Research by a Canadian group (Ontarian, to be exact), found that the Great Lakes sea rocket (the perfect name for a beach weed), aka Cakile edentula, appears to be able to distinguish between plants that are related to it, and those that are not (published in Biology letters - and if anyone can tell me why this was buried in this journal, I will be forever grateful).
The bottom line here is that plants do not have consciousness (which should go without saying...). But through some yet unknown mechanism they are able to sense when they are in a pot with siblings, and they decrease their root allocation in this situation compared to when they share a pot with strangers (i.e. non-related plants). Presumably, the plants can tell through some chemical signal when they are surrounded by other plants, allocating to their roots in order to out-compete them. Somehow the signal is different when the surrounding plants are siblings, resulting in decreased allocation (and fitness, importantly). The difference in allocation seems pretty significant, and the error bars are not enormous. The question remains - what signals are given off by sibling plants telling them to decrease allocation (maybe whoever answers that will have themselves a Science paper).
The world is a fascinating place on it's own, so please do not try to explain this by invoking psychic ability of plants!