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planktonic foraminifera ( pf ) are unicellular organisms that commonly live in the sea surface and intermediate water rarely in the deepest part of water column .
pf are very sensible to the seasonal temperature variations , and in particular some species prefer sea surface tropical water , while other species prefer temperate or polar water @xcite .
the study of dynamic population of pf permit to obtain climatic curves through two methods : i ) study of the percentage ratio between tropical and temperate / polar species ; ii ) analysis of the oxygen isotope @xmath0 variations by carbonatic test of pf @xcite .
pf are in fact good markers for the reconstruction of earth climate @xcite .
moreover other methods are used to reconstruct the earth s climate history , as that based on the analysis of variations of ( @xmath0 ) , present in the ice cores from greenland and antarctic @xcite . according to refs .
@xcite , climatic fluctuations were essentially produced by cyclical variations of sun energy received by earth , that periodically change its astronomical parameters ( equinox precession , 21 ky ( @xmath1 ) ; obliquity of earth s axis , 41 ky ; eccentricity of the orbit @xmath2 ky ) .
these astronomical cyclicities are known in earth sciences as milankovitch s cycles , and they can be considered a quasi - deterministic signal that periodically produced drastic changes in earth climate .
the astronomical forcing is not the only reason for glacial / interglacial oscillations .
in fact insolation variations produce changes in the atmospheric temperature , but the geographical distribution , and position , of continent and margin plates are extremely important .
the presence of a barrier , as the continental marginal plate , indeed can influence the atmospheric and oceanic currents .
in addition to these global events , other `` randomic '' events occur : ( i ) tectonic uplift of belt ridge ; ( ii ) volcanic activity , in particular explosive eruptions ; ( iii ) meteor impacts , that occasionally strike the earth and that caused several catastrophic mass extinctions @xcite . the mediterranean sea ,
because of its geographical position , between tropical and temperate area , is a good laboratory for the study of the climatic variations of earth history @xcite .
high resolution studies carried out on marine sediments and ice cores from greenland and antarctic , have demonstrated that in the last @xmath3 kyr , in addition to the classic milankovitch cycles , other cyclic variations were present with a higher frequencies , known as sub - milankovian cycles . in particular spectral analysis carried out on these sequences
has permitted to recognize periodicities of @xmath4 , @xmath5 , @xmath6 and @xmath7 years @xcite .
recently geochemical isotopes of ice cores from greenland have suggested that earth s climate variations occur according to the model based on stochastic resonance phenomenon @xcite .
in this work we analyze data from : ( i ) mediterranean core sediments ( sites @xmath8 , leg @xmath9 ) , taken during ocean drilling program ( odp ) , and compared with upper pleistocene ice cores ( grip and gisp2 ) , from greenland @xcite ; ( ii ) landscape section outcropping in southern sicily , and compared with pliocene - pleistocene core sediments come from atlantic ocean sites @xmath10 @xcite . for detailed description of experiments
see refs .
@xcite .
-0.6 cm    -0.6 cm    -0.6 cm [ fig.3 ]    \(i ) * _ mediterranean odp sites _ * - the core from site 963 ( central part of mediterranean sea , sicily channel ) , consisting of grey marls rich of pf , was sampled each @xmath11 cm in order to have a continuous sequence from today to @xmath12 ky before present ( b.p . ) .
the pf fluctuation abundances @xcite are compared with oxygen isotope of gisp2 .
there is a good correlation between the fluctuation percentage ratio of a particular warm species ( _ globigerinoides ruber _ ) and @xmath0 variations . in particular
g. ruber _ is always present in the interval today-@xmath13 ky , even if small oscillations in percentage ratio have been observed , in some particular intervals , between @xmath14 ky and @xmath12 ky , _
g. ruber _ is absent or very rare ( fig .
2 ) due to the drastic decrease of global temperature during younger dryas and last glacial maximum periods .
\(ii ) * _ southern sicily _ * - the bonsignore section ( near ribera ) is characterized by a continuous sequence of marly - limestone and marls of trubi and monte narbone formations @xcite , rich in pf .
this sedimentary sequence is coeval with punta piccola section ( agrigento ) , where lithological cycles @xmath15 were described @xcite .
bonsignore section recover a time interval between @xmath16 my ( million years ago ) and @xmath17 my . from @xmath16
to @xmath18 my , lithological and foraminifera cyclicities are mostly controlled by precession forcing ( fig .
3a ) , while after @xmath18 my the obliquity forcing becomes dominant @xcite .
this change in climatic earth system is connected with a casual event as the uplift of panama area and , consequently , with the closure of panamian isthmus .
