Learn French: Les maladies émergentes effrayent le troupeau. - The emerging diseases frighten the herd.

This highlights the exact difference between a verbal adjective and a present participle! The present participle of the verb émerger is émergeant (it requires an a to maintain the soft g sound). However, the verbal adjective form changes the spelling completely to émergent. Because it acts as an adjective here describing les maladies, it takes the feminine plural agreement: émergentes.

How do I know whether to use the present participle (émergeant) or the verbal adjective (émergent) in my own sentences?

If the word describes a characteristic or a state, it is an adjective and must agree in gender and number with the noun (e.g., des maladies émergentes). If it expresses an active action, it is a present participle and is invariable (it never changes). You will often see the present participle followed by a preposition or object, such as: Les maladies émergeant de la forêt (The diseases emerging from the forest).

I usually see this verb conjugated as effraient. Is effrayent a typo?

No, both spellings are perfectly correct! For verbs ending in -ayer (like effrayer, payer, essayer), you always have the choice to either keep the y or change it to an i in front of a silent e. Therefore, ils effrayent and ils effraient are completely interchangeable.