compared using the physiological datamatrix that included the four variables shown in Table 1. All theseanalyses were carried out using the statistical software R.

2.4.1. Unsupervised learningWe used unsupervised learning to know a priori the physiological

behavior of the species distributed along the environmental gradients.In this sense, the application of unsupervised algorithms helped us togroup the physiological behavior of the species and to determine if theywere correlated with geographic variation and/or environmental gra-dients. For the above, we used two different algorithms: k-means andexpectation maximization (EM), which are similar in their iterativeforms, but differ in their metric performances (Jung et al., 2014):

2.4.1.1. k-means. The well-known k-means clustering algorithm is usedto discover natural groupings within a data set. The number of clusters(k) must be specified by the user before running the algorithm. Toovercome this problem, several methods for automatically selecting themost plausible number of clusters have been developed. Here, weselected k by computing Dunn's cluster validity index (Havens et al.,2008).

2.4.1.2. Expectation maximization algorithm (EM). The EM algorithm isan iterative procedure to compute the Maximum Likelihood (Ml)estimate for the presence of missing or hidden data. With this, it ispossible to estimate the model parameter(s) for which the observeddata are the most plausible. In this study, as an alternative to k-means,we used the EM algorithm for clustering as well, where the missing or

Table 1Generalized linear mixed model of physiological traits (cephalothorax length, heat coma, chill coma and metabolic rate) for the three crab species (significantdifferences at different levels: 0.001= "***", 0.01= "**", 0.05= "*", 0.1= "*").

C. cinereus P. violaceus P. tuberculosus C. cinereus P. violaceus P. tuberculosusCoefficients Metabolic Rate at 14 °C Chill Coma

Estimate (Conf. Int.) Estimate (Conf. Int.) Estimate (Conf. Int.) Estimate (Conf. Int.) Estimate (Conf. Int.) Estimate (Conf. Int.)

Fixed EffectIntercept 1.61 (0.13–3.09) 2.07 (−0.73 to 4.88) 5.04 (1.67–8.42) ** 5.25 (3.70–6.80) * 6.90 (6.52–7.28) ** 5.23 (4.48–5.98) *Latitude −0.05 (−0.09 to 0.00) −0.06 (−0.15 to −0.02) −0.16 (−025 to −0.06) *** −0.05 (−0.10 to 0.00) −0.06 (0.07 to −0.05) * −0.01 (−0.04 to 0.01)Random Effectσ2 0.737 0.953 0.864 0.994 0.323 0.673τ00, Geo 0.107 0.662 1.772 0.108 0.000 0.013Biogeographic

breaksNorth-Center *** *** ***Center-South * *** **Observations 192 186 183 192 186 183AIC 506.180 540.320 515.913 562.885 336.379 465.122

C. cinereus P. violaceus P. tuberculosus C. cinereus P. violaceus P. tuberculosusCoefficients Heat Coma Cephalothorax Length

Estimate (Conf.Int.)

Estimate (Conf. Int.) Estimate (Conf. Int.) Estimate (Conf.Int.)

Estimate (Conf. Int.) Estimate (Conf. Int.)

Fixed EffectIntercept 22.66

(14.69–30.63) **34.48 (29.79–39.18) *** 33.73 (30.01–37.45) *** 7.83 (2.27–13.39) * −10.61 (−25.19 to 3.96) −5.30 (−15.73 to 5.12)

Latitude 0.30 (0.14–0.47) * −0.22 (−0.35 to −0.10) ** −0.24 (−0.34 to −0.14) *** 0.05 (−0.10 to 0.20) 0.74 (0.40–1.09) *** 0.52 (0.23–0.82) **Random Effectσ2 2.271 1.469 0.874 2.314 9.717 8.638τ00, Geo 27.805 4.275 2.890 5.508 70.511 15.666Biogeographic

breaksNorth-Center *** *** *** *** *** ***Center-South *** *** *** ***Observations 192 186 183 192 186 183AIC 727.295 622.280 518.712 727.735 971.602 932.378

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hidden data corresponded to the cluster labels of each instance (row) ofthe data matrix, using a priori from two to eight mixtures (i.e. clusters)(see Fort and Mungan, 2015; Garriga et al., 2016). While k-means uses adistance measure (typically Euclidean distance) to assign each datapoint to a cluster, the EM algorithm computes the posterior probabilityof each data point belonging to a cluster.

