Bolzoni L. , G. A. De Leo, M. Gatto,
A. P. Dobson Body-size scaling in an SEI model of wildlife diseases
Theoretical Population Biology, 73: 374-382,
2008.
Bevacqua D. , P. Melià, A. J. Crivelli, M.
Gatto, G. A. De Leo Multi-objective assessment of conservation
measures for the European eel (Anguilla anguilla): an application to the Camargue
lagoons ICES Journal of Marine Science,
64: 1483-1490, doi:10.1093/icesjms/fsm126, 2007.
Corani G., M. Gatto Structural
Risk Minimization: a robust method for density-dependence detection and model
selection Ecography,
30: 400–416, doi: 10.1111/j.2007.0906-7590.04863.x, 2007.
Casagrandi R., L. Mari, M. Gatto Modeling
the local dynamics of the zebra mussel (Dreissena polymorpha) Freshwater
Biology, 52: 1223-1238, 2007.
Bertuzzo E., A. Maritan, M. Gatto,
I. Rodriguez-Iturbe, A. Rinaldo River networks and ecological corridors:
reactive transport on fractals, migration fronts, hydrochory Water
Resources Research, 43, W04419, doi:10.1029/2006WR005533,
2007.
Gatto M. I
cambiamenti climatici: incertezze ed evidenze scientifiche AEIT,
11: 54-58, 2006.
Bevacqua D., Melià P. , Crivelli A. J. , De
Leo G. A. , Gatto M. Timing and rate of sexual maturation
of European eel in brackish and freshwater environments Journal
of Fish Biology, 69 (Supplement C), 200–208, 2006.
Melià P., Bevacqua D. , Crivelli A. J. , Panfili
J. , De Leo G. A. , Gatto M. Sex differentiation of the
European eel in brackish and freshwater environments: a comparative analysis
Journal of Fish Biology, 69, 1228-1235, 2006.
Corani G. , Gatto M. VC-dimension
and structural risk minimization for the analysis of nonlinear ecological
models Applied Mathematics and Computation,
176: 166-176, 2006.
Melià P., Bevacqua D. , Crivelli A. J. , De
Leo G. A., Panfili J. , Gatto M. Age and growth of the
European eel Anguilla anguilla in the Camargue lagoons Journal
of Fish Biology, 68: 876-890, 2006.
Casagrandi R. , Gatto M. The intermediate
dispersal principle in spatially-explicit metapopulations Journal
of Theoretical Biology, 239: 22-32, 2006.
Corani G. , Gatto M. Model selection
in demographic time series using VC-bounds Ecological
Modelling, 191: 186-195, 2006.
Fiorese G. , Gatto M. ,Guariso G.
Utilizzo delle biomasse a scopo energetico: un’applicazione alla Provincia
di Cremona L'Energia Elettrica, 82: 1-8,
2005.
Melià P. , Gatto M. A stochastic
bioeconomic model for the management of clam farming Ecological
Modelling, 184: 163-174, 2005.
De Leo G. ,Focardi S. , Gatto M. ,
Cattadori I. The decline of the grey partridge in Europe: comparing demographies
in traditional and modern agricultural landscapes Ecological
Modelling, 177: 313-335, 2004.
Melià P. , De Leo G.A. , Gatto M.
Density and temperature-dependence of vital rates in the Manila clam Tapes
philippinarum: a stochastic demographic model Marine
Ecology Progress Series, 272: 153-164, 2004.
Gatto M. , Paris G. , Ranci Ortigosa
G. , Scherini G. Metodi quantitativi per la gestione della fauna selvatica
in provincia di Sondrio Journal of Mountain Ecology,
7 (Suppl.):17-26, 2003.
Melià P. , Nizzoli D. , Bartoli M. , Naldi M.
, Gatto M. , Viaroli P. Assessing the potential impact
of clam rearing in dystrophic lagoons: an integrated oxygen balance Chemistry
and Ecology, 19: 129-146, 2003.
Cattadori I.M. , Ranci Ortigosa G. , Gatto
M., Hudson P.J. Is the rock partridge Alectoris graeca saxatilis
threatened in the Dolomitic Alps? Animal Conservation,
6: 71-81, 2003.
De Leo G. A. , Gatto M. , Caizzi A.,
Cellina F. The ecological and economic consequences of global climate
change Recent Research Developments in Biotechnology
and Bioengineering, Special issue on “Biotechnology and Bioengineering
of CO2 fixation” pp. 1-21, 2002.
Melià P. , Casavola N. , Gatto M.
