That claim is founded on a series of undeclared but contestable assumptions to do with timescales, geology and industrial processes. Show your workings and prepare to have them pooh-poohed. I will allow, for the sake of argument, that there is no second Earth.
It's a problem typically related to population increase in the past. It is not caused directly by it (unless humans are sea dwelling mammals that crap PCBs). We can simultaneously increase population and decrease quantities of crap we offload into the oceans. It requires better management of water on farms (which is a good idea anyway), less polluting power stations (also a good idea in and of itself) and many other things that are in general all good ideas that should be done anyway.
On a more cynical level, you are changing your logic and I will be leveraging that if you don't revert to your original course. The planet's ability to sustain a given number of human lives is not a factor of any single resource other than oxygen* or water neither of which is in any danger of reaching lethal levels of scarcity. The seas can lose all of their edible species of fish without necessitating hunger. We can take to farming more species of fish if we like. In a few decades (maybe less) we can probably grow Cod in a petri dish. In the meantime there are plenty of delicious vegetables for all. The shift you are subtly, and no doubt unconsciously making, is to drift away from the empirical claim that the world cannot support x number of people, towards a normative attitude that it shouldn't. But that is a different claim.
The price increases. A thing that economists call a 'price signal' then applies. Supply is diverted away from frivolous uses such as relatively cheap jewellery and gimmicky deodorants, towards applications where an increasingly expensive commodity adds greater value (investment, "hoarding", and those few industrial uses where it is an essential ingredient to a high value product). The market sends price signals and suppliers, investors and customers respond to them. Silver jewellery becomes rarer and more expensive over a very long time period. Civilisation does not collapse. Easy.
And each year, we also improve our ability to discover more resources, find new uses for what used to be discarded, and retrieve resources that once were nonviable. Not only has this pattern been demonstrated by generation after generation ever since the dawn of the industrial revolution, but it has gathered momentum with every year also. You are neglecting a crucial factor. Innovations are driven by a variety of factors, but primary among them is demand. Things sometimes pop up ahead of the need (lasers being the obvious example), but their availability tends to create demand for their application. Most innovation though are designed to solve the problem that is in front of their creator. Academic studies show that in the 19th century American industrial patents were skewed towards labour saving innovations, whereas British ones tended towards conservation of fuel - this reflected the huge availability of wood in America at the time (a resource since massively depleted, but without which they continue to thrive) and the much looser labour supply in Britain at the time. The greatest economic gains on both sides of the Atlantic still went to firms that could make the most of both resource types.
*I was highly disappointed by the results of googling "Peak Oxygen". Why is there no campaign to preserve this most precious of all the resources? Has our supply of panicking Cassandras peaked?
