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the study of the effects of noise is a well established subject in several different disciplines ranging from physics , to chemistry and to biology @xcite .
the essential role of the noise in theoretical ecology however has been recently recognized .
some key questions in population ecology are related to the understanding of the role that noise , climatic forcing and nonlinear interactions between individuals of the same or different species play on the dynamics of the ecosystems @xcite .
more recently noise induced effects on population dynamics have been investigated @xcite . in this paper
we study the dynamics of two and three interacting species in the presence of multiplicative noise and a periodic driving force .
specifically we consider : ( a ) two competing species and ( b ) three interacting species .
the multiplicative noise models the interaction between the species and the environment , and the driving force mimics the climatic temperature oscillations . in case ( a )
the interaction parameter between the species is a stochastic process which obeys an ito stochastic differential equation .
the noise induces spatio - temporal patterns , quasi - deterministic oscillations , stochastic resonance ( sr ) phenomenon @xcite and noise delayed extinction , which is akin of the noise enhanced stability @xcite . in case ( b )
we find noise induced spatial patterns whose time evolution is strongly dependent on the initial conditions .
specifically we consider two different initial conditions : ( i ) an uniform initial distribution which gives rise to anticorrelated spatio - temporal patterns between the two preys , and ( ii ) a peaked initial distribution which gives rise periodically to a strong correlation between the patterns of the three species .
time evolution of two competing species is obtained within the formalism of the lotka - volterra equations  @xcite using the ito scheme    @xmath0    where @xmath1 is gaussian white noise with zero mean and @xmath2@xmath3 = @xmath4 .
the multiplicative noise models the interaction between the environment and the species .
the interaction parameters @xmath5 and @xmath6 are characterized by a critical value corresponding to @xmath7 .
we choose @xmath8 . for @xmath9 a coexistence regime of the two species
is established , while for @xmath10 an exclusion regime takes place , i.e. in a finite time one of the two species extinguishes .
the two regimes correspond to stable states of the deterministic lotka - volterra model .
it is then interesting to investigate the time evolution of the ecosystem for @xmath11 varying around the critical value @xmath12 in the presence of fluctuations , due to the significant interaction with the environment .
the interaction parameter @xmath11 therefore can be described by a stochastic process which obeys the following differential equation    @xmath13    where @xmath14 is a bistable potential ( see fig.1 )    @xmath15    @xmath16 is a gaussian white noise with the usual statistical properties : @xmath17 and @xmath18 .
we perform simulations of eqs .
( 1 ) and ( [ lotvol ] ) by using a bistable potential @xmath14 centered at @xmath19 , i.e. in the coexistence region .
we consider as initial value of the interaction parameter @xmath20 , which corresponds to the left minimum of the potential well ( see fig.1 ) .
we fix the intensity of the multiplicative noise at a constant value @xmath21 , and we vary the intensity of the additive noise . for low noise intensity
the two species coexist all the time , while by increasing noise one species dominates the other one for a random time and quasi - deterministic oscillations take place . by increasing even more the noise intensity the coherent response to environment variations
is lost ( see figs.2(a),(b ) and ( c ) ) .
these time variations of competing populations are due to noise induced phenomena , namely quasi - deterministic oscillations and stochastic resonance . in fig.2(d ) we report the snr of the squared difference of population densities @xmath22 . at a finite noise intensity @xmath23
the snr exhibits a maximum , which characterizes the sr phenomenon .
now we consider the effect of the additive noise @xmath24 in eq.([beta_eq ] ) on the extinction time of the species and we neglect the multiplicative noise and the periodical forcing . because of the initial condition , the ecosystem is in the coexistence region , then the deterministic extinction time of both species is infinity . by introducing noise , exclusion takes place and a finite mean extinction time ( met ) appears . by increasing the noise intensity
we obtain a noise delayed extinction : both species survive because of the noise
. then the average extinction time grows reaching a saturation value , which corresponds to the absence of the barrier of the potential @xmath14 .
the met as a function of the noise intensity @xmath24 takes a minimum at a finite noise intensity @xmath25 .
we perform 1000 realizations of eqs .
( [ lotvol ] ) and the results are shown in fig.3 .
in this section we study the effects of the noise on the spatial distribution of interacting species .
in particular we analyze the spatial distribution of two different ecosystems : ( a ) two competing species , ( b ) three interacting species , one predator and two preys . to study the spatial effects we consider a discrete time evolution model , which is the discrete version of eqs.(1 ) and ( 2 ) with diffusive terms , namely a coupled map lattice  @xcite .
the time evolution of the spatial distribution for the two species is given by the following equations    @xmath26    where @xmath27 and @xmath28 are the densities of the species in the site _
( i , j ) _ at the time step _
n _ , @xmath29 is the interaction parameter at the same time , _ d _ is the diffusion constant and @xmath30 indicates the sum over the four nearest neighbors .
the @xmath31 and @xmath32 terms are independent gaussian random variables with zero mean and variance unit .
the interaction parameter @xmath33 is a stochastic process obtained by solving iteratively eq.([beta_eq ] ) .
the bistable potential is centered at @xmath34 and @xmath35 , which corresponds to the minimum of the left well .
the results of our simulations are shown in fig .
