English: The photographer is unknown to me, and the photo is unattributed by the author of the article in which it appears. In it one might estimate that Anderson was in his 60s, and the photo taken in the 1880s or 1890s.
Date
Source
Jepson, Willis Lynn. 1929. The Botanical Explorers of California - V. Madrono 1:214-216;
Unknown. Based on the appearance of the subject (C. L. Anderson), the photo was taken in the 1880s, when the subject was in his 60th year. The author of the article in which this photo (unnamed source) appeared died in 1946.
Note that it may still be copyrighted in jurisdictions that do not apply the rule of the shorter term for US works (depending on the date of the author's death), such as Canada (50 p.m.a.), Mainland China (50 p.m.a., not Hong Kong or Macao), Germany (70 p.m.a.), Mexico (100 p.m.a.), Switzerland (70 p.m.a.), and other countries with individual treaties.
Reasons for believing this to be in the Public Domain:
I recently copied (snipped) and cropped the photo as found in an article published 90 years ago (Willis Linn Jepson. 1929. The Botanical Explorers of California - V. Madrono 1:214-216., available online at: https://www.biodiversitylibrary.org/page/47993035#page/166/mode/1up).
The subject, Charles Lewis Anderson, died in 1910. The source of the photo was not given in the article. I haven't been able to find the name of the photographer. American botanists (and no doubt other professionals) of the later 1800s sometimes exchanged photos of themselves in lieu of actually meeting, due to the often great distances separating them. The photo used by Jepson may have circulated that way.
The author of the article (Willis Linn Jepson) died 73 years ago.
Captions
Charles Lewis Anderson, unattributed photo in Jepson, 1929 (Madrono, 1:214)