Biological material

We sowed the seeds of a heterozygous plant of A. hypochondriacus to produce the inflorescences of plants with determinate and indeterminate growth. We moved them forward towards homozygosis by the single-seed method (^{Fehr, 1993}), selected determinate and indeterminate plants and made a generational progress until obtaining a homogeneous population of each phenotype. We did sowings in trays of 200 cavities, in a commercial substrate (Peat Moss Sunshine Mix 3). Plants were irrigated every third day and we planted the fifth generation seed for studying apical meristems.

Sample preparation

We conducted plant samplings from emergence and until flowering. The apical meristem was disclosed with a dissection forceps and we observed it with a stereoscopic microscope (S8 APO, Leica, Germany) to determine its phenological status. The morphology of the apical meristem was observed with a variable pressure scanning electron microscope (EVO LS40, Zeiss, Germany), coupled to a peltier stage with a temperature range of -25 to 50 ° C, at 50 Pa, at room temperature of 17 ° C (Deßen EVO^® XVP^® Coolstage, United Kingdom), and the sample was fixed to the stage by a copper conductive tape. In all the experiments, we maintained the following operating conditions: high voltage (EHT) 20 kV, Fil I Target 2.508 A, working distance 22 mm and Spot Size of 600 ± 5. The micrographs were captured at 164X, 200X, 800X and 1.00KX magnification with a resolution of 1024x768 pixels in gray scale. In this format, we set a gray scale with 0 for black and 255 for white. Afterwards we took new samples and placed them in Herr's solution (phenol: chloral hydrate: 85% lactic acid: xylene: clove oil [1: 1: 1: 0.5: 1]) (^{Acosta-García and Vielle-Calzada, 2004}), for 24 h and observed it with a compound microscope (Axio Scope, A1, Zeiss, Germany) to analyze the anatomical structure of the apical meristem.

To analyze the morphology of the determinate and indeterminate phenotypes, we collected five plants of each growth type in a mature phenological stage, that is, at the end of the growth cycle. To determine the effect of the type of growth on the yield, we took 25 F₅ plants of each growth type. Each inflorescence was divided into three strata (basal, middle and apical), and in each stratum the branches were divided into base and apex. We separated seeds from each fragment of the inflorescence, and counted at random in triplicate 1000 seeds of each of the sections of each plant and weighed them on an analytical balance. The experimental design consisted of randomized complete blocks; we analyzed data with the SAS GLM procedure and compared the means with the Tukey test (p ≤ 0.01).

Types of inflorescences and their effect on seed size

The growth of the inflorescence in A. hypochondriacus is usually indeterminate. In the Arabidopsis and Antirrhinum model plants the determinate inflorescences are characterized by the appearance of a terminal flower at the apex of the branches (^{Coen and Nugent 1994}, ^{Bradley et al., 1996}, ^{Cremer et al., 2001}, ^{Ezhova and Penin, 2001}; ^{Penin et al., 2004}). However, the determinate inflorescences in the Amaranthus genus are reported only for A. caudatus (^{Kulakow and Jain, 1987}) and A. edulis (^{Sauer, 1950}). ^{Espitia (1994)} described the presence of determinate growth in A. hypochondriacus Aztec race (Figure 1).

Figure 1 Plant of Amaranthus hypochondriacus A) Inflorescence of indeterminate growth, B) inflorescence of determinate growth, C) branch in indeterminate inflorescence, and D) branch in determinate growth. 

During the development of the determinate and indeterminate inflorescences in A. hypochondriacus the phenological phases of both phenotypes were equal during the vegetative phase and the transition to the reproduction phase. However, in the determinate growth after the establishment of a variable number of primordia, the apex emerged as a terminal flower.

To analyze whether the type of growth of the inflorescence affected the yield, we analyzed the seed weight in both genotypes. Among the types of growth, the weight of 1 000 seeds was different (p ≤ 0.01): 0.676 g for the plants of determinate growth (Figure 2A); those with indeterminate growth (Figure 2B) presented greater weight in the middle strata, whereas the apical and basal ones had the lowest weight. In the amaranths of determinate growth (Figure 2D) the highest seed weight was also found in the middle stratum, while the apical stratum and the basal recorded the lowest weight. This makes sense as flowering begins in the middle part of the inflorescence, from where it moves towards the apical meristem, and flowering in the basal part of the inflorescence will most probably happen at the same time than the flowering in the apical part. That is, there is competition between the flowers of the two strata, the movement of photoassimilates is greater towards the apical part (^{Bertin, 1995}) and this could be the reason that the lower weight of the seed is in the basal layer, both in amaranth of indeterminate and determinate growth (^{Marcelis, 1993}). It is likely that at the beginning of flowering in the middle stratum there is no competition for seed filling by the basal and apical strata; therefore, the highest weight of seeds is in the middle stratum.

