The thesis focuses on exploring the population dynamics produced by different mathematical models by studying qualitatively the prominent features of population behaviour and by using time series and spectral analysis. The main emphasis is on numerical simulations.

 The model used in the second and third part of the thesis is a discrete-time, host-parasitoid model, which is suited for describing arthropod host-parasitoid systems. The model produces complex dynamics, which include multiple attractors, basins of attraction with fractal properties, intermittency, supertransients and chaotic transients. In this thesis we present new features of the well-studied class of models by showing that a basic predator-prey model produces many dynamic complexities which have previously been observed only separately in models of various disciplines.

In the same way as in wavelengths in light we can use different colours to describe the frequency distribution of the population abundances. Time series is red if it is dominated by long-term changes and blue if the short-term variations are more prominent. "Ecological colour problem" refers to the fact that many common population models exhibit blue dynamics unlike the observations in nature, which indicate the dominance of longer-term variations. In the thesis we investigate two frequently-used discrete-time population models and observe that in some cases the insertion of environmental stochasticity into the model may turn blue dynamics into red. Spectral analysis has been used to study population dynamics not only in the time domain but also in the frequency domain. This thesis shows that in addition to internal dynamics of the population other components of the ecological time series, e.g., interactions with other populations and stochastic environment shoud be considered.