3a represents the time interval around the major step in panama closure .
this event produced a drastic change in oceanic and atmospheric circulation with the amplification of gulf current gyre and an increase of the formation of north atlantic deep water ( nadw ) in consequence @xcite . in fig .
3 it is possible to observe that the drastic increase of oscillation amplitude of cold species , recognized in the mediterranean sea , starts in coincidence with sharp increase of oxygen isotope ( atlantic ocean ) .
the mediterranean sea has perfectly recorded this important global climatic cooling that favored the formation of polar ice sheet @xcite .
the dynamics of the biological system above described appear rather complex due to the presence of periodicities which sometimes disappear .
the main peculiarities observed from experimental time series of pf are : ( i ) geological events produce `` time windows '' characterized by quasi - periodic fluctuations with almost constant intensity , which can be ascribed to different _ `` noise levels '' _ ; ( ii ) some periodicities appear in one of this `` time window '' , while are absent in all the other ones ; ( iii ) the two species _ g. ruber _ and _ globigerina bulloides _ coexist in a competing dynamical regime . as a first approximation we try to describe the behavior of our ecosystem by a stochastic model of two competing species by using the following generalized lotka - volterra ( lv ) equations @xcite    -0.6 cm @xmath19 where @xmath20 and @xmath21 are statistically independent @xmath22-correlated gaussian white noises with zero mean .
the multiplicative noise models the interaction between the environment and the species .
the interaction parameters @xmath23 is characterized by a critical value corresponding to @xmath24 . for @xmath25 a coexistence regime of the two species
is established , while for @xmath26 an exclusion regime takes place , i.e. in a finite time one of the two species extinguishes .
it is then interesting to investigate the time evolution of the ecosystem for @xmath23 varying around the critical value @xmath27 in the presence of fluctuations , due to the significant interaction with the environment .
this behavior can be obtained assuming @xmath23 subjected to a bistable potential and a periodic driving according to the following stochastic differential equation @xcite @xmath28 where @xmath29 , @xmath30 , and @xmath31 is a generalized bistable potential @xmath32 .
the stable states correspond to the two regimes of the deterministic lv model . in eq.([beta_eq ] ) @xmath33 is a @xmath22-correlated gaussian white noise with zero mean .
-0.3 cm    -0.3
cm [ time_series ]    to analyze the dynamics of the two species we fix the additive noise intensity at the value @xmath34 @xcite . the time series of the two species are obtained for two different values of the multiplicative noise intensity @xmath35 ( see fig .
[ time_series ] ) . for @xmath36
the two species coexist and quasi - periodic oscillations appear with random periodical inversions of populations ( fig .
[ time_series ] ) .
an increase of the noise ( @xmath37 ) produces an enhancement of the amplitude of these quasi - periodical oscillation as observed in experimental data ( see fig .  3 ) .
the appearance of some periodicities , previously `` hidden '' , are due to the stochastic resonance phenomenon .
the periodical signal of small amplitude , that is the obliquity in fig .  3 , is enhanced by the presence of the noise  @xcite .
we note finally that the theoretical model , based on the stochastic resonance phenomenon , predicts a time behavior of the two species abundances , which can not be obtained by using models which are simply periodic or stochastic @xcite .
the main peculiarities observed by analyzing our experimental data of pf in sicily channel can be explained within the proposed model of sr in population dynamics @xcite .
the nonlinearity of the natural system together with a periodical forcing and a `` _ _ noise signal _ _ '' produces a coherent response of the ecosystem , by enhancing the effect of the geological causes .
c. , pujol , c. , _ vergnaud - grazzini .
distribution patterns of live planktic foraminifers as related to regional hydrography and productive systems of the mediterranean sea _ , _ marine micropaleontology _ * 25 * ( 1995 ) 187 - 217 .
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gargano , _ a high - resolution record of the last deglaciation in the sicily channel based on foraminifera and calcareous nannofossil quantitat . distribution _ , _ palaeogeo .
paleoeco . _ * 202 * ( 2003 ) 119 - 142 .
the study of planktonic foraminifera abundances permits to obtain climatic curves on the basis of percentage ratio between tropical and temperate / polar forms . 
 climatic changes were controlled by several phenomena as : ( i ) milankovitch s cycles , produced by variations of astronomical parameters such as precession , obliquity and eccentricity ; ( ii ) continental geodynamic evolution and orogenic belt ; ( iii ) variations of atmospheric and oceanic currents ; ( iv ) volcanic eruptions ; ( v ) meteor impacts . but while astronomical parameters have a quasi - regular periodicity , the other phenomena can be considered as `` noise signal '' in natural systems . the interplay between cyclical astronomical variations , the `` noise signal '' and the intrinsic nonlinearity of the ecologic system produces strong glacial or interglacial period according to the stochastic resonance phenomenon .