2.4.2. Supervised learning (classifiers)We used supervised learning to determine if the physiological pat-

terns integrated using different machine learning models followed adistribution in function of predetermined data subsets. The two pre-determined subsets were defined: a fine model, in which we constructedone subset for each sample site (seven subsets in total), and a coarsemodel where three subsets were constructed to represent the three re-gions previously described (north, center and south). This design waschosen to identify the most important traits and potential groupingbetween close or environmentally similar sites. We recognized thepossibility that traits could vary integrally or could vary inter-dependently of the environmental gradients. Overall, this analysis wasemployed to provide knowledge of whether differences among traitswere determined by environmental pressure at small or large spatialscales. Here, algorithms that differ mainly in their metrics were used tointegrate the traits. We also evaluated the yields of each classifier toknow the integration strategy of the physiological traits in marine in-vertebrates inhabiting environmental gradients. We considered thefollowing classifiers:

2.4.2.1. Linear discriminant analysis (LDA). This classificationtechnique divides the sample space into sub-spaces by hyperplanesthat best separate the study groups (Rao, 1948). In particular, Clunies-Ross and Riffenburgh (1960) and Press and Wilson (1978) define adiscriminant function for the case when the assumptions of equalcovariance matrices are met.

2.4.2.2. Naive Bayes (NB). This is a probabilistic model that assumesstrong independence among traits, assuming, in a “naive” way, that alltraits are conditionally independent given the classification variable.Here the model classifies each example given a set of attributes usingthe Bayes rule (Murphy, 2006).

2.4.2.3. k nearest neighbors (knn). The knn does not include a learningalgorithm or a training phase, in fact it carries out the classificationdirectly using the training dataset. It uses a distance measure, typically,the Euclidean distance, to assign the class label of a new example basedon the labels of the k nearest neighbors of that example (Liu et al.,2005).

2.4.2.4. Artificial neural networks (ANN). The complexity of the humanbrain to recognize patterns has led the scientific community tounderstand and relate these capabilities in a computational way. Inthis method, artificial neural networks are used to simulatemathematically biological neurons that are called nodes (Haykin andPrincipe, 1998). Their non-linear capabilities makes them a powerfultool for modeling complex relationships between inputs and outputs(Mohandes et al., 1998). We use this algorithm to know if the non-linear relationships between the selected physiological traits couldexplain the interactions between them and the differentiation of theseinteractions with the environment.

2.5. Model evaluation

To evaluate the performance of all classifiers for all of the species weused n-fold cross validation (Witten and Tibshirani, 2011). In n-foldcross validation, the original data set is randomly divided in n equallysized groups. Then, n-1 partitions are used to train the classifier, andthe remaining partition is used for testing. This process is repeated n

times, so that each partition is used as a test set once. The correctclassification or accuracy of the test set is averaged to obtain a finalestimation of the performance of the classifier. In this study, n=10 wasused as suggested in Witten and Tibshirani (2011).

For this study we used the following packages implemented in RSoftware language Open source: clValid package (Brock et al., 2011) forcalculating the Dunn index and Mclust (Fraley and Raftery, 2006) forthe EM algorithm. For classification using naive Bayes, LDA, NeuralNetworks, and knn the following packages were used, e1071, MASS,Class, nnet (Dimitriadou et al., 2006; Ripley, 2015; Ripley et al., 2016),respectively.

3. Results

3.1. Thermal variability in the intertidal

The 12 month high resolution temperature data showed a clear la-titudinal cline; temperature decreased towards higher latitudes with athermal difference of 4.5 °C between the north and south extremes inthe studied sites (Fig. 1B, C, D). The largest annual thermal range (i.e.,the difference between the warmest and coolest temperatures) wasfound at the Talcaruca site located at the biogeographical break(13.8 ± 2.88 °C, mean ± sd - annual statistic). Comparing the tem-perature dynamics with the tolerance capacities (CTmin and CTmax, re-spectively) showed that crabs from the high-intertidal exhibit higherthermal safety at high temperatures than individuals inhabiting thelower intertidal. Here it was found that individuals in the lower inter-tidal sometimes experience temperatures that exceed their CTmax(Fig. 1A, B, C, D). Additionally, individuals from sites in the south ex-perience thermal conditions very close to their CTmin (Fig. 1B, C, D).

