  Unraveling patterns of animals' movements is important for understanding the
fundamental basics of biogeography, tracking range shifts resulting from
climate change, predicting and preventing biological invansions. Many
researchers have modeled animals' dispersal studying their behavior under the
assumptions of some movement strategies pre-determined or affected by some
external factor(s) but none of them have compared the efficiency of different
dispersal strategies in providing population survival and fitness. We
hypothesize that 1) successful expansion could result from some evolutionary
stable strategy (ESS) and 2) such strategy could be based particularly on
deferred gain, when animals invest in travel to reach some high-quality habitat
("habitat of dream"). Using simulation model we compare the ecological success
of three strategies: i) "Smart" - choosing the locally optimal cell; ii)
"Random" - random movement between cells without taking into account the
quality of the environment; iii) "Dreamer" - movements that aims to find "a
habitat of dream" with quality much higher than that of the initial and
neighboring cells. The population fitness was measured as survival rate,
dispersal distance, accumulated energy and quality of settled habitat. The most
general conclusion is that while survival and wealth of the population is
affected presumably by overall habitat quality, the dispersal depends mainly on
the behavioral strategy. The "Dreamer" strategy or the strategy of deferred
gain belongs to the Pareto frontier in the Fitness$\times$Dispersal space but
only in optimal and suboptimal habitat and in the relatively mild climate.
