Culinary evolution models for Indian cuisines

Anupam JainCenter for System Science, Indian Institute of Technology Jodhpur, Jodhpur, 342011, India

Ganesh Bagler∗

Center for Biologically Inspired System Science, Indian Institute of Technology Jodhpur, Jodhpur, 342011, India(Dated: August 8, 2018)

Culinary systems, the practice of preparing a refined combination of ingredients that is palatableas well as socially acceptable, are examples of complex dynamical systems. They evolve over timeand are affected by a large number of factors. Modeling the dynamic nature of evolution of regionalcuisines may provide us a quantitative basis and exhibit underlying processes that have driven theminto the present day status. This is especially important given that the potential culinary space ispractically infinite because of possible number of ingredient combinations as recipes. Such studiesalso provide a means to compare and contrast cuisines and to unearth their therapeutic value.Herein we provide rigorous analysis of modeling eight diverse Indian regional cuisines, while alsohighlighting their uniqueness, and a comparison among those models at the level of flavor compoundswhich opens up molecular level studies associating them especially with non-communicable diseasessuch as diabetes.

PACS numbers: 89.75.-k, 82.20.Wt, 87.18.Vf, 87.10.Vg, 89.90.+n

I. INTRODUCTION

Culinary systems are examples of complex dynamicalsystems. Culinary practices and hence food preparationprocedures (recipes) have evolved to the present day tra-ditional cuisines by tuning them so as to suit human sen-sibilities. Knowing the complexity of culinary evolutionthe question is whether it could be modeled to identifykey elements that drive its nature.

Lately, culinary science has attracted the attentionof physicists due to invariant patterns observed acrosscuisines as well as owing to cuisine-specific features thathighlight evolutionary mechanisms whose understandingfacilitate various applications [1–3]. Understanding theprocess of culinary evolution can help bring to the sur-face, the guiding principles behind the development ofthe cuisine.

While the choice of food ingredients and their combina-tions is dictated by a range of factors such as geography,culture, climate and genetics [4–9], the sensory mecha-nisms of taste (gustatory) and smell (olfactory) play adominant role to lock-in ingredients into recipes [10].

Various cuisines have been reported to have generic na-ture of recipe size distribution and frequency-rank distri-bution [7, 11]. Yet these cuisines are unique in preferringcertain ingredients and ingredient combinations. Indiahas had a long culinary history and is characterized bydiverse geographies and climates. While the cuisine ofIndia could be seen as a single cuisine, it is representedby a blend of regional cuisines.

Earlier studies have reported most cuisines to have pos-itive food pairing i.e. they tend to use ingredient pairs ofsimilar flavor and taste [2], Indian cuisine in contrast is

∗ bagler@iitj.ac.in

reported to have negative food pairing i.e. Indian recipestend to have ingredients of complementary flavors [3].This is an important distinction which, apart from re-flecting geoclimatic and cultural differences, says a lotabout the trajectory that Indian cuisine has followed andperhaps bears specific culinary milestones in specifyingrecipe compositions.

Herein we ask the following questions in the context ofIndian regional cuisines. (a) Could a model generate acuisine which is similar to the real world not only in termsof its statistical patterns but also in terms of its flavorprofile? (b) What are the dominant factors in shapingthe recipe size distribution?

Towards addressing the above questions we createdmodels of culinary evolution: (a) Copy-mutate modelfitness random (CM-fitness random) (b) Copy-mutatemodel fitness ranked (CM-fitness ranked) (c) Copy-mutate-add-delete model (CMAD model). CM-randomserves as a null model and when compared with CM-ranked, indicates the role of ingredient rank (frequencyof use) in food pairing pattern.

In the second section we describe the data acquisitionand correction methods with corresponding final statis-tics. The third section explains our model’s methodologyand parameters involved. It also explains the modality ofauthenticity study, carried out to find the most legitimateingredients belonging to each regional cuisine. Then weprovide results on reproduction of certain statistical fea-tures of the Indian cuisine (and its regional cuisines).

II. DATA ACQUISITION AND STATISTICS

We began with extracting data for Indian cuisine fromthe website tarladalal.com (November, 2014) [12] whichis the largest online repository of recipes for Indian cui-

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sine. After curating the data for redundant charactersand words (such as contributor’s name) from recipes, wewere left with 2543 recipes and their corresponding ingre-dients. The ingredients being listed in different spellingsand usage amounts and forms (chopped, sliced etc.) wererequired to be aliased separately after which we had194 ingredients for the whole cuisine. Since the intentof current study was extended beyond simple statisti-cal modeling of cuisine to look for flavor patterns withinthe model cuisine, we also gathered information of flavorcompounds present in the ingredients and ended up withan overall list of 1170 flavor compounds correspondingto above 194 ingredients through existing data [2, 3] andresources of flavor compounds [13]. Table I lists statisticsof recipes and ingredients in each of the regional cuisines.