Estimating daily egg production of European anchovy in the Adriatic Sea:
a critical appraisal P.S.Z.N.: Marine Ecology,
23, Supplement 1, 272-279, 2002.
Gatto M., Caizzi A. , Rizzi L., De
Leo G. A. . The Kyoto Protocol is cost-effective Conservation
Ecology 6(1): r11. [online] URL: http://www.consecol.org/vol6/iss1/resp11,
2002.
Caizzi A , Gatto M., De Leo G. , Rizzi
L. Benefici economici del Protocollo di Kyoto AEI
89: 34-41, 2002.
Gatto M. Matematica
ed Ecologia: un’interazione feconda Bollettino
dell’Unione Matematica Italiana, Sez. A, La Matematica nella
Società e nella Cultura, Serie VIII, V-A, Dicembre 2002, pp. 515-540.
Casagrandi R. , Gatto M. (2002)
Habitat destruction, environmental catastrophes and
metapopulation extinction Theoretical Population
Biology 61: 127 -140 .
Casagrandi
R. , Gatto M. (2002) A persistence criterion for metapopulations
Theoretical Population Biology
61:
115 -125 .
De Leo G., Rizzi L. , Caizzi A., Gatto M. (2001)
The economic benefits of the Kyoto Protocol Nature
413: 478-479.
Gatto M. , De Leo G. (2001) Pricing
biodiversity and ecosystem services: Response from Gatto and De Leo BioScience,
51: 271-272 .
De Leo GA, Gatto M. (2001) A stochastic bioeconomic
analysis of silver eel fisheries Ecological
Applications 11:281-294.
Porcher E., Gatto M (2000) Quantifying the
Dynamics of Prion Infection: a Bifurcation Analysis of Laurent's Model
Journal of theoretical Biology 205: 283-296.
De Leo GA, Gatto M (2000) Pricing biodiversity
and ecosystem services: The never-ending story BioScience
50: 347-355.
Ranci Ortigosa G, De Leo GA, Gatto M (2000)
VVF: Integrating modelling and GIS in a software tool for habitat suitability
assessment Environmental Modelling &
Software 15: 1-12.
Casagrandi R, Gatto M (1999) A mesoscale approach
to extinction risk in fragmented habitats Nature
400: 560-562.
Gragnani A, Gatto M, Rinaldi S (1998) Acidic
deposition, plant pests, and the fate of forest ecosystems
Theoretical Population Biology 54: 257-269.
Gatto M, De Leo GA (1998) Interspecific competition
among macroparasites in a density-dependent host population
Journal of Mathematical Biology 37: 467-490.
Paris G, De Leo G, Menozzi P, Gatto M (1998)
Region-based citation bias in science Nature
396: 210-210.
De Leo G, Paris G, Gatto M, Menozzi P (1998)
Spotlight needed on Italian policy Nature
391: 12-12.
Capurro AF, Gatto M, Tosi G (1997) Delayed
and inverse density dependence in a chamois population of the Italian Alps
Ecography 20: 37-47
De Leo GA, Gatto M (1996) Trends in vital
rates of the European eel: Evidence for density dependence?
Ecological Applications 6: 1281-1294.
Gatto M, Ghezzi LL (1996) Optimal life strategies
in organisms exposed to recurrent critical events
Journal of Optimization Theory and Applications 90:
79-94
Abstract: The optimal partition of energy between survival
and reproduction is considered for a population subject to recurrent and potentially
lethal critical events. The best
strategy is found by maximizing fitness, a functional derived
from the Lotka equation. The dynamics is governed by a second-order, age-varying,
nonlinear system. The energy storage and the probability of survival are the
state variables, while the amounts of energy placed into and withdrawn from
the storage are the controls. The optimal life strategy is shown to be as
follows: build up the storage at the very beginning of life, and then progressively
deplete it to resist the critical events.
De Leo GA, Gatto M (1995) A size and age-structured
model of the European eel (Anguilla anguilla)
Canadian Journal of Fisheries and Acquatic Sciences 52:
1351-1367
Abstract: The life cycle of the European eel (Anguilla
anguilla) presents several distinctive features, such as high plasticity
in body growth, marked sexual dimorphism, sex ratio strongly skewed in favor
of females and sexual maturation largely dependent upon the size of individuals.
