Remember the most important rule of a food-chain: the source of energy at the base must be renewable.
Photosynthesis has always been the base of all major food chains (major as in involving transitions of great amounts of energy) because it is based on the free, easily available and longest lasting source of energy: sunlight.
Chemosynthesis
This is usually believed to be the earliest type of respiration on Earth. The primitive beings, the ancestors of archaea used to live by eating sulfurous compounds found abundantly in the oceanic hot springs.
It has happened once, it can happen again on another planet. The advantages are:
- The process is very simple and does not require complex digestive system. Highly suitable for simple life forms.
- Creatures relying on this method of respiration can (and do) populate closed places where sunlight never reaches (deep, closed caverns and endemic habitats on seafloor). Simple food webs can be designed for such localities, with these creatures on the base.
- Also provides an excellent biological channel for converting these compounds into products which are more easily utilized by intelligent life forms (humanoids?) on the planet. For example, archaea eating hydrogen sulfide would convert it to sulfur dioxide, which disperses into the air. At other locations strong reducing agents would reduce sulfur dioxide back to amorphous sulfur, creating sulfur ores. This would help assemble all crustal sulfur into ores which are easily utilized by the humanoids. On the contrary, it would be practically impossible for your humanoids to go on collecting small amounts of hydrogen sulfide from several cave systems and deep-sea vents.
However, this might not be a very good idea for serving as the base for all food webs on your planet. Here are some of the disadvantages of this method:
It does not create large amounts of energy (as compared to glucose combustion) which means that it cannot power complex, multicellular organisms.
Another reason for not supporting complex life is that the waste products of most chemosynthesizing processes (specially those involving sulfur and nitrogen) produce highly toxic waste products (anywhere from sulfur powder to sulfuric and nitric acids). While it is easy to quickly expel such disastrous chemicals from a single cell, it would be impossible to collect and expel all the toxic waste created by all the body cells in a complex organism.
High-energy chemical can be present on a planet in large quantities, but without any proper cycle, they are always exhaustible and non-renewable. This means that in the long run, most of chemosynthesizing organisms would go extinct (as their food sources deplete and vanish), ultimately leaving on small, isolated population around limited locations where natural process recreate some of the high-energy chemicals.
Radiosynthesis
I don't even know where this idea came from and how it is supposed to work. There are only two (possible) advantages of this method:
Radioactive decay is usually orders of magnitude more energetic than chemical reactions (1 kg atomic bomb versus 1 kg TNT) so a creature relying on this method would require very minute amounts of food for sustenance. If a creature is somehow able to power itself through fusion (instead of fission) it would only require to eat once in its entire lifetime (violent pun intended).
It would be extremely cool to have such creatures around!
However, powering a biological engine by this method does not come without some nuisances. Few that I can think of, right now, are following:
It happens that nuclear decay does not only release huge amounts of energy, but also creates deadly radiation including gamma and X-rays. These rays are known to irrepairably damage DNA. A population of radiosynthesizing creatures would gradually sterilize the whole area of all life. There is no question of a food-chain appearing in the first place.
Without thick sheets of radiation absorbing material (lead comes to mind), the creatures themselves would be at risk of severe mutations, hereditary diseases and cancers. We are basically talking about a creature which has a lead-shield around each of its organs. Note that there are types of radiation-resistant bacteria, but they are all bacteria (single celled). No complex life form has ever been seen to be able to cope with high energy radiation.
Such organisms and the food chains based on them, would only be active in regions where there are at least moderate concentrations of radioactive elements in the soil. This means that like chemosynthesis, radiosynthesis can also only support limited, endemic populations of simple creatures.
Magnetosynthesis
This comes even crazier than radiosynthesis. Earth has a colossal magnetic field. But how on Earth can an organism utilize this magnetic field to obtain energy is anybody's guess. Rotating an electricity-conductive coil in a magnetic field induces the flow of current in the coil, true. But how can a creature generate such a coil and how is it going to rotate that coil without applying more mechanical energy than electrical energy it is going to obtain?
Despite all the absurdities and impossibilities regarding the origin and biology/physics of such a creature, there is still one advantage of such a (hypothetical) creature:
- It will baffle the scientists out of their wits and someone will receive a nobel prize for disproving the law of conservation of energy.
However, there is also a downside of this scenario:
Other (Hypothetical) Possibilities
By this term, I mean using sunlight for creating high-energy compounds without the complexities of chlorophyll-related processes. The possibilities include:
Creatures which convert sunlight into electrical energy through biological solar cells.
Creatures which create glucose through a process not involving chlorophyll.
Creatures subsisting on chemosynthesis, but replenishing their exhausted chemical supplies by reconverting spent chemicals back into high-energy chemicals, using sunlight. For example:
Hydrogen Sulfide + Oxygen => Hydrogen oxide + Sulfur dioxide + energy
Hydrogen oxide + Sulfur dioxide + sunlight => Hydrogen Sulfide + Oxygen
