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The mother spider was a large spider who grew because of toxic waste dumped at Jack Robertson’s hotel.
The spider began life as a test animal in Dr Jade McIntyre’s experiments. The creature was bred to be longer lived and have stronger webs than a normal spider to harvest the beneficial characteristics of arachnids.
When it was believed that the subjects had perished, the body was improperly disposed of and dumped in a landfill polluted with toxic waster materials. This was mixed with the spider’s altered biology, causing it to grow larger and produce a large brood of young.
Eventually, the mother spider became so big, it began to suffocate, as it could not absorb enough oxygen, even in a ballroom inside the hotel. When the Thirteenth Doctor, Yaz, Ryan, and Graham with Dr Jade McIntyre went to deal with it, they realised it was dying anyway, with Jade stating that the spider was more afraid of them than they were of it.
Robertson shot and killed it, much to the anger of everyone present. (Arachnids In The UK)