III. THE CULINARY EVOLUTION MODELS

For the purpose of random copy-mutate model [1], weassign a number selected uniformly randomly from therange [0, 1] to each available ingredient as its ‘fitness’value. The meaning of this fitness value in the real worldcan be taken to be a quantifying parameter describingthe possible preferential efficacy of an ingredient basedon factors such as availability, nutritional aspect, relativepopularity, flavor and cost [1].

The copy-mutate algorithm begins by creating a seedpool, R0 of 20 recipes generated by random selection ofS = 7 ingredients for each such recipe from an initial ran-dom pool I0 of 10 ingredients. Further at each time stepwe selected a recipe randomly from the pool as ‘mother’recipe and made a copy of it for mutation. Within thecopied recipe we chose an ingredient (of fitness fi) ran-domly and compared its fitness value fi with the fitnessvalue fj of another ingredient from the ingredient pool,also chosen randomly. If fj > fi we replace the old ingre-dient (i) with this new one (j). Thus the copied recipe ismutated 1 time. This process of mutation is carried outM number of times after which the mutated copy recipeis added back to the pool as another possible candidateof being a mother recipe in next time step.

To introduce new ingredients we also check and main-tain at each time step a ratio r of size of ingredients pool

TABLE I. Statistics of recipes and ingredients in regionalcuisines.

Cuisine Recipe count Ingredient countBengali 156 102Gujarati 392 112Jain 447 138Maharashtrian 130 93Mughlai 179 105Punjabi 1013 152Rajasthani 126 78South Indian 474 114

and size of recipe pool. The value of r for current studywas taken to be this ratio, calculated from empirical data.If the ratio falls below the required threshold then newingredients are introduced in the pool by random selec-tion from the overall available list of ingredients.

The overall process of recipe selection-mutation is re-peated till we get R number of recipes which is equal tothe empirical recipe count of 2,543. For normalizationpurposes, we create 24 such sets of random copy-mutaterecipes and study overall statistics over average of all sets.

We implemented three different models:

• Copy-mutate Fitness RandomIn this model, the ‘fitness’ values are assigned to in-gredients on a uniform random basis. This modelstarts with no a priory basis or bias about the fit-ness of certain ingredients.

• Copy-mutate Fitness RankedIn this model, an ingredient is assigned ‘fitness’value based on its empirical frequency. Thus, aningredient with higher frequency in real world cui-sine would have a higher fitness value. Obviouslythis model depends on fitness of an ingredient thatis ascertained retrospectively.

• Copy-mutate-add-delete ModelGoing further from previously models, where thesize of the recipes in a cuisine is fixed, we gener-ated another model that has a provision for addi-tion and deletion of an ingredient. In this model,an additional factor was introduced to choose aningredient for addition, deletion and mutation ateach time-step.

IV. INGREDIENT AUTHENTICITY

Further, In order to understand and highlight the dif-ferences among regional cuisines and uniqueness of eachone, we carried out a study on finding the most authenticingredients. This study highlights ingredients more com-monly used in one cuisine as compared to other cuisines.In order to compute this, we use the prevalence [2] P c

i

of an ingredient i in a cuisine c as P ci = nc

i/Nc where nci

is the number of recipes that contain the particular in-gredient i in the cuisine and Nc is the number of recipesin the cuisine. The relative prevalence pci measuring theauthenticity of the ingredient i is computed as the dif-ference between the prevalence of i in cuisine c and theaverage prevalence of i in all other cuisines.

V. RESULTS

All eight regional cuisines reflect the culinary diversityof Indian culture. This is not only evident by the recipesbelonging to each cuisines but also by the pattern of in-gredient usage. This could be observed by looking at the

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FIG. 1. Frequency-rank distributions of ingredients for In-dian cuisine and corresponding copy-mutate model (‘Fitnessrandom’ having randomly assigned fitness values for ingredi-ents) and its variant (‘Fitness ranked’) with frequency scaledfitness values for ingredients. The distribution in both casesmatch closely to that of the real world cuisine. The loggeddata was fitted with equation (f(x) = a ∗ expbx) giving valueof coefficient b as 0.5664 for Indian cuisine, 0.5873 for fitnessrandom model and 0.4809 for the fitness ranked model.

most authentic ingredients for regional cuisines. A list oftop 5 most authentic ingredients for each of the regionalcuisines is given in table II.