3.2. Traits selection, comparisons of the physiological traits and phenotypicplasticity index

Four informative traits (out of a total of nine traits) were identifiedusing the trait selection algorithm. These four informative traits in-cluded cephalothorax length (CL), CTmax, CTmin, and metabolic rate at14 °C (MR). It should be noted that the classification model did not losesignificant statistical power after reducing the traits (p > 0.05).

Comparison of the means of physiological traits using mixed modelsindicated that the traits vary with latitude (see Fig. 2; Table 1). Fur-thermore, the most drastic changes in physiological traits in the lati-tudinal gradient were found for organisms that inhabit chronicallyvariable environments (i.e., high-intertidal), and these differences weredue to the effect of environmental breaks. Overall, the biogeographicbreak had a greater effect on the physiological components of C. ci-nereus, inhabits high-intertidal, and P. violaceus, inhabits mid-inter-tidal, compared to P. tuberculosus. Additionally, the greatest variation inphysiological traits was within the biogeographic break (30°S) betweenthe Peruvian Province and the Intermediate Province; where specifi-cally, significant differences in the mean values of almost all of thestudied traits were found (see Table 1). On the other hand, the phy-siological traits of P. tuberculosus, which inhabits the low intertidal,differed according to latitude rather than due to the presence of the twoenvironmentals barrier (see SM1, Table 1 and Fig. 1 to identify en-vironmental barrier).

In all the species studied it was possible to appreciate that themetabolic rate determined at 14 °C is the trait that had the greatestplasticity according to the RDPI. On the contrary, the trait studied towhich has a lower plastic capacity is CTmax, whose tendency was similarfor all the species studied. It is also observed that for the four physio-logical traits the species that showed a lower plastic capacity (i.e. lowerRDPI) was C. cinereus, evidenced by significant differences in: MR14 (F= 156.42,453; p < 0.01), CL (F = 29.452,453; p < 0.01), CTmin (F =22882,453; p < 0.01) y CTmax (F = 25752,453; p < 0.01), (see Fig. 3).

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Fig. 2. Latitudinal effect on various morphological and physiological traits (cephalothorax length, heat coma, chill coma, and metabolic rate). Cyclograpsus cinereus(A, B, C, D), Petrolisthes violaceus (E, F, G, H) and Petrolisthes tuberculosus (I, J, K, L). Both lines model the tendency of the data, in particular the red line is a linearregression whereas the blue line is a polynomial regression adjusted to the means values of each trait. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

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3.3. Phenotypic integration with machine learning

In unsupervised learning, the number of clusters increased or de-creased depending on the species and the shore level. These resultsindicate the physiological traits studied here grouped according tohabitat specifically, the traits of individuals inhabiting the lower in-tertidal grouped into few clusters, while traits of individuals inhabitinglocations in the upper intertidal grouped into more clusters.Specifically, we observed that the trait values for C. cinereus, whichinhabits the high-intertidal grouped into eight cluster according to theEM algorithm and were higher than those of individuals of P. violaceusand P. tuberculosis, which inhabit the mid-intertidal and lower inter-tidal, respectively. The traits of P. violaceus and P. tuberculosus groupedinto seven and six clusters respectively, and these were distributedalong the coast (Table 2). According to the k-means analysis wherek= 2 to k= 8 were tested, the traits of each species grouped into thefollowing amount of putative clusters: C. cinereus (8 clusters), P. viola-ceus (6 clusters), and P. tuberculosus (3 clusters). The above-mentionedresults show that the traits of C. cinereus grouped largely according tosample site, while the traits of crabs from low intertidal, the groupingwas smaller, because populations could share similar physiologicalcharacteristics across the latitudinal gradient.

