Population Dynamics Modeling of Arapaima gigas

Abstract

Pirarucu (Arapaima gigas) has been of the most important natural fishing resources of the Amazon region. Due to its economic importance, and the necessity to preserve the species hand, field research concerning the habits and behavior of the pirarucu has been increasing for the last 20 years. The aim of this paper is to present a mathematical model for the pirarucu population dynamics considering the species peculiarities, particularly the male parental care over the offspring. The solution of the dynamical systems indicates three possible equilibrium points for the population. The first corresponds to extinction; the third corresponds to a stable population close to the environmental carrying capacity. The second corresponds to an unstable equilibrium located between extinction and full use of the carrying capacity. It is shown that lack of males' parental care closes the gap between the point corresponding to the unstable equilibrium and the point of stable non-trivial equilibrium. If guarding failure reaches a critical point the two points coincide and the population tends irreversibly to extinction. If some event tends to destabilize the population equilibrium, as for instance inadequate parental care, the model responds in such a way as to restore the trajectory towards the stable equilibrium point avoiding the route to extinction. The parameters introduced to solve the system of equations are partially derived from limited but reliable field data collected at the Mamirauá Sustainable Development Reserve (MSDR) in the Brazilian Amazonian Region. KEY WORDS: Pirarucu (Arapaima gigas), population dynamics, Mamirauá, Mathematical Modeling Modelagem da Dinâmica Populacional de Arapaima gigas RESUMOPirarucu (Arapaima gigas) tem sido um dos mais importantes recursos pesqueiros naturais da Amazônia. Devido à sua importância econômica, por um lado, e a necessidade de preservar a espécie, por outro lado, o domínio da investigação relativa a hábitos e comportamento do pirarucu tem sido crescente nos últimos 20 anos. O objetivo deste trabalho é apresentar um modelo matemático para a dinâmica populacional do pirarucu considerando as peculiaridades da espécie, particularmente o cuidado parental do macho sobre seus descendentes. A solução dos sistemas dinâmicos indicaram três possíveis pontos de equilíbrio para a população. O primeiro corresponde à extinção; o terceiro corresponde a uma população estável próxima da capacidade suporte do ambiente. O segundo corresponde a um equilíbrio instável localizado entre a extinção e a capacidade suporte do ambiente. Foi mostrado que a falta do cuidado parental de machos aproxima o ponto que corresponde ao equilíbrio instável e o ponto de equilíbrio estável não trivial. Se a falta de cuidado dos machos alcança um ponto crítico, os dois pontos coincidem e a população tende irreversivelmente à extinção. Os parâmetros introduzidos para resolver o sistema de equações foram derivados parcialmente de limitados, mas confiáveis dados de campo coletados na Reserva de Desenvolvimento S...

Evidence of polygamy in the socially monogamous Amazonian fish Arapaima gigas (Schinz, 1822) (Osteoglossiformes, Arapaimidae)

“…Even though it has been exploited commercially for many years, much basic life history data are still lacking. However, several recent publications have made significant advances of our understanding of growth and reproductive behavior (Arantes et al, 2010), population dynamics (Coutinho et al, 2010;Castello et al, 2011), spatial and temporal distribution and trophic ecology (Watson et al, 2013) as well as population structuring (Hrbek et al, 2005;Hrbek et al, 2007;Araripe et al, 2013).…”

MONITOREO DE LA ABUNDANCIA DE Arapaima gigas EN LA CUENCA BAJA DEL RÍO PACAYA, RESERVA NACIONAL PACAYA SAMIRIA, AMAZONÍA PERUANA

“…Los aspectos estudiados sobre el paiche, están enfocados mayormente a la piscicultura (Bard & Imbiriba, 1986;Imbiriba, 1991;Alcántara & Montreuil, 2003;Pereira-Filho et al, 2003;Cavero et al, 2003;Cavero et al, 2004;Alcántara et al, 2005;Padilla et al, 2005;Rebaza et al, 2005;de Oliveira et al, 2012), a la producción de alevinos (Núñez, et al, 2011), dietas alimenticias (de Menezes et al, 2006;Velásquez et al, 2007;Del Risco et al, 2008) y a la determinación del sexo (Chu-Koo et al, 2009;Carreiro et al, 2011). Mientras que, los trabajos realizados en el medio natural, están referidos a los aspectos bioecológicos del paiche (Castello, 2008a;Figuereido, 2013) como la caracterización genética (Farias et al, 2003;Marques, 2003;Hrbek et al, 2005;Leão, 2009), crecimiento y desarrollo sexual (Guerra, 1980;Arantes et al, 2010), parásitos (Kritsky et al, 1986;Serrano-Martínez et al, 2015), rendimiento de la carne (Imbiriba et al, 1994), desplazamiento (Castello, 2008b;Arantes et al, 2011;Núñez-Rodríguez, et al, 2015), dinámica poblacional (Coutinho et al, 2010;Castello et al, 2011), gobernanza (Castello et al 2009;Castello y Steward., 2010) y manejo comunitario en la conservación del paiche (Alcántara & Montreuil, 2003;Castello, 2004;…”

Movement patterns and home range of wild and re-stockedArapaima gigas(Schinz, 1822) monitored by radio-telemetry in Lake Imiria, Peru

“…In spite of the tremendous economic and cultural importance of this species, behavioural studies of A. gigas in its natural habitat are scarce. Studies on the distribution and migration indicate that its population density is strongly dependent on the morphological and hydrological characteristics of the area, such as flooding duration, surface area of the water body, water depth and connectivity (Queiroz, ; Coutinho et al., ; Arantes et al., ). Similarly, studies on the reproduction and growth (Queiroz, ; Godinho et al., ; Castello, ; Arantes et al., ), and on the population dynamics of this species (Castello, ; Castello et al., ) have been carried out in Brazil, but most of this information comes from a single area no larger than 1000 km 2 , the Mamirauá Reserve (Amazonas State, Brazil), which represents less than 1% of the total distribution of the species (Castello and Stewart, ).…”