A. Frequency-rank distribution

While the authenticity study highlights uniqueness ofeach regional cuisine, the generic nature of frequency-rank distribution has been shown to be a rather interest-ing statistical feature of cuisines around the world. Itsconsistent nature across regional Indian cuisines has beenshown earlier [3], making it a feature of special interestand an indicator of generic culinary evolution mechanism.We began our study by adopting the model for the pur-pose of reproducing this pattern.

Fig. 1 shows the frequency-rank distributions for In-dian cuisine and corresponding copy-mutate models ofboth random fitness values and empirical frequency basedfitness values. The figure indicates that the frequency-rank distribution pattern gets reproduced by both themodels. This can further be emphasized by looking atthe coefficient values for the exponential fitting of thecurves, as listed in figure caption.

The reproduction of frequency-rank could also be seengenerically across all the eight regional cuisines in In-dia, as shown in Fig. 2. All the curves were fitted withequation f(x) = a∗expbx and corresponding b coefficientvalues are presented in table III.

B. Food pairing pattern

The notion of food pairing is well-known in culinaryscience. The food pairing hypothesis, that two ingre-dients sharing common flavor compounds taste well to-gether, has been widely researched upon in previousstudies [2, 3]. Beginning from pairs of ingredients andcorresponding number of shared flavor compounds (N),calculating the average flavor sharing of a recipe (NR

s )and that of a cuisine (average Ns) has also been well-established in these studies. For our current study wehave made use of these calculation methodologies onlyin order to test our model’s capability of flavor pairingeffect regeneration.

While studying and regenerating the frequency-rankdistribution of ingredients itself is statistically interest-ing enough, can such a model reproduce empirically ob-served flavor sharing patterns as well? To answer thisquestion, we began with comparing the average Ns val-ues [2, 3] of both the copy-mutate cuisines with that ofthe Indian cuisine (Fig. 3). As shown, the model cuisinewith occurrence based fitness of ingredients has a closeraverage Ns value to that of the Indian cuisine, while therandom fitness based model cuisine’s average Ns is muchhigher indicating that certain fitness domain can producea better model in terms of overall flavor effect observed.This further established that certain highly used ingredi-ents play a vital role in defining the characteristic of thecuisine.

The model was applied for all the eight regionalcuisines so as to check its applicability across cuisines.Interestingly, for all regional cuisines, barring Jain andRajasthani, the copy-mutate model with ranked fitnessvalues of ingredients produced better results for averageNs. This is shown in Fig. 4.

However, the average Ns over entire cuisine is not nec-essarily a strong reflector of the underlying flavor pattern.So we look a level deeper and check the recipe level dis-tribution of the NR

s values. As indicated by Fig. 5, thedistribution of NR

s values over the cuisine (average of 24sets in case of copy-mutate model) also gets closer to em-pirical distribution as we move from random fitness to oc-currence based fitness domain. The model with randomfitness, as expected, shows the pattern closer to that ofthe uniform random model of the cuisine (one in whichrecipe-size distribution was preserved but recipes com-posed of uniformly selected ingredients). This furtherenhances our observation that the model with specificfitness domain is capable of producing a cuisine compa-rable with Indian cuisine in terms of flavor profile as well.

As another alternative, we tried to create a modelwhich could recreate the recipe-size distribution of a cui-sine with inclusion of probabilistic addition and deletionof ingredients from recipes instead of only replacementof ingredients (mutation). Though exact replication ofrecipe-size distribution could not be achieved, as Fig. 6indicates, certain probability values of addition, deletionand mutation get the recipe-size distribution similar to

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FIG. 2. Frequency-rank distributions for all eight regional cuisines and corresponding models. The distributions for modelsclosely match that of the empirical data in each one consistently.

FIG. 3. Average Ns values of Indian cuisine and the two copy-mutate models (‘Fitness random’ and ‘Fitness ranked’) andtheir z-scores. The model with ranked values of fitness produces closer average Ns value compared to that of the random one.Corresponding statistical significance is shown by the z-score.

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TABLE II. Top 5 most authentic ingredients for each of the regional cuisine.

Bengali Gujarati Jain Maharashtrian Mughlai Punjabi Rajasthani South Indiancoriander asafoetida butter turmeric milk garam masala ghee curry leafegg plant green bell pepper corn grit coconut cardamom wheat fennel black beanturmeric sesame seed banana cayenne ghee sunflower oil cayenne black mustard seed oil

milk black mustard seed oil tomato cinnamon cream cottage cheese chickpea riceginger garlic paste chickpea corn clove clove onion cumin tamarind

FIG. 4. Average Ns values of eight Indian regional cuisines, their copy-mutate models (‘Fitness random’ and ‘Fitness ranked’)and their z-scores.

