sich vermehren
to reproduce
The number of living beings (people, animals, plants) increases through reproduction.
Kaninchen vermehren sich sehr schnell.
Rabbits reproduce very quickly.

to reproduce / increase
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to reproduce
The number of living beings (people, animals, plants) increases through reproduction.
Kaninchen vermehren sich sehr schnell.
Rabbits reproduce very quickly.

The word 'vermehren' (to reproduce / increase) is inseparable and is derived from the word 'mehr' (more). The prefix 'ver-' here strengthens the idea of increase that is already contained in the root 'mehr'.
Durch die neuen Maßnahmen soll die Sicherheit vermehrt werden.
The new measures are intended to increase safety.
The use of 'vermehren' (to reproduce / increase) changes the meaning. 'Sich vermehren' (reflexive; to reproduce) is used for living beings that reproduce. 'Etwas vermehren' (transitive with an accusative object; to increase something) means to increase an amount or a value.
Die Algen im Teich haben sich stark vermehrt.
The algae in the pond have reproduced rapidly.
The reflexive form 'sich vermehren' (to reproduce) is used almost exclusively in biological contexts for animals, plants, bacteria, or cells. Typical adverbs are 'schnell' (quickly), 'rasant' (rapidly), or 'unkontrolliert' (uncontrollably).
In diesem feuchten Klima vermehren sich die Mücken rasant.
In this humid climate, mosquitoes reproduce rapidly.
The transitive form 'etwas vermehren' (to increase something) is often used for abstract things or possessions. Typical objects are 'das Vermögen' (fortune), 'das Kapital' (capital), 'das Wissen' (knowledge), or 'den Reichtum' (wealth).
Durch Lesen kann man sein Wissen täglich vermehren.
By reading, you can increase your knowledge every day.
to increase
'erhöhen' and 'vermehren' can both express that something becomes more. 'erhöhen' is very general and works well with numbers, prices, temperatures, or risks. 'vermehren' is used when the amount or number becomes larger, often with money, possessions, or living beings. With animals and plants, 'sich vermehren' is especially typical because it is about reproduction. For abstract values like pressure, volume, or temperature, 'erhöhen' sounds more natural.

Im warmen Wasser vermehren sich die Bakterien sehr schnell.
In warm water, the bacteria reproduce very quickly.
Der Trainer erhöht das Tempo, damit die Mannschaft fitter wird.
The coach increases the pace so that the team gets fitter.