According to the supervised classification algorithms: in a finemodel where the species were pre-classified according to the samplingsites, they showed that the highest classification percentage belonged toC. cinereus (48%), then P. violaceus (43%) and finally P. tuberculosus(34%). These differences were shown for all the classifiers used (i.e.,NB, Knn, LDA, ANN), which suggests that the integration of the traits isstronger in C. cinereus than P. violaceus and P. tuberculosus (ANOVA,P < 0.01, 3.316,108) (Fig. 4A). As mentioned in the methods, the spe-cies were also grouped into one of three regions (i.e. north, center, andsouth). Fig. 4B shows the percentage of correct assignments for eachspecies in geographic site using the different classifiers. Using su-pervised classification algorithms to classify each species to a geo-graphic region, a statistically higher percentage of correct assignmentswas obtained for C. cinereus (80% correct assignments) than for P.

violaceus (74% correct assignments) or P. tuberculosus (63% correctassignments), and this held for all classifiers used. Such results reflectthat, like using a pre-classification with the sampling sites, it was foundthat C. cinereus maintains a greater integration of the physiologicaltraits compared to P. violaceus and P. tuberculosus (ANOVA, P < 0.05,31.032,108) (Fig. 4B). It should be noted that the significant differenceswere only at the species level and that there were no significant dif-ferences between classifiers (Fig. 4).

4. Discussion

Variation in the phenotypes of ectothermic organisms has beenshown to be associated with thermal gradients, which are known togenerate strong gradients of selection (Angilletta et al., 2002; Yamahiraet al., 2007). In order to understanding how physiological traits varyspatially, it is necessary to quantify the degree of association betweenthe traits of spatially distributed populations (Via and Hawthorne,2005). Here, we show that the integration of traits of species that in-habit acute thermal environments is reduced, and therefore greaterplasticity can be achieved. Therefore, in highly heterogeneous habitatswith extreme acute thermal events, individuals often show adaptivephenotypic plasticity (Schulte et al., 2011) (see SM1), which allows forimproved fitness in response to local micro-environmental factors.Conversely, in environments with constant and chronic environmentalvariability, organisms can experience less variable trait expressiongiven that costs to plasticity are sufficiently strong and the selection forplasticity is likely weaker in these environments, benefiting a morelocal adaptation (Baythavong, 2011).

As was expected, the temperature at the sampling sites increasedtowards lower latitudes, showing a clear environmental gradient (seeFig. 1B, C, D). The highest thermal means were found at the northernsite (i.e., Iquique), and then decreased gradually towards the southernregion due to oceanographic and climatic processes (Broitman et al.,2001; Barros and Silvestri, 2002). Also, high thermal variation wasobserved at 30°S likely due to local oceanographic patterns includingsemi-permanent coastal upwelling (Aravena et al., 2014); this resultreinforces the existence of a biogeographic break at this latitude (30°S).Additionally, we found the environmental conditions of the intertidalzones studied to be highly variable, reaffirming that organisms in-habiting this ecosystem must face extreme thermal conditions (Helmuthand Hofmann, 2001; Helmuth et al., 2006, 2016; Harley et al., 2009).Luckily, many organisms can perform behavioral thermoregulation(Chapperon and Seuront, 2011), especially those found in intertidalhabitats (Harley, 2011; Evans and Hofmann, 2012).

The results reflect that the effects on the physiological traits from aunivariate perspective can have a differential behavior between thespecies and between the traits studied, that is, some traits may increasewith latitude and vice versa (see Table 1; Fig. 2). Using the holisticapproach, we can suggest that populations could present differences intheir adaptive mechanisms, where populations that inhabit chronicthermal environments could prevail local adaptation, while in popula-tions inhabiting acute thermal environments could prevail phenotypicplasticity. Therefore, the physiological traits studied here may be moreinfluenced by environmental or other types of variation at large spatialscales than at local scales. Such effects have also been found for ex-ample in several species of plants (Messier et al., 2017).