Figure 2 Seed weight of amaranth plants (Amaranthus hypochondriacus) of the two growth types (A), inflorescence strata (B and D) and position in the branches (C and E). 

These results agree with those reported by ^{Ramírez et al. (2012)} regarding the greater growth of the seed in the middle and apical strata. In relation to the position in the branch in indeterminate growth (Figure 2C), there were significant differences and the apical position presented greater seed weight. In the determinate growth (Figure 2E) there were no differences between the three strata, suggesting a homogeneous growth during inflorescence.

The determinate and indeterminate inflorescences of A. hypochondriacus can be simple or compound, depending on the region in which they are cultivated, and thus shows an important phenotypic plasticity. In determined inflorescences we observed the terminal flower placed at the top of the main axis and in the flower branches.

In the indeterminate inflorescences primary branches were longer, they were 4 to 15 cm long and the distance between nodes was smaller, 0.2 cm; therefore, they were inflorescences with a greater number of floral branches. Thus, there were inflorescences from first to fifth order, a characteristic not present in determinate inflorescences. In this last phenotype the primary branches were on average 10 cm long and the distance between nodes varied from 1 to 2 cm.

In both phenotypes, branches showed an organized basipetal growth in glomeruli. Determinate growth had more complex or agglomerated glomeruli (Figure 3I), unlike indeterminate growth because the primary branches derived from the main axis do not branch and, therefore, the production of flowers occurs at the glomerulus level and not at branch (Figure 3H).

Figure 3 Different stages of female and male flowers of Amaranthus hypochondriacus: A) female flower in early development and next to it the ovule of the contiguous flower can be observed, B) female flower composed of three stigmas, three internal tepals and two external tepals , C) female flower in stage of maturation of the seed, D) seed filling, E) different degrees of flower maturation, F) male flower accompanied by two female flowers, G) secondary branches in indeterminate inflorescences, H) determinate secondary branching, I) determinate glomerulus, and J) indeterminate glomerulus. 

Determinate growth presented greater seed weight, which confers agronomic advantages to the crop, like better seed and industrialization quality. This can result in greater use of determinate growth varieties that, in addition to not presenting phenological overlap, facilitates mechanized harvesting by having greater uniformity in maturity (^{Espitia et al., 2012}).

Flowering system in A. hypochondriacus

The structure of the inflorescence in plants of A. hypochondriacus was composed of an ordered set of floral branches and these emerged in the most distal region of the axillary buds located between the petiole of the leaf and the main axis.

During the stage of maturation and elongation of the plant, the main axis was composed of a repetitive set of knots that appeared along the main axis and from which caulinar leaves grew, supported by a petiole; this occurred during the vegetative phase of the plant and the floral branches during the reproductive phase. However, we found interspersed leaves in the inflorescence. The distance between the knots shortened in the area near the apex.

The helical growth of knots and floral stems along the stem was similar in both types of growth; however, the difference was in the position of the flowers and branching of the lateral shoots. In the determinate inflorescences, terminal flowers appeared adjacent to the stem in the axilla of the bract and at the end of the lateral branch. In the indeterminate inflorescences the floral production was indefinite during the life cycle of the plant and branching was observed in lateral shoots (Figure 3G).

Floral biology

Amaranthus hyponchondriacus is a monoecious plant (Espitia et al., 2010). The process of floral transition in A. hypochondriacus occurred gradually in the basipetal direction; the meristem of the inflorescence is responsible for the establishment of a series of floral meristems (Figure 3A), which will give shape to floral branching or differentiate in the organs of flowers (Figure 3B).

Flowering in both types of growth (determinate and indeterminate) occurred gradually and appeared organized in dichasic tops which as a whole formed glomeruli (Figure 3E). The first floral structures that developed were the organs of the male flowers (Figure 3F); firstly the external tepals, internal tepals and finally the stamens. There was a variable number of flowers in each glomerulus.

The staminated flowers were found in the bifurcations of the floral structure. In determinate inflorescences a terminal flower grew in the axilla, directly from the stem or at the top of the floral branches and top of the main axis. In indeterminate inflorescences an initial staminated flower was followed by an indefinite number of pistillate flowers, and all of them gave rise to the glomeruli; this reiterative growth continued during the life cycle of the plant.

A terminal flower appeared on the main axis and secondary axes of determinate inflorescences while, at the glomerulus level, the production of flowers continued. The floral development ceased gradually and was evident as there were no anthers. Thus, it is likely that at the glomerulus level there is also determinate growth. In contrast, in indeterminate inflorescences the glomeruli continued to flower, though they were less dense than the determinate (Figure 3J).

