The Drake equation has proven fertile ground for speculation about the abundance, or lack thereof, of communicating extraterrestrial intelligences (CETIs) for decades. It has been augmented by subsequent authors to include random variables in order to understand its probabilistic behaviour. However, in most cases, the emergence and lifetime of CETIs are assumed to be independent of each other. In this paper, we will derive several expressions that can demonstrate how CETIs may relate to each other in technological age as well as how the dynamics of the concurrent CETI population change under basic models of interaction, such as the Allee effect. By defining interaction as the change in the expected communication lifetime with respect to the density of CETI in a region of space, we can use models and simulation to understand how the CETI density can promote or inhibit the longevity and overall population of interstellar technological civilizations.

Fertilization success will determine the rate at which a population can expand and is especially important when considering small, establishing or enduring communities. Introduced species frequently fail to establish reproductively functional populations due to strong Allee effects associated with low densities. The native European oyster, Ostrea edulis broods its fertilized eggs in the pallial cavity for a period of 8–10 days before releasing the larvae. It is considered a partial broadcast spawner and was used as a model species to assess the importance of Allee effects such as inter-individual distance on reproductive success. Distances between individual oysters within test plots in areas of known oyster density were used in conjunction with standardized brood size (n larvae g−1 total wet weight) to assess fertilization success. A significant, positive relationship was observed between brood size and oyster density. Oysters with a nearest neighbour ≤1.5 m were found to brood significantly more larvae than individuals with nearest neighbours ≥1.5 m. Therefore, high density sites need to be maintained to ensure the recovery and enhancement of this OSPAR Convention recognized species in decline.

This article is concerned with a stochastic multipatch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch model that was recently introduced by Kang and the author. The main objective is to understand the effect of the geometry of the network of interactions, which represents potential migrations between patches, on the long-term behavior of the metapopulation. In the limit as the number of patches tends to ∞, there is a critical value for the Allee threshold below which the metapopulation expands and above which the metapopulation goes extinct. Spatial simulations on large regular graphs suggest that this critical value strongly depends on the initial distribution when the degree of the network is large, whereas the critical value does not depend on the initial distribution when the degree is small. Looking at the system starting with a single occupied patch on the complete graph and on the ring, we prove analytical results that support this conjecture. From an ecological perspective, these results indicate that, upon arrival of an alien species subject to a strong Allee effect to a new area, though dispersal is necessary for its expansion, fast long-range dispersal drives the population toward extinction.

The introduction of the ragweed leaf beetle in the South of Russia in 1978–1989 wasaccompanied by a number of spectacular phenomena that determined the general success ofthe ragweed control and further dispersal and acclimatization of the beetles:(i) formation of solitary population waves (SPW), characterized by anextremely high density of the phytophage population at the narrow band of the front of amoving wave defoliating nearly all ragweed plants, and (ii) rapid, within5-6 generations, development of flight in the leaf beetle species that in its homelandlost the ability to fly. We present here a demogenetic model capable of reproducing boththese phenomena, assuming that the flight ability of a phytophage population is governedby a single diallelic locus with flight and flightless alleles that determine threegenotypes of the ragweed leaf beetle. Simulation results agree well with the practicalrecommendation of retaining a high density of common ragweed in the release area in orderto provide the necessary conditions for the initial increase of the leaf beetle populationand the formation of the wave. The model confirms the earlier hypothesis that the SPW isthe key factor that determines efficiency of weed biocontrol program. We demonstrate alsothat the formation of the wave has crucially accelerated the development of the beetles’ability to fly.

This work deals with the consequences on structural stability of Gause type predator-preymodels, when are considered three standard functional responses and the prey growth rateis subject to an Allee effect.

An important consequence of this ecological phenomenon is the existence of a separatrixcurve dividing the behavior of trajectories in the phase plane. The origin is an attractorfor any set of parameters and the existence of heteroclinic curves can be also shown.

Conditions on the parameter values are established to ensure the existence of a uniquepositive equilibrium, which can be either an attractor or a repellor surrounded by one ormore limit cycles.

The influence of the Allee effect on the number of limit cycles is analyzed and theresults are compared with analogous models without this phenomenon, and which mainfeatures have been given in various above works. Ecological interpretations of theseresults are also given.

The Oriental White Stork Ciconia boyciana is threatened with extinction due to anthropogenic habitat destruction. The scaling of its environmental capacity (K) with number of patches (P) has been studied and its response to the cumulative impact of anthropogenic habitat destruction has been simulated by a non-autonomous population model for single species. The results are: 1) The scaling index of environmental capacity of the Oriental White Stork to number of patches is 0.9768, i.e., K∝P0.9768. 2) By designing different scenarios to improve habitat quality, we find that it is more beneficial for the long-term persistence of the Oriental White Stork to increase average patch size than to increase the number of patches, if the total area of habitat remains the same. 3) If the Allee effect is significant, the Oriental White Stork is a ‘living dead’ species – one which is doomed to local extinction. To avoid extinction, habitat quality must be considerably improved.

Southern fur seals Arctocephalus australis in Peru have declined gradually over the past decade, and declined dramatically (72%) as a result of low food availability during the severe El Niño in 1997–98. In 1999, seals abandoned some historically important breeding sites. This is particularly alarming because new sites were not colonized. Our objective was to examine how habitat features and human disturbance influenced whether sites were currently used, abandoned or apparently not used in the past by fur seals for breeding. Data were collected on 14 variables at 70 potential breeding sites at three guano reserves in Peru. Discriminant analysis revealed significant multivariate differences among sites currently used for breeding, abandoned sites and unused sites (F=5.97, P<0.00001), and the model classified 74% of sites correctly. Currently used sites were less likely to have human disturbance and more likely to have offshore islands, stacked rocks, tide pools and abundant shade. Separate discriminant analyses for each reserve produced similar results. Habitat associated with thermoregulation (e.g. shade or pools) may be more important to fur seals in Peru, which breed at lower latitudes and are at greater risk of overheating on land than other populations. Habitat with minimized human access may be especially important to seals in small populations in which individuals may perceive themselves as more vulnerable because of decreased vigilance and dilution effects. Seals in our study selected breeding habitat with stacked rocks, which create shade and tide pools for thermoregulation and make human access difficult; but pups might suffer higher mortality in this habitat. We hypothesize that fur seals in Peru may exhibit an Allee effect, whereby suitability of habitat varies with population abundance.