Step 1: Understanding the Concept:
Soil actinomycetes, particularly species of the genus *Streptomyces*, are valuable sources of biologically active secondary metabolites.
These metabolites are widely used in agriculture as natural antibiotics, insecticides, acaricides, and fungicides.
Step 3: Detailed Explanation:
Let us analyze the biological origins of the listed compounds:
1. Tetranactin:
This macrotetrolide antibiotic is produced by *Streptomyces aureus*.
Thus, Option (A) is incorrect.
2. Avermectins:
This group of insecticidal and anthelmintic compounds is produced by the soil bacterium *Streptomyces avermitilis*.
Thus, Option (B) is incorrect.
3. Strobilurins:
This class of natural fungicides was originally isolated from the wood-rotting mushroom fungus *Strobilurus tenacellus*, not a bacterium.
Thus, Option (C) is incorrect.
4. Milbemycins:
Milbemycins are a group of macrolide compounds with potent acaricidal and insecticidal activity.
They are produced by fermenting the soil actinomycete *Streptomyces hygroscopicus* (specifically *Streptomyces hygroscopicus* subsp. *aureolacrimosus*).
They function by opening glutamate-gated chloride channels in the nervous systems of insects and mites.
Step 4: Final Answer:
The group of compounds produced by *Streptomyces hygroscopicus* is Milbemycin.
Therefore, the correct option is (D).