+    we observe periodical formation of correlated patterns .
after 600 time steps the spatial distributions of the two species appear almost independent . after 3000 time steps the anticorrelation between the two species densities increases
. a further evolution of the system produces again spatial distributions which are independent after 4800 time steps and anticorrelated after 5400 time steps .
the two competing species tend to occupy different spatial places periodically without overlap .
finally we analyzed an ecosystem composed by three species : two preys and one predator .
we use the same coupled map lattice model of the previous section    @xmath36 + \sqrt{\sigma_z}z_{i , j}^n z_{i , j}^n + d\sum_\delta ( z_{\delta}^n - z_{i , j}^n),\label{}\end{aligned}\ ] ]    where @xmath27 , @xmath28 and @xmath37 are respectively the densities of preys _ x _ , _ y _ and of the predator _ z _ in the site _ ( i , j ) _ at the time step _
_ , @xmath38 and @xmath39 are the interaction parameters between preys and predator and d is the diffusion coefficient .
the interaction parameter @xmath11 between the two preys is a periodical function whose value , after _
n _ time steps , is given by    @xmath40    with @xmath41 , @xmath42 and @xmath43 .
we consider two different initial conditions : ( i ) a homogeneous initial distribution and ( ii ) a peaked initial distribution . in the first case we find exactly anticorrelated spatial patterns of the two preys , while the spatial patterns of the predator show correlations with both the spatial distributions of the preys ( see fig .
the preys tend to occupy different positions as in the case of two competing species . in the second case we use delta - like initial distributions for the two preys and a homogeneous distribution for the predator .
after @xmath44 steps we find strongly correlated spatial patterns of the preys which almost overlap each other .
the maximum of spatial distribution of the predator is just at the boundary of the spatial concentrations of the preys , so that the predator surrounds the preys ( see fig.6 ) .
the preys now tend to overlap spatially as it occurs in real ecosystems when preys tend to defend themselves against the predator attacks .
we analyzed the role of the noise on the spatio - temporal behaviors of two ecosystems composed by two and three interacting species .
we use lotka - volterra generalized equations with multiplicative noise , climatic periodic forcing and random interaction parameter .
the main conclusions of this work are : ( i ) in the case of two interacting species the appearance of noise induced phenomena such as quasi - deterministic oscillations , stochastic resonance , noise delayed extinction and spatial patterns ; ( ii ) in the case of three interacting species the formation of dynamical spatial patterns exhibiting correlations which are strongly dependent on the initial conditions .
our population dynamical model could be useful to explain spatio - temporal experimental data of interacting species strongly interacting with the noisy environment @xcite
. a more detailed study of the dynamics of spatial patterns through stochastic partial differential equations will be the subject of future investigations .
this work has been supported by intas grant 01 - 450 , by infm and miur .
f. de pasquale and b. spagnolo `` _ _ stochastic model of population dynamics _ _ '' , in `` chaos and noise in biology and medicine '' , eds .
m. barbi and s. chillemi , world scientific * 7 * biophysics , ( 1998 ) 305 - 314 .
a. f. rozenfeld , c. j. tessone , e. albano , h. s. wio _ on the influence of noise on the critical and oscillatory behaviour of a predator - prey model : coherent stochastic resonance at the proper frequency of the system , phys .
a _ * 280 * ( 2001 ) 45 - 52 .
lotka , proc .
sci . u.s.a . * 6 * , 410 ( 1920 ) ; v. volterra , _ variazioni e fluttuazioni del numero di individui in specie animali conviventi , mem . accad .
nazionale lincei ser .
_ serie 6 * 2 * ( 1926 ) 31 - 113 .
j. garcia lafuente , a. garcia , s. mazzola , l. quintanilla , j. delgado , a. cuttitta , b. patti , _ hydrographic phenomena influencing early life stages of the sicilian channel anchovy , fishery oceanography _ * 11/1 * ( 2002 ) 31 - 44 .
a. caruso , m. sprovieri , a. bonanno , r. sprovieri , _ astronomical calibration of the upper serravallian / tortorian boundary at case pelacani section 8(sicily , italy ) , riv .
_ * 108/2 * ( 2002 ) 297 - 306 .
r. sprovieri , e. di stefano , a. incarbona , m. e. gargano , _ a high - resolution record of the last deglaciation in the sicily channel based on foraminifera and calcareous nanofossil quantitative distribution , palaeogegraphy , palaeoclimatology , palaeoecology _ ( 2002 ) , in press .
we study the time evolution of two ecosystems in the presence of external noise and climatic periodical forcing by a generalized lotka - volterra ( lv ) model . in the first ecosystem , composed by two competing species , we find noise induced phenomena such as : ( i ) quasi deterministic oscillations , ( ii ) stochastic resonance , ( iii ) noise delayed extinction and ( iv ) spatial patterns . in the second ecosystem , composed by three interacting species ( one predator and two preys ) , using a discrete model of the lv equations we find that the time evolution of the spatial patterns is strongly dependent on the initial conditions of the three species .