EDIT

List of Areas in advanced search aren't sorted in any way (http://test.e-taxonomy.eu/dataportal/preview/fauna-europaea/cdm_dataportal/search)

The function to sort them assumes to sort them by orderIndex.
https://dev.e-taxonomy.eu/gitweb/cdm-dataportal.git/blob/HEAD:/modules/cdm_dataportal/cdm_dataportal.search.php#l695

Although for all areas the order index is 0.
http://test.e-taxonomy.eu/dataportal/preview/fauna-europaea/cdm_dataportal/taxon/e5b22697-cf8f-49e8-aa90-82db69f4769d

Solution: change to sort them by representation_L10n in cdm_dataportal.api.module or the webservice should provide the proper orderIndex.

{
  "prevIndex": 0,
  "records": [
    {
      "representation_L10n_abbreviatedLabel": "GR-AEG",
      "representation_L10n": "Vóreion Aiyáion (North Aegean Is.)",
      "partOfUuid": "",
      "orderIndex": 0,
      "class": "TermDto",
      "uuid": "d6fba8ab-8444-497f-a47a-1ea03ca21512",
      "vocabularyUuid": "0f955dba-4b88-4af5-b2fd-ff022c518b42"
    },
    {
      "representation_L10n_abbreviatedLabel": "HU",
      "representation_L10n": "Hungary",
      "partOfUuid": "",
      "orderIndex": 0,
      "class": "TermDto",
      "uuid": "d4ac836a-ff6d-413d-8a17-0f24c369ff49",
      "vocabularyUuid": "0f955dba-4b88-4af5-b2fd-ff022c518b42"
    },
    {
      "representation_L10n_abbreviatedLabel": "NL",
      "representation_L10n": "The Netherlands",
      "partOfUuid": "",
      "orderIndex": 0,
      "class": "TermDto",
      "uuid": "a47a5c46-67a0-4bfb-a383-d6ef6c35fdbb",
      "vocabularyUuid": "0f955dba-4b88-4af5-b2fd-ff022c518b42"
    },
    {
      "representation_L10n_abbreviatedLabel": "RU-RUE",
      "representation_L10n": "East European Russia",
      "partOfUuid": "",
      "orderIndex": 0,
      "class": "TermDto",
      "uuid": "8ba4c423-5933-4180-aab4-41d9036a6635",
      "vocabularyUuid": "0f955dba-4b88-4af5-b2fd-ff022c518b42"
    },

...