4.1. Traits selection, comparisons of the physiological traits and phenotypicplasticity index

Trait selection is different than analyses that reduce the di-mensionality of datasets (for example, principal components analysis“PCA”) (Saeys et al., 2007; Janecek et al., 2008). Both methods seek toreduce the number of traits, but typically dimensionality reductionestablishes new combinations of traits that confer more variance in thedataset. Conversely, the selection of traits through machine learning

Fig. 3. Relative distance plasticity index (RDPI) estimated for each species andcalculated for each trait along the latitudinal gradient. The figure shows themean and standard deviation for the three species studied. Different lettersindicate significant differences between crabs species (Tukey post hoc, error5%).

Table 2Number of clusters that best represent the data according to the EM algorithm(Expectation – Maximization) for the different species under study, n is thesample size, df represents degrees of freedom, BIC represents Bayesian in-formation criterion, and ICL represents Integrated Complete-data Likelihood.

Species log likelihood n df BIC ICL Number ofclusters

C. cinereus −603.75 192 98 −1722 −1744 8P. violaceus −917.62 186 41 −2049 −2099 7P. tuberculosus −600.06 183 69 −1559 −1603 6

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includes and excludes traits without modifying them (Hira and Gillies,2015), the traits selected have been shown by others to be highly plasticin marine crustaceans (Sokolova and Pörtner, 2003; Le Lann et al.,2011). The four variables selected vary directly depending on thetemperature; CTmin and CTmax, and are directly linked to the averageacclimatization temperature in their habitat (Peck et al., 2009). Meta-bolic rates have been shown to differ along latitudinal gradients (Weberet al., 2015), and morphometrics are often related to biogeographicrules such as Bergmann's rule (Walczyńska et al., 2017).

Thermal sensitivities (i.e., critical temperatures and metabolic rate)of the studied species vary in relation to geographic spatial scale. Thecritical temperatures of the studied crabs decreased with latitude, apattern that has been shown for several other ectotherms (Deutschet al., 2008; Gaston et al., 2009; Schulte et al., 2011; Angert et al., 2011;Gaitán-Espitia et al., 2014; Dowd et al., 2015). This pattern is clearlysupported by data in ectotherm terrestrial organisms, however formarine species the evidence is less strong (Sunday et al., 2011). Thephysiological differences among populations that inhabit the high-in-tertidal were more abrupt than differences among populations of thelower intertidal. These results could be related to the effects of tem-perature that are probably damped by the higher heat capacity of theocean compared to high-intertidal microhabitats (Okafor, 2011). Wehave shown that organisms that inhabit low intertidal, where thetemperature is generally more stable, tend to live closer to their criticaltemperatures than organisms that inhabit higher latitudes where thethermal variance is greater. Furthermore, our results show that crabshabiting the high-intertidal are more adapted to these fluctuating en-vironments than many other crabs (Stillman, 2002; Somero, 2002,2010). It should be noted that in some sites, the upper thermal limits ofthe crabs inhabiting the lower intertidal exceeded the thermal max-imum; as such these organisms may be seriously impacted to potentialincreases in temperature. Despite this, behavioral mechanisms could beused to avoid the negative effects of increased temperature (i.e., Bogerteffects, see Mitchell et al., 2013).

Oxygen limitation may play a crucial role in the regulation ofthermal tolerance (Pörtner, 2001, 2010; Pörtner and Knust, 2007),especially for intertidal ectotherms that can maximize their PO2 duringnormoxy to maintain their heart rate and thereby not affect theirthermal tolerance (Pörtner et al., 1985; Bjelde et al., 2015). There areno clear patterns of metabolic rates along environmental gradients,nevertheless Fusi et al. (2016) have shown that high-intertidal organ-isms are better adapted to thermal stress due to the physiologicalbenefits provided by atmospheric oxygen (see also Lardies et al., 2011).Despite this, it is known that low temperatures are expected to reducemetabolic rates (Yamahira and Conover, 2002; Gaitán-Espitia andNespolo, 2014; Gaitan-Espitia et al., 2017), and sometimes organismshave to make compensations if there is a reduction, for example, infitness (Fangue et al., 2009). Similar to the results of Gaitan-Espitiaet al. (2017) for P. violaceus and Monaco et al. (2010) for P. granulosus,here we found no differences in the metabolic rates of C. cinereus and P.

violaceus distributed along a latitudinal gradient. However, we did de-tect significant differences in the metabolic rates of P. tuberculosus alongthe gradient studied, which could be related to metabolic compensa-tions (Catenazzi, 2016).