Development and floral growth emerged simultaneously in each type of inflorescence. The ovules presented different degrees of maturity, the largest corresponded to the most developed flowers and so on until finding flowers in development. This was due to the fact that the primordia adjacent to the growing flowers originated the floral organs of the contiguous flower from the last whorl (^{Flores et al., 2008}). This caused the female flowers to present different stages of development, which indicated the existence of phenological overlap. According to ^{Kaur et al. (2015)}, indeterminate growth tends to accentuate competition in the plant for resources within the stem leaving seeds unfilled.

Floral structure

The inflorescence of A. hypochondriacus is composed of male and female flowers. At the base of the male flowers, sessile female flowers grew (Figure 3F), and this type of growth allowed the formation of dichasic tops since new flowers emerged with this same pattern of development (Figure 3A). There were female flowers composed of one bract, five tepals and the gynoecium, and the bract was subtending the new flower (Figure 3C). The gynoecium when releasing the seed had a horizontal abscission in the middle of it (Figure 3D). Male flowers were composed of two bracts and five tepals that cover the stamens, which coincides with that reported by ^{Townsend (1993)}.

In determinate growth plants, we found terminal flowers with five, seven, eight, nine and six stamens, while in indeterminate plants there were only pentameric flowers (Figure 4). Terminal flowers are pedicelled, male or hermaphroditic and can appear in the node of the main axis, top of the main axis and top of the floral branches in determinate growth plants.

Figure 4 Terminal flower in determinate inflorescences of Amaranthus hypochondriacus: A) terminal flower before anther exposure, B) non-functional terminal flower, C) terminal flower with seven stamens releasing pollen, and D) terminal flower with five stamens. 

Meristematic development

Phase I: Vegetative. The meristem appeared immersed in the stem, completely covered with leaf primordia, these in turn had subsequent axillary primordia, and the leaves grew along the stem helically. The meristem in this stage produced the stem, branches and leaves (Figure 5 A-B).

Figure 5 Development of the apical meristem of Amaranthus hypochondriacus: A) vegetative phase, meristem immersed in the main axis, B) transition to reproductive phase, C) and D) elongation of the apical meristem and appearance of floral primordia, E) increase in number of bracts and growth of floral primordia. MA, apical meristem; BR, bract and PF, floral primordium. 

Phase II: Reproductive. During floral induction, the apical meristem lengthened producing an inflorescent meristem (Figure 5 C-D). In this stage, the meristem gave rise to a combination of branches, bracts and flowers. The floral transition process began with the production of bract primordia which were observed in the form of a lobe and, when developed, they completely covered the apical meristem, preventing their ongenetic changes from being observed. However, we could observe the moment of transition because the number of bracts increased with respect to the number of leaves (Figure 5 E).

Each one of the bracts had a floral meristem in its axilla, a characteristic also described in Cladium jamaicence (^{Richards, 2002}) and Chenopodium quinoa (^{Bertero et al., 1996}, ^{Bull-Hereñu and Claben-Bockhoff, 2013}). The axillary meristems were differentiated into a branch or a floral bud, and this growth process repeated along the floral branching. Thus, thickening was observed at the apex of the plant covered with a set of bracts growing around the apical meristem at different levels, and this was possible due to a longitudinal cut of the early growth of the inflorescence (Figure 6). According to ^{Preston (2010)}, during the floral induction the levels of cell division increase, which causes the apical meristem to lengthen, producing an inflorescent meristem. The floral transition process occurred in a basipetal direction along the axis of the inflorescence.

Figure 6 Development of the inflorescence in Amaranthus hypochondriacus: A-D) increase of floral primordia, E) male flower in development. BR, bract; FL, flower; MA, apical meristem; PF, floral primordium; T, tepal. 

Phase III. Differentiation of the apical meristem. The time of appearance of the terminal flower occurred after the establishment of floral meristems. ^{Bull-Hereñu and Claben-Bockhoff (2013)} noted that the size of the apical meristem predetermines the number of nodes it can produce before transforming into a terminal flower. Before the appearance of the terminal flower, we observed that the meristem flattens and then the floral organs, sepals, stamens and carpel developed. In simple terminal inflorescences, the first to mature was the terminal flower.

A basipetal floral development is described for A. hypochondriacus, but ^{Endress and Peter (2010)} mention that if in a determinate inflorescence the flower opens before the lateral flowers it is incorrect to describe flowering as basipetal because the terminal flower belongs to a lower axis in the order of appearance of the flowers.