A demographic model incorporating all these characteristics is derived on
the basis of a multiple classification of individuals by age and size, and
variability in individual growth is explicitly included. Existing theory for
size-structured stocks is extended to include the dependence of sexual maturation
on size, while natural mortality is age specific. Using 1989 population data
from Comacchio lagoons (Italy), we estimate mortality and metamorphosis rate
and abundance in each age- and size-class for both yellow and silver eels,
crucial information for the management of the Comacchio fishery. The use of
a nonparametric technique (bootstrapping) yields not only the moments, but
also the distributions of these estimates. Validation of the model is performed
on the data collected in 1990. The approach adopted is very flexible and different
assumptions about survival, sexual maturation, and net selectivity can be
easily incorporated in the model.
Gatto M (1995) Sustainability - is it a well-defined
concept? Ecological Applications5:
1181-1183
Ferrière R, Gatto M (1995) Lyapunov
exponents and the mathematics of invasion in oscillatory or chaotic populations
Theoretical Population Biology 48:
126-171
Abstract: This paper concisely reviews the mathematical
properties of the dominant Lyapunov exponent of a matrix sequence in the context
of population biology. The concept of Lyapunov exponent provides a valuable
tool for investigating processes of invasion in ecology or genetics, which
are crucial in shaping community diversity, determining the spread of epidemics
or the fixation of a new mutation. The appeal of the invasibility criterion
based on the dominant Lyapunov exponentlies in the opportunity it offers to
deal with population structure, complex life cycles, and complex population
dynamics resulting from the model nonlinearities (oscillations, chaos), as
well as random fluctuations arising from a stochastic environment. We put
emphasis on the issues of the existence, numerical approximation, and regularity
of the dominant Lyapunov exponent. Our presentation is aimed at showing that,
despite our inability to compute the exponent analytically, which adds to
its high intrinsic instability, important biological insights can nevertheless
be achieved at the cost of fairly mild assumptions on the features of the
models considered.
Gatto M (1993) The evolutionary optimality
of oscillatory and chaotic dynamics in simple population-models Theoretical
Population Biology 43: 310-336
Abstract: The problem is considered of whether natural
selection favors genotypes characterized by oscillatory or chaotic population
dynamics. This is done with reference to two simple one-dimensional models,
which display a variety of dynamical patterns according to the different values
of their parameters: the semelparous and iteroparous Ricker models. To lind
the optimal genotype (or genotypes) within a given feasibility set, the concept
of Continuously Stable Strategy (CSS) and a haploid model of competition between
genotypes are used. The parameters subject to evolution are the intrinsic
finite rate of increase and respectively the juvenile mortality in the semelparous
model and the adult survival in the iteroparous one. In the semelparous case
a single feasible CSS exists, while in the other case more than one CSS might
exist. The dynamical nature of the optimal genotype (stable equilibrium, stable
sustained oscillations or chaos) is basically determined by the shape of the
set of feasibility for the parameters defining each genotype. However, if
the feasibility set is drawn at random, the probability that the corresponding
optimal genotype (or genotypes) be oscillatory or chaotic is quite low. This
result, however, might not hold with more complex models.
De Leo G, Del Furia L, Gatto M (1993) The
interaction between soil acidity and forest dynamics - a simple-model exhibiting
catastrophic behavior Theoretical Population
Biology 43: 31-51
Abstract: Several hypotheses have been made to explain
the forest decline due to acidic deposition. One of the most credited is the
mobilization of toxic aluminium ions when soil pH falls below 4.2. A simple
model is presented here that couples soil chemistry with tree biomass dynamics
in order to investigate the influence of different proton loads on the existence,
stability, and bifurcations of ecosystem equilibria. It is shown that, owing
to the intrinsic nonlinear nature of the vegetation response to acid deposition,
the equilibrium manifold can have, under certain conditions, the structure
of a fold catastrophe. Increasing acidic load can thus drive the forest through
a catastrophic transition from a viable equilibrium to extinction. Simulations
using realistic ranges for model parameters and acidic input show that forests
may indeed meet the conditions for a catastrophic collapse resulting from
accumulation of acidic stress in the soil.
Ferrière R, Gatto M (1993) Chaotic
population-dynamics can result from natural-selection
Proceedings of the Royal Society of London B-Biological Sciences
251: 33-38
Abstract: The question of whether animal populations
display chaotic dynamics has motivated a thriving body of research for two
decades. Yet unambiguous evidence for chaos in the wild remains scarce. Accordingly,
it has been proposed that evolutionary forces act to preserve populations
from chaos as well as oscillations. We have tested for this hypothesis by
considering the dynamics associated with evolutionarily stable life histories
(including age of maturity, adult survivorship and recruitment to adulthood)
in a simple, but general, demographic model. Contrary to expectation, individual
selection operating on demographic traits should often lead to oscillatory
or chaotic dynamics for species with late feasible ages of maturity and many
age classes. Also, the optimality of chaos is more likely whenever trade-offs
constrain recruitment to rapidly decrease with increasing adult survival or
decreasing age of maturity. Our results bring evolutionary support to the
possibility that chaotic population dynamics might be much more widespread
than inferred until now from data analyses. Furthermore, these findings provide
novel support for the view that chaos could be an optimal regime for several
biological systems.