As mentioned above, metabolic rate was the trait that increasedphenotypic plasticity according to the RDPI. Metabolism plays a centralrole in all biological processes; therefore the degree of flexibility thatadjusts to the metabolic rate could allow the animals to face the con-stant extreme thermal variations of the intertidal. Conversely, the traitsof thermal sensitivities would be adjusted by local adaption at thetemperature most frequently experienced by animals, thus the pheno-typic flexibility of these traits is weaker.

4.2. Phenotypic integration with machine learning

It is known that natural selection by local thermal environmentsleads to population divergence (Dillon et al., 2009; Gangloff et al.,2015). Thus, the thermal physiology of ectothermic organisms is likelysubject to strong selection (Artacho and Nespolo, 2009; May et al.,2017). Here, using machine learning, we found differences in thephysiological performance among the studied species, and these dif-ferences were mainly related to the environmental variability of thehabitat in which the species are present. Our results suggest adaptivedivergence of the integrated physiological traits of the intertidal crabsstudied. The previous is in agreement with recent studies showing thatenvironmental gradients can exert strong selection on the thermalphysiology of ectotherms (Richter-Boix et al., 2010). The degree ofdivergence among the integrated traits is likely related to the level ofthermal environmental heterogeneity experienced because phenotypicplasticity is directly linked to phenotypic integration (Gianoli andPalacio‐López, 2009). Here, the highest degree of trait integration wasfound for organisms in the high-intertidal in the greatly variable en-vironmental. We hypothesize that the chronic variability of the high-intertidal does not favor plasticity but rather encourages adaptation.Greater phenotypic integration was found for C. cinereus according tosamples sites, this was contrary to that found for population that in-habit low-intertidal zones, where lower thermal variability would likelypromote plasticity to cope with sporadic thermal events occur such inextreme low tides, which can also be reflected in the RDPI (see Fig. 3).In this sense, in a functional and integrated phenotype, any canaliza-tion, homeostasis or absence of plasticity of a certain trait should reflectsome type of damping of plasticity in some other trait (Forsman, 2015).Interestingly, the classification accuracy of the machine learning algo-rithms used here decreased with increased depth in the intertidal (seeFig. 4A, B; Table 2). This result could be due to the more stable phy-sical-chemical features of the low-intertidal (Stillman and Somero,1996; Somero, 2002; Stillman, 2002), which could facilitate themaintenance of homeostasis. Here the unsupervised machine learningalgorithms (EM algorithm and k-means) showed that maintained aclustering associated to the study sites, that is, the groups assigned were

ledomesraoCledomeniF(A) (B)

Fig. 4. Correct assignments with performance measures for the different algorithms used to classify the three species: Naive Bayes (NB); Linear discriminant analysis(LDA); k nearest neighbors (knn); Neural networks (ANN). (A) Fine model. (B) Coarse model.

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similar to the number of localities used in the study, the results of whichwere similar in both algorithms (i.e., EM algorithm and k-means), evenhaving different types of metrics (Jung et al., 2014). Both methodsshowed that the level of associations of populations that are distributedin the latitudinal gradient varies depending on the crab species, thismeans that the degree of plasticity of the species is inversely linked tothe level of associations between the traits. On the other hand, all of thesupervised learning algorithms used showed similar results. Here theclassification values were distributed within two standard deviations ofthe mean (see Fig. 4A, B). According to the results of the classifications,it is surprising to observe that the non-linear methods had similar re-sults with the linear modeling (NB, LDA and knn).

