Table 1 Indexes constructed for integrating information of the study, definitions, and scales of values

INDEX OF CULTURAL IDENTITY (ICI) = 0.4 × AAT + 0.25 × QL + 0.2 × AIA + 0.1 × SFA + 0.05 × SChA

- AAT = Appropriation of Agricultural Traditions

Indicates the number of traditions associated to agriculture (customs, rituals, festivities) recognized, practiced, and transmited by a household head in relation to all traditions associated to agriculture identified in our study.

- QL = Quechua Language

Indicates the degree of use of the Quechua language by the household: 1 = only Quechua, 0.5 = bilingual (Sapnish-Quechua), y 0 = only Spanish.

- AIA = Age as Independent Agriculturalist

Indicates the inverse relation between age at which households' heads started to cultivate native tubers as an independent and the minimum age identified amonh households heads studied.

- SFA = Stimuli of Father as Agriculturalist

Indicates the age at which the household's head learned agriculture (1 = child, 0.5 = teen ager, 0.25 = adult), the proportion of varieties inherited in relation to all varieties documented, the proportion of land area inherited in relation to the maximum area identified, and origin of land cultivated as independent agriculturalist: 1 = inherited; 0.75 = repartición; 0.50 = renting, an 0.25 = buying.

- SChA = Stimuli of Children as Agriculturalists

Indicates the traditional ways (knowledge, technology, mutual help, seeds, land) that consider necessary to give to children to continue withtraditional agriculture of native tubers, minus the modern ways (education, fertilizer, insecticides) also mentioned.

0 to < 0.2 = Very weak identity

INDEX OF TRADITIONAL AGRICULTURAL MANAGEMENT (ITAM) = 0.75 × SiCAgT + 0.25 × SiCFSm

1.0 = Total traditional management

- CTA = Conservation of Traditional Agriculture

$\text{CTA}=\frac{\text{ACNT}+\text{TT}+\text{MH}}{3}$

- ACNT = Area Cultivated with Native Tubers, which is the area cultivated with native tubers per agriculturalist in relation to the largest area cultivated by the agriculturalists documented.

0.80 a < 1,00 = Very strong traditional management

0.60 a < 0.80 = Strong traditional management

0.40 a < 0.60 = Intermediate traditional management

0.20 a < 0.40 = Weak traditional management

0 a < 0.20 = Very weak traditional management

- TT = Traditional Technologies, which is a relation of key traditional technologies: (i) proportion of land use and fallow, (ii) tilling system (1 = raway, 0.5 = pampay, and 0.25 = furrowing), (iii) proportion of dung bags used in relation to the average used per agriculturalist, and (iv) traditional seed stroring (1 = coyonaor saway-piles of tubers covered with straw-; 0 = platforms/nets/sacks).

- MH = Mutual Help1 = only mutual help, 0.5 = mutual help and payed laborers, y 0.33 = low mutual help and high payed laborers.

- CSF = Conservation of Seed Flow

$\text{CSF}=\frac{\text{SE}+\text{SOM}}{2}$

- SE = Search Effort, the search effort of each agriculturalist relation to the maximum effort identified, calculated as the product of thesearch area: 1 = only local; 2 = only regional; 3 = only inter-regional; 4 = local/regional; 5 = local/inter-regional; 6 = regional/interregional; 7 = local/regional/inter-regional, and the search intensity as the summatory of the number of places visited: No. local places + 2 × No. regional places + 3 × No. in-terregional places.

- SOM = Seed Obtaining Mechanisms, indicating presence or absence of traditional mechanisms: 1 = barter and present; 0.8 = barter or present; 0.6 = barter, present and buying; 0.4 = buying, barter or present; 0.2 = buying; 0 = none.