Gatto M, Ricci C, Loga M (1992) Assessing
the response of demographic parameters to density in a rotifer population
Ecological Modelling 62: 209-232
Abstract: A multiage class model of population growth,
the parameters of which are estimated partly from life and fertility schedules
and partly from mass culture data, is presented. The estimation procedure
is applied to the data provided by a cohort of about 100 isolated animals
and by ten replicate batch cultures of Philodina roseola, a bdelloid rotifer.
The identification of an appropriate demographic model permits the evaluation
of how various demographic parameters (such as the mean age at death and the
duration of the reproductive period) respond to density. The mean age at death
is influenced only by densities close to the carrying capacity, while fecundity
is affected by density over its whole range of variation. Specifically, total
life span is dramatically extended by extreme crowding, whereas total egg
production is depressed and the duration of reproduction prolonged by gradually
increasing the density. The ecological and evolutionary implications of these
results are briefly discussed.
Gatto M, Ghezzi L (1992) Taxing overexploited
open-access fisheries - The role of demand elasticity
Ecological Modelling 60: 185-198
Abstract: The paper aims at identifying the effects exerted
by a tax levy on an overexploited and previously unregulated fishery. The
analysis is carried out by means of a dynamic model that includes fish stock
and harvesting effort as state variables. Attention is focused on the role
played by demand elasticity which is shown to affect both transients and equilibria.
According to the analysis, a levy induces a contraction in effort, which is
sharper in the short term. As a consequence, the fish population recovers
and ultimately settles at a higher equilibrium level. Therefore, a larger
amount of fish is caught in the long run and sold at a lower price than in
the unregulated setting. The more inelastic the demand, the smaller both the
equilibrium price for fish and the tax imposed.
Viganò L, Galassi S, Gatto M (1992) Factors
affecting the bioconcentration of hexachlorocyclohexanes in early life stages
of Oncorhynchus-mykiss Environmental Toxicology
and Chemistry 11: 535-540
Abstract:
A commercial mixture of alpha-, beta-, gamma-, and delta-hexachlorocyclohexane
(-HCH) isomers has been tested for bioconcentration on early life stages of
Oncorhynchus mykiss. Experimental results were elaborated by means of BIOCON,
an interactive program for personal computers that provides bioconcentration
factors (BCFs) and kinetic uptake and depuration coefficients as well as their
standard deviations. The comparisons performed on a statistical basis evidenced
few differences among the bioconcentration capability of larval stages, contrary
to what was observed in previous studies with other chemicals. In the early
juvenile stage, alpha- and delta-HCH are characterized by higher BCFs than
the gamma-isomer. The role of lipids is also investigated. The total lipid
content seems to play a major role in influencing bioaccumulation parameters
but cannot thoroughly explain BCF variability, which must be ascribed to other
factors such as life stage and lipid composition.
Gatto M, Ghezzi L (1992) Optimal diffusion
of a new technology when both demand and supply are nonstatic
Journal of Optimization Theory and Applications 73:
75-87
Abstract: The investment problem of a monopolized sector
selling an innovated product is explored. Learning by doing is supposed to
occur on the supply side, while learning by using is introduced to explain
demand growth. Pontryagin's maximum principle is applied to the resulting
optimal control problem, which includes supply capacity and cumulative output
as state variables. The optimal investment policy turns out to be of a very
simple form: all profit is retained and invested until capacity achieves its
optimal size. In spite of this, the new technology price displays a variety
of time patterns that heavily depend on the actual demand and cost conditions,
as one would expect in the real world.
Gatto M, Ghezzi L, Rinaldi S (1991) Optimal
investment in the reclamation of eutrophic water bodies
Journal of Optimization Theory and Applications 71:
389-398
Abstract: Eutrophication, i.e., the abnormal growth of
phytoplankton, is considered in this note, which focuses on the optimal treatment
of eutrophic water bodies. The issue is addressed by the use of a nonlinear
model where phytoplankton and the number of wastewater treatment plants in
operation are the state variables. The decision maker is a governmental agency
which has to define the time pattern of investment in new plants so as to
minimize the present value of environmental and treatment costs. The optimal
solution is shown to have the following features. First, the optimal size
for the wastewater treatment system is attained in minimum time. Subsequently,
investment replaces wornout treatment plants, and phytoplankton adjusts asymptotically
to its optimal equilibrium value.