Machine learning is an important tool for incorporating trait in-tegration and possibly local adaptation when classifying groups.According to Amzallag (2000) and Guerrero-Bosagna and Skinner(2012), the heritability of a trait decreases with the degree of connec-tion it has with other traits, and this degree of connection is inverselyinvolved in plasticity. At the phenotypic level, the study of integrationmay have evolutionary implications because selection should favor aseries of traits that result in a functional phenotype (Cheverud, 1996;Pigliucci and Preston, 2004). Mechanistically, it is clear that physiolo-gical performance of organisms is the result of an integrated phenotypeand that such integration depends on the environmental variabilitywhere these organisms inhabit. For example, the close relationshipbetween the metabolic rates and the thermal tolerance capacities (in C.cinereus populations) can be attributed to the fact that these organismsare more likely to experience chronic thermal variations compared toorganisms that are distributed in the low-intertidal. Furthermore, wefound that the crab C. cinereus exhibited high metabolic rates withelevated energy costs as compensation to tolerate to extreme tem-peratures (see also Berger and Emlet, 2007). Namely, energy costs candecrease fitness in environments where organisms are often subjectedto their thermal extremes (Sokolova et al., 2012; Sokolova, 2013;Kingsolver et al., 2013).

These results highlight the complexity of adaptive thermal re-sponses of multiple traits in natural populations and the role of localthermal variation as a selective force that drives diversity in physiolo-gical traits. Consequently, the integration of physiological traits pro-vides an understanding more holistic of the thermal effects to en-vironmental change and how this could affect different species on smallor large spatial scales. Nevertheless, we cannot discard a possiblephylogenetic effect on thermal physiological traits in the studied crabsbecause two species are closely related and only future analysis withmore species added and applying phylogenetically independent con-trasts to comparative data could help us to clarify this aspect. Despitethis, our results increase the understanding of physiological integrationalong environmental gradients and how to analyze phenotypic plasti-city of integrated phenotypes

In relation to using machine learning in this study, we can point outas strengths, the fact that the clustering algorithms used (unsupervisedlearning) can effectively discover the natural grouping of the data forthis application. These clusters are identified regardless of the datasample size. The trait selection algorithm (commonly known as featureselection in machine learning) uses a wrapper approach, this meansthat the selected traits are obtained based on the effect of these on thepredictive performance of the classifier. Here the purpose was toidentify a subset of traits, regardless of the relation (or not) amongstthem, but that obtained the best predictive performance which is thefinal goal. Of course, there are limitations or weaknesses when using amachine learning approach that cannot be neglected. For example,given that machine learning is data-driven, with little intervention of adomain expert, the first assumption is that the input data is correct andreliable. Any conclusion drawn from the models will be conditioned tothe quality of the data. This means that how the experimental data isacquired and what type of data preprocessing was used are funda-mental. Also, unlike the unsupervised learning techniques, the

predictive performance of the supervised learning algorithms dependson the training sample size, moreover, the evaluation of the general-ization power of the predictive models depends of the test set samplesize. These limitations (and others) should not be forgotten when usinga machine learning approach. In this work, we have adopted somestrategies to reduce the effect of these limitations, through the use of n-fold cross validation which allowed us to get the most out of the data totrain and test the models. Also, for classification, we have not assumedone specific machine learning technique beforehand to use, instead wehave evaluated several techniques of different nature, some of thesewhich do not learn any parameters, like k-nn, in comparison with ar-tificial neural networks, that must learn from the training set theparameters of the network (weights and biases). Also, standard ex-perimental protocols were employed throughout the data acquisitionprocess to ensure the quality of the input data to the algorithms.Overall, future studies should aim using machine learning algorithm'sto make precise predictions about the distribution range shifts ofmarine ectotherm organisms in the scenario of global warming.

Acknowledgements

The study received financial support from CONICYT FONDECYT1140092 grant to MAL. The Millennium Nucleus Center for the Study ofMultiple-drivers on Marine Socio-Ecological Systems (MUSELS) byMINECON Project NC120086 also gave support to MAL and SJO duringfinal stages of the project. MAL acknowledge the support of PIACONICYT ACT-172037. SJO acknowledges BECAS CONICYT No.21150739 for financial support. All experiments were conducted ac-cording to common Chilean law.

Appendix A. Supplementary material

Supplementary data associated with this article can be found in theonline version at doi:10.1016/j.jtherbio.2018.09.016.

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