$\mathbf{I}\mathbf{N}\mathbf{D}\mathbf{E}\mathbf{X}\mathbf{O}\mathbf{F}\mathbf{S}\mathbf{E}\mathbf{L}\mathbf{F}-\mathbf{S}\mathbf{U}\mathbf{F}\mathbf{F}\mathbf{I}\mathbf{C}\mathbf{I}\mathbf{E}\mathbf{N}\mathbf{C}\mathbf{Y}\left(\mathbf{I}\mathbf{S}\mathbf{S}\right)=\frac{\mathbf{V}\mathbf{P}\mathbf{D}\mathbf{C}}{\mathbf{V}\mathbf{P}\mathbf{D}\mathbf{C}+\mathbf{T}\mathbf{I}}$

1.0 = Total self-sufficiency

- VPDC = Value of Production for Direct Consumption

Calculated as the monetary value of agricultural production destined to direct consumption by households.

0.80 a < 1.00 = Very high self-sufficiency

0.60 a < 0.80 = High self-sufficiency

0.40 a < 0.60 = Intermediate self-sufficiency

- TI = Total Incomes

Calculated as the summatory of monetary value of total agricultural production, salaries and incomes derived of social assistance programs.

0.20 a < 0.40 = Low self-sufficiency

0 a > 0.20 = Very low self-sufficiency

$\mathbf{I}\mathbf{N}\mathbf{D}\mathbf{E}\mathbf{X}\mathbf{O}\mathbf{F}\mathbf{F}\mathbf{A}\mathbf{M}\mathbf{I}\mathbf{L}\mathbf{Y}\mathbf{S}\mathbf{I}\mathbf{Z}\mathbf{E}\left(\mathbf{I}\mathbf{F}\mathbf{S}\right)=\frac{{\mathbf{N}}^{\circ }\mathbf{m}\mathbf{e}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{o}\mathbf{f}\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{h}\mathbf{o}\mathbf{u}\mathbf{s}\mathbf{e}\mathbf{h}\mathbf{o}\mathbf{l}\mathbf{d}}{\mathbf{M}\mathbf{a}\mathbf{x}\mathbf{i}\mathbf{m}\mathbf{u}\mathbf{m}{\mathbf{N}}^{\circ }\mathbf{m}\mathbf{e}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{h}\mathbf{o}\mathbf{u}\mathbf{s}\mathbf{e}\mathbf{h}\mathbf{o}\mathbf{l}\mathbf{d}\mathbf{s}\mathbf{s}\mathbf{t}\mathbf{u}\mathbf{d}\mathbf{i}\mathbf{e}\mathbf{d}}$

0.80 a 1.00 (9-11 members) = Very numerous

0.50 a < 0.80 (6-8 members) = Numerous

0.30 a < 0.50 (4-5 members) = Intermediate

0.10 a < 0.30 (1-3 members) = Small

$\mathbf{I}\mathbf{N}\mathbf{D}\mathbf{E}\mathbf{X}\mathbf{O}\mathbf{F}\mathbf{F}\mathbf{A}\mathbf{M}\mathbf{I}\mathbf{L}\mathbf{Y}\mathbf{S}\mathbf{I}\mathbf{Z}\mathbf{E}\left(\mathbf{I}\mathbf{F}\mathbf{S}\right)=\frac{{\mathbf{N}}^{\circ }\mathbf{m}\mathbf{e}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{o}\mathbf{f}\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{h}\mathbf{o}\mathbf{u}\mathbf{s}\mathbf{e}\mathbf{h}\mathbf{o}\mathbf{l}\mathbf{d}}{\mathbf{M}\mathbf{a}\mathbf{x}\mathbf{i}\mathbf{m}\mathbf{u}\mathbf{m}{\mathbf{N}}^{\circ }\mathbf{m}\mathbf{e}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{h}\mathbf{o}\mathbf{u}\mathbf{s}\mathbf{e}\mathbf{h}\mathbf{o}\mathbf{l}\mathbf{d}\mathbf{s}\mathbf{s}\mathbf{t}\mathbf{u}\mathbf{d}\mathbf{i}\mathbf{e}\mathbf{d}}$

0.80 a 1.00 = Very high

0.60 a < 0.80 = High

0.40 a < 0.60 = Intermediate

0.20 a < 0.40 = Low