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Population dynamics is affected by environmental fluctuations (such as climate variations), which have a characteristic correlation time. Strikingly, the time scale of predictability can be larger for the population dynamics than for the underlying environmental fluctuations. Here, we present a general mechanism leading to this increase in predictability. We considered colored environmental fluctuation acting on a population close to equilibrium. In this framework, we derived the temporal auto and cross-correlation functions for the environmental and population fluctuations. We found a general correlation time hierarchy led by the environmental-population correlation time, closely followed by the population autocorrelation time. The increased predictability of the population fluctuations arises as an increase in its autocorrelation and cross-correlation times. These increases are enhanced by the slow damping of the population fluctuations, which has an integrative effect on the impact of correlated environmental fluctuations. Therefore, population fluctuation predictability is enhanced when the damping time of the population fluctuation is larger than the environmental fluctuations. This general mechanism can be quite frequent in nature, and it largely increases the perspectives of making reliable predictions of population fluctuations.

IntroductionObservational and modeling studies have examined the interactions between El Niño-Southern Oscillation (ENSO) and the equatorial Atlantic variability as incorporated into the classical charge-recharge oscillator model of ENSO. These studies included the role of the Atlantic in the predictability of ENSO but assumed stationarity in the relationships, i.e., that models’ coefficients do not change over time. A recent work by the authors has challenged the stationarity assumption in the ENSO framework but without considering the equatorial Atlantic influence on ENSO.MethodsThe present paper addresses the changing relationship between ENSO and the Atlantic El Niño using an extended version of the recharge oscillator model. The classical two-variable model of ENSO is extended by adding a linear coupling on the SST anomalies in the equatorial Atlantic. The model’s coefficients are computed for different periods. This calculation is done using two methods to fit the model to the data: (1) the traditional method (ReOsc), and (2) a novel method (ReOsc+) based on fitting the Fisher’s Z transform of the auto and cross-correlation functions.ResultsWe show that, during the 20th century, the characteristic damping rate of the SST and thermocline depth anomalies in the Pacific have decreased in time by a factor of 2 and 3, respectively. Moreover, the damping time of the ENSO fluctuations has doubled from 10 to 20 months, and the oscillation period of ENSO has decreased from 60-70 months before the 1960s to 50 months afterward. These two changes have contributed to enhancing ENSO amplitude. The results also show that correlations between ENSO and the Atlantic SST strengthened after the 70s and the way in which the impact of the equatorial Atlantic is added to the internal ENSO variability.ConclusionsThe remote effects of the equatorial Atlantic on ENSO must be considered in studies of ENSO dynamics and predictability during specific time-periods. Our results provide further insight into the evolution of the ENSO dynamics and its coupling to the equatorial Atlantic, as well as an improved tool to study the coupling of climatic and ecological variables.

Environmental fluctuations can create population-depleted areas and even extinct areas for the population. This effect is more severe in the presence of the Allee effect (decreasing growth rate at low population densities). Dispersal inside the habitat provides a rescue effect on population-depleted areas, enhancing the population resilience to environmental fluctuations. Habitat reduction decreases the effectiveness of the dispersal rescue mechanism. We report here how the population resilience to environmental fluctuations decreases when the dispersal length or the habitat size are reduced. The resilience reduction is characterized by a decrease of the extinction threshold for environmental fluctuations. The extinction threshold is shown to scale with the ratio between the dispersal length and the scale of environmental synchrony, i.e. it is the dispersal connection between non-environmentally-correlated regions that provides resilience to environmental fluctuations. Habitat reduction also decreases the resilience to environmental fluctuations, when the habitat size is similar to or smaller than the characteristic dispersal distances. The power laws of these scaling behaviors are characterized here. Alternative scaling functions with spatial scales of population synchrony are found to fit the simulations worse. These results support the dispersal length as the critical scale for extinction induced by habitat reduction.