TABLE III. Values of fitting coefficient ‘b’ for all eight regionalIndian cuisines and corresponding models.

Cuisine RCa CM-FRandb CM-FRankc

Bengali 0.4302 0.4842 0.4608Gujarati 0.5204 0.507 0.5241Jain 0.4784 0.4947 0.4758Maharashtrian 0.463 0.4709 0.4601Mughlai 0.5347 0.4794 0.4794Punjabi 0.5702 0.4783 0.5075Rajasthani 0.5761 0.505 0.5382South Indian 0.5696 0.5321 0.4997

a Regional cuisineb Copy-mutate fitness randomc Copy-mutate fitness ranked

that of the real cuisine.Interestingly, mutation seemed to have been the dom-

inating factor in evolution of the Indian cuisine as onlythose trials of the CMAD model gave better results forthe recipe-size distribution which had higher probabilityvalue for mutation to occur compared to addition or dele-tion. If historical data were available, this observationcould prove useful in generating the phylogenetic tree ofrecipes.

VI. CONCLUSIONS

Quantitative as well as data-centric analysis of worldcuisines has caught attention of physicists recently. Wehad earlier shown that the Indian cuisine is unique in itsstrong negative food pairing pattern [3]. In this study

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FIG. 5. Cumulative distribution of P (NRs ) vs NR

s values of eight regional cuisines of India and their copy-mutate models.

we focused on models [1] of eight Indian regional cuisinesto probe for mechanisms that might have been dominantin their evolution over centuries. Our models highlightthe role of ‘ingredient frequency’ in rendering the char-acteristic food pairing pattern of Indian recipes. Fur-ther, we looked for the processes that are central to therecipes-size distribution and observed that phenomenonof mutation (change of one ingredient with another) verywell explains the observed pattern. Our models and cor-responding studies highlight the possibility of having analgorithmic way to suggest novel ingredient combinationsas recipes [14] while still maintaining the flavor signature

of a cuisine.

ACKNOWLEDGMENTS

G.B. acknowledges the seed grant supportfrom Indian Institute of Technology Jodhpur(IITJ/SEED/2014/0003). A.J. thanks the Ministryof Human Resource Development, Government of Indiaas well as Indian Institute of Technology Jodhpur forscholarship.

[1] O. Kinouchi, R. W. Diez-Garcia, A. J. Holanda, P. Zam-bianchi, and A. C. Roque, New Journal of Physics 10,1 (2008), arXiv:0802.4393.

[2] Y.-Y. Ahn, S. E. Ahnert, J. P. Bagrow, andA.-L. Barabasi, Scientific Reports 1, 1 (2011),arXiv:arXiv:1111.6074v1.

[3] A. Jain, N. Rakhi, and G. Bagler, arXiv:1502.03815 , 1(2015), arXiv:1502.03815.

[4] M. Pollan, Cooked: A Natural History of Transformation(Penguin Books, 2014) p. 480.

[5] A. Appadurai, Comparative Studies in Society and His-tory 30, 3 (2009).

[6] P. W. Sherman and J. Billing, Bioscience 49, 453 (1999).[7] Y.-X. Zhu, J. Huang, Z.-K. Zhang, Q.-M. Zhang,

T. Zhou, and Y.-Y. Ahn, PloS one 8, e79161 (2013).[8] L. L. Birch, Annual Review of Nutrition 19, 41 (1999).[9] A. K. Ventura and J. Worobey, Current Biology 23, R401

(2013).[10] P. A. S. Breslin, Current biology : CB 23, 409 (2013).[11] K. R. Varshney, L. R. Varshney, J. Wang, and

D. Myers, “Flavor Pairing in Medieval European Cui-sine : A Study in Cooking with Dirty Data,” (2013),arXiv:arXiv:1307.7982v1.

[12] T. Dalal, “Tarladalal.com,” (2014).

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FIG. 6. Recipe size distributions for the Indian cuisine and trials of CMAD model with varying probabilities of addition,deletion and mutation of recipes.

[13] G. A. Burdock, Fenaroli’s Handbook of Flavor Ingredi-ents, 6th ed. (CRC Press, 2010) p. 2159.

[14] L. R. Varshney, F. Pinel, K. R. Varshney, D. Bhattachar-jya, A. Schoergendorfer, and Y.-M. Chee, , 1 (2013),arXiv:1311.1213.