adhaś cordhvaḿ prasṛtās tasya śākhā
guṇa-pravṛddhā viṣaya-pravālāḥ
adhaś ca mūlāny anusantatāni
karmānubandhīni manuṣya-loke

Translation of Bhagavad Gita 15.2

The branches of this tree extend downward and upward, nourished by the three modes of material nature. The twigs are the objects of the senses. This tree also has roots going down, and these are bound to the fruitive actions of human society.

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

The description of the banyan tree is further explained here. Its branches spread in all directions. In the lower parts, there are variegated manifestations of living entities—human beings, animals, horses, cows, dogs, cats, etc. These are situated on the lower parts of the branches, whereas on the upper parts are higher forms of living entities: the demigods, Gandharvas and many other higher species of life. As a tree is nourished by water, so this tree is nourished by the three modes of material nature. Sometimes we find that a tract of land is barren for want of sufficient water, and sometimes a tract is very green; similarly, where particular modes of material nature are proportionately greater in quantity, the different species of life are manifested accordingly.

The twigs of the tree are considered to be the sense objects. By development of the different modes of nature we develop different senses, and by the senses we enjoy different varieties of sense objects. The tips of the branches are the senses—the ears, nose, eyes, etc.—which are attached to the enjoyment of different sense objects. The twigs are sound, form, touch, and so on—the sense objects. The subsidiary roots are attachments and aversions, which are byproducts of different varieties of suffering and sense enjoyment. The tendencies toward piety and impiety are considered to develop from these secondary roots, which spread in all directions. The real root is from Brahmaloka, and the other roots are in the human planetary systems. After one enjoys the results of virtuous activities in the upper planetary systems, he comes down to this earth and renews his karma, or fruitive activities for promotion. This planet of human beings is considered the field of activities.

Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

The branches of this tree spread down (adhah) in the form of animals and others, and upward in the form of the birth of devatas and other elevated beings. These branches increase and increase by the watering, in the form of actions of the three gunas (guna pravrddha). The small twigs of the branches are the sense objects such as sound (visaya pravalah). Moreover, it can be inferred that, at the base of the tree, unknown to all people, is some great treasure. There are external roots from the branches of the asvattha, meaning in this case banyan tree, which is dependent for support on both the main root and the external roots. These secondary roots, the cause of continued action, spread out everywhere  (anusantantani) below Brahmaloka (adhah), in the planet of humans. Karma anubandhini means that after enjoying the results of ones actions, those actions become stimulus for actions in another human birth.

Commentary by Sri Ramanuja of Sri Sampradaya:

15.2 The ‘secondary roots’ of this tree having the main roots in the world of Brahman and its crest in men ramify below in the world of men. They bind them according to their Karma. The meaning is that the effects of acts causing bondag become roots in the world of men. For, the effect of actions done in the human state brings about the further condition of men, beasts etc., down below, and of divinities etc., up above.

Commentary by Sri Sridhara Swami of Rudra Sampradaya:

The branches of this ancient banyan tree are the perishable jivas or embodied beings from Brahma the secondary creator who lives for trillions of years down to humans who may live for a hundred years down to an insect that may live only for some hours. All regardless of their span of life have their limiting adjuncts and restricted effects and represent the branches of this tree. Of those jivas who have the inclination for evil and demoniac activities their births will be in the reptile and insect species. Those jivas who are oblivious to their divine nature and act like beasts will correspondingly take birth in the animal kingdom and those jivas of virtuous and pious nature nature will take birth among the Brahmins, Vaisnavas and demigods. All jivas constitute the unlimited branches of this ancient banyan tree represented in the mundane material existence. Furthermore it should be understood that they are nutured by the three gunas or modes of goodness, passion and nescience according to their qualifications and propensities. The tips of the branches are the senses and the innumerable sprouts and shoots are the sense objects. The roots are spread out above and below with the central primary tap root representing the Supreme Lord alone with the roots below representing desires for enjoyment and the roots above representing subtle impressions of past enjoyments. The effects of such are specifird by the words karma anubandhani which refers to actions according to the proclivity to perform righteous or unrighteous activities which results in corresponding reactions some positive, some benign and some negative. When past reactions eventually have been finally exhausted the jiva once more takes birth in the world of humans directly related to the influence of the subtle impressions accumalated from enjoyments experienced in the previous lives and worlds which are the subtle motivating impetus for the inclinations and propensity to experience these activities again. The ability to experience these actions is limited to the worlds of humans alone and so Lord Krishna states manusya-loke meaning the world of men.

Commentary by Sri Madhvacharya of Brahma Sampradaya:

Since the unmanifest atma or immortal soul exists in an impreceptible sub- atomic form within the bodies of all jivas or embodied beings, they are described as spread upwards and downwards. The attributes are the modes of material nature, the three gunas of sattva or goodness, rajas or passion and tamas or ignorance. The pleasurable experiences are the sprouts and desires are the buds. The main central root is the divine resplendence representing the Supreme Lord and the subsidary roots are the results acquired due to following righteousness or unrighteousness. This is described in the Ballava section.

In this ancient asvattha or banyan tree representing material existence the brahman or spiritual substratum pervading all existence as manifestation of the Supreme Lord is the primary and central root. The subsidary root is prakriti the material substratum pervading physical existence and the three gunas are its attributes. The elements earth, water, fire, air and ether are the branches and the leaves are the Vedic hymns. The demigods who administer universal management are the smaller branches and human beings are the twigs. From adherance or rejection of the injunctions and prohibitions defined in the Vedic scriptures do sweet and bitter fruits results which are the karmas or reactions to the previous actions one has performed. Righteous actions bestow pleasant rewards and unrighteous actions bestow unpleasant rewards. This ancient banyan tree rewards liberation and bondage as well depending upon the merit of righteousness enacted. It also has fruits, branches and roots that are unmanifest as well as those that are apparent and manifest. This does not otherwise come to happen neither does it not come not to happen. This means that the cause is enveloped in the effect and that the effect is containing the cause. In this way as a tiny seed contains an entire tree and a tree contains a tiny seed the roots and the branches are intertwined eternally.

Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

Describing the roots and branches of the asvattha or banyan tree allegorically to symbolise material existence. Lord Krishna further explains that the branches that rise upwards symbolise the higher level jivas or embodied beings such as the demigods and humans. The branches that turn downwards are lower level jivas such as animals, birds, fish and plants. The roots extend upwards to Satya loka the highest material planet of Brahma and extends downwards also into the worlds of humans where innumerable new sub-roots manifest which are the karma or reactions to actions performed by every human. The twigs are impressions from past desires and the sprouts are the desired sense objects. All parts of this tree are within prakriti the material substratum pervading physical existence and are nourished by the three gunas or modes of material nature which are sattva or goodness, rajas or passion and tamas or nescience. Those lower level jivas who have degenerated into various forms of demoniac entities due to performing evil activities to others as well as degraded activities unto themselves inevitably sink into the fiery hellish worlds for aeons and aeons of atonement. Contrarily the higher level jivas who adhered to the injunctions and prohibitions of the Veidc scriptures receive meritorious births in the heavenly worlds of the demigods. Possessing the nature of good or evil each jivas karma binds them in samsara the perpetual cycle of birth and death and is manifested in manusya the worlds of humans.

The purport is that after exhaustion of all karma and its residue of the jiva enjoying ecstatically in the heavenly worlds or suffering in misery in the hellish worlds due to either following or ignoring the injunctions and prohibitions of the Vedic scriptures. One is rewarded after death by performing meritorious deeds or punished by performing degraded deeds during each human lifetime in pursuit of pleasure and sense gratification. After hundreds of thousands of such lifetimes these desires for pleasure become deep rooted tendencies that causes subtle impressions to be imprinted upon the subtle body of the jiva who takes birth in the worlds of humans. These impressions are so resolute that subconsciously the jiva craves and seeks the same pleasures enjoyed in the previous life and performs the same and similar activities in which they had achieved fulfillment before.

Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

15.2 Sakhah, the branches, as it were; tasya, of that Tree; prasrtah, extending; adhah, downwards, from the human beings to the immobile (trees etc.); ca, and; urdhvam, upwards, upto Brahma-beginning from the Creator of the Cusmos to Dharma (Death) [According to A.G. ‘human beings’ stands for the world of human beings, and ‘Brahma ‘ for the ‘world of Brahma’ (Satva-loka). So Dharma may mean the ‘world of Death’ (pitr-loka).-Tr.], which, ‘in accordance with their work and in conformity with their knowledge’ (Ka. 2.2.7), are the results of knowledge and actions; are guna-pravrddhah, strengthened, made stout, by the qualities sattva, rajas and tamas, which are their materials; and visaya-pravalah, have the sense-objects as their shoots. The sense-objects (sound etc.) sprout, as it were, like new leaves from the branches (bodies etc.) which are the results of actions. Thereby the branches are said to have sense-objects as their shoots. The supreme Root, the material cause of the Tree of the World, has been stated earlier. And now, the latent impressions of attraction, repulsion, etc. born of the results of action are the subsidiary roots, as it were, which grow later on and become the cause of involvement in righteousness and and unrighteousness. And those mulani, roots; karma-anubandhini, which are followed by actions; anu-santatani, spread, enter; adhah, downwards, as compared with the world of gods; manusya-loke, into the world of human beings particularly-for it is well known that (only) here men have competence for rites and duties. They (these roots) are said to be karma-anubandhini since actions (karma) that are characterized as righteous and unrighteous follow as their product (anubandha), (i.e.) succeed the rise of those (attraction, repulsion, etc.).

Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:

15.1-2 Urdhva-mulam etc. Adhas ca etc. In other scriptural texts it is delcared ‘All is the holy Fig-tree; that alone is to be meditated upon’. The present verse tells us this : What is intended by that declaration is only the religious meditation of the Brahman, the Bhagavat. Root : the one with a highly tranquil nature. That is high (above) : Becasue it can be attained by him alone who has withdrawn himself from every other [lower] thing. The [Vedic] hymns are the leaves [of it] etc. : Just as the girth, height, the fruits and the taste etc. of a tree are indicated by its leaves, in the same fashion the idea of the Brahman-being is through the scriptures that are included in the ‘Vedic hymns’. This is what is narrated here. With Strands : i.e., with the Sattva etc. Well developed : i.e., starting from gods down to the stationary ones. Of this tree, the roots, that are below, are the good and bad actions.

Sanskrit Shloka Without Transliteration Marks:

adhas cordhvam prasrtas tasya sakha
guna-pravrddha visaya-pravalah
adhas ca mulany anusantatani
karmanubandhini manusya-loke

Sanskrit to English Word for Word Meanings:

adhaḥ — downward; ca — and; ūrdhvam — upward; prasṛtāḥ — extended; tasya — its; śākhāḥ — branches; guṇa — by the modes of material nature; pravṛddhāḥ — developed; viṣaya — sense objects; pravālāḥ — twigs; adhaḥ — downward; ca — and; mūlāni — roots; anusantatāni — extended; karma — to work; anubandhīni — bound; manuṣya-loke — in the world of human society.