Slobodkin LB, Bossert P, Matessi C, Gatto M
(1991) A review of some physiological and evolutionary aspects of body
size and bud size of hydra Hydrobiologia
216: 377-382
Abstract: Green hydra with endosymbionts are smaller
than brown asymbiotic ones. Regeneration experiments, mitotic index studies
on algal and hydra tissue, and evidence for consumption and expulsion of algae
are reviewed and it is suggested that larger green hydra have more difficulty
controlling algal increase than smaller ones and that hydra have an upper
size limit for maintenance of stable symbioses. A mathematical model is discussed
which starts with simple physiological assumptions about hydra and generates
field testable conclusions about how body and bud size, and reproductive rates
depend on food particle size, quantity and temporal distribution. Unlike most
analytic ecological-evolutionary models, this one integrates physiology, ecology
and evolution without needing simplifying assumptions.
Gatto M (1991) Some remarks on models of
plankton densities in lakes The American
Naturalist 137: 264-267
Gatto M, Ghezzi L, Rinaldi S (1991) The optimal
reclamation of eutrophic water bodies Applied
Mathematics and Computation 43: 105-115
Abstract: The reclamation of a eutrophic water body is
set as an optimal control problem. The aim is to take account of some basic
biological and economic features which were disregarded in previous analyses
of the problem. To this end, an optimization model is developed where phytoplankton
and nutrients are the state variables, the efficiency of the wastewater treatment
system is the control variable, and minimizing the discounted stream of both
environmental and treatment cost is the objective. Through a singular perturbation
argument a reduced order dynamic model is obtained, to which Pontryagin's
principle is applied. The optimal solution is such that (1) an optimal equilibrium
for phytoplankton is achieved in the long run, and (2) both phytoplankton
and the efficiency of the treatment system strictly decrease with time.
Other
Publications
- Gatto M (1990) A general minimum principle
for competing populations - Some ecological and evolutionary consequences
Theoretical Population Biology 37:
369-388
- Gatto M, Guariso G (1989) A report on some
recent experiences in developing environmental software
Ecological Modelling 47: 19-32
- Gatto M, Matessi C, Slobodkin LB (1989) Physiological
profiles and demographic rates in relation to food quantity and predictability
- An optimization approach Evolutionary
Ecology 3: 1-30
- Gatto M, Muratori S, Rinaldi S (1988) A
functional interpretation of the logistic equation
Ecological Modelling 42: 155-159
- Gatto M, Muratori S, Rinaldi S (1988) On
the optimality of the logistic growth Journal
of Optimization Theory and Applications 57:
513-517
- Gatto M, Rinaldi S (1987) Some models of
catastrophic behavior in exploited forests
Vegetatio 69: 213-222
- Matessi C, Gatto M (1984) Does K-selection
imply prudent predation? Theoretical Population
Biology 25: 347-363
- Gatto M, Rinaldi S (1982) Special issue
- ecology, renewable resources and optimal-control
Ecological Modelling 14: 151-151
- Gatto M, Locatelli A, Laniado E, et al. (1982)
Some problems of effort allocation on 2 noninteracting fish stocks
Ecological Modelling 14: 193-211
- Frelek B, Gatto M, Locatelli A (1982) Optimal
allocation of vessels along a fish migration path
Ecological Modelling 14: 229-250
- Gatto M Comments on MacArthur's
minimization principle:A footnote(1982) The
American Naturalist 119: 140-144
- Deklerk P, Gatto M (1981) Some remarks
on periodic harvesting of a fish population
Mathematical Biosciences 56: 47-69
- Gatto M, Rinaldi S (1980) A method for
the real-time forecast of the outflow from a lake
Applied Mathematical Modelling 4: 322-324
- Gatto M, Rinaldi S (1980) Determination
of a commercial fishery production-model
Ecological Modelling 8: 165-172
- Gatto M, Rinaldi S (1980) Estimating escapements
of anadromous fishes via upstream test fishing data
Ecological Modelling 8: 173-188
- Peterman RM, Gatto M (1978) Estimation
of functional responses of predators on juvenile salmon J
FISH RES BOARD CAN 35: 797-808