SCIENTIFIC RepoRTs | 7: 16777 | DOI:10.1038/s41598-017-16859-4
Territory holders and non-territory
holders in Ayu sh coexist only in
the population growth process due
, Takashi Uehara
, Hiromu Ito
, Jin Yoshimura
, Kei-ichi Tainaka
Ayu sh form feeding territories during a non-breeding (growing) season. When the density of the
sh increases, phases gradually change. In the early growing season, all sh can hold territories at
low density. Once all territory sites are occupied, newcomers become oaters. As the density further
increases, territory holders have to spend much more time in defending their own territory and lose
the time to feed on algae. Eventually, all sh give up their own territories and then form a school. In
contrast, when the density decreases, territories are directly reformed from the school. In short, ayu
sh exhibit a dierent transition, called hysteresis, where the two transitions occur widely-apart from
each other. The dynamics of this intrinsic phenomena has not been demonstrated in previous studies.
We develop a rate equation to describe the population dynamics within territorial competition. Our
model successfully reproduces territorial hysteresis and indicates that territory holders and oaters can
coexist only in the process of population growth. Moreover, we also nd that the two critical densities
of territorial hysteresis are conspicuously dierent from each other when the increase of the density of
oaters sharply inuences (step-function-like) the territories.
Territoriality and group foraging are classical examples of behavioral strategies to adapt to dierent ecological
. ese strategies are two dierent ways of adaptation
. Territorial behavior is an adaptation of
while group foraging is an adaptation of animals living as a group
. ese two dierent evo-
lutionary adaptations may occur in closely related species
. For example, in most migratory birds, mating pairs
oen form breeding territories while they forage as groups during non-breeding (growing) seasons. However, it
is extremely rare to see a transition between territoriality and group foraging in a single season. Here, we provide
a unique case study of sh which exhibit both territoriality and group foraging (school) as adaptive responses
during a single season.
Ayu sh (Plecoglossus altivelis, Osmeridae) are an endemic migratory sh in Japan
. is sh has a distinc-
tive life as follows
. e life cycle of ayu is completed in one year. In autumn (late August–early September),
eggs are spawned downstream of river hatch. e hatched larvae dri to an estuary near the sea within a few days
and mostly feed on zooplankton and small aquatic insects. In spring (April–May), juvenile sh migrate to mid-
stream (and/or upstream) of a river, where algae (diatoms) grow on rocks and stones of riverbeds in rapids (swi
current). ey feed on these algae from spring to fall. In this stage, especially large sh can hold their own terri-
tories in rapids, and territorial competition for food violently occurs between territory holders and non-territory
Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu, Shizuoka, 432-
Department of Computer Science, School of Computing, Tokyo Institute of Technology, Yokohama,
Kanagawa, 226-8502, Japan.
Department of Preschool Education, Nagoya College, 48 Takeji, Sakae-cho, Toyoake,
Aichi, 470-1193, Japan.
Department of International Health, Institute of Tropical Medicine, Nagasaki University,
Nagasaki, 852-8523, Japan.
Graduate School of Science and Technology, Shizuoka University, Hamamatsu,
Shizuoka, 432-8561, Japan.
Department of General Systems Studies, University of Tokyo, Meguro, Tokyo, 153-8902,
Department of Environmental and Forest Biology, State University of New York College of Environmental
Science and Forestry, Syracuse, NY, 13210, USA.
Marine Biosystems Research Center, Chiba University, Uchiura,
Kamogawa, Chiba, 299-5502, Japan. Correspondence and requests for materials should be addressed to G.I. (email:
Received: 5 April 2017
Accepted: 19 November 2017
Published: xx xx xxxx