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## Time sampling optimization for a growth model of $Pomacea\:canaliculata$ (Prosobranchia:Ampullaridae).

### Andrés O. Porta

#### Universidad Nacional de San Martín, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakac7c52e4467b41e1efa6b867f95b1684').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyac7c52e4467b41e1efa6b867f95b1684 = 'h&#117;gp&#111;rt&#97;' + '&#64;'; addyac7c52e4467b41e1efa6b867f95b1684 = addyac7c52e4467b41e1efa6b867f95b1684 + 'y&#97;h&#111;&#111;' + '&#46;' + 'c&#111;m' + '&#46;' + '&#97;r'; var addy_textac7c52e4467b41e1efa6b867f95b1684 = 'h&#117;gp&#111;rt&#97;' + '&#64;' + 'y&#97;h&#111;&#111;' + '&#46;' + 'c&#111;m' + '&#46;' + '&#97;r';document.getElementById('cloakac7c52e4467b41e1efa6b867f95b1684').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyac7c52e4467b41e1efa6b867f95b1684 + '\'>'+addy_textac7c52e4467b41e1efa6b867f95b1684+'<\/a>';

Freshwater mollusks of the American genus $Pomacea$ (Gastropoda:Prosobranchia:Ampullariidae), commonly called apple snails, have been object of intensive ecological studies because of the important damage over crops caused by invasive species of this genus, particularly in southern and eastern Asia. Most of the modeling of the growth of the species has been done adjusting a von Bertalanffy's growth curve or a polinomial curve to empirical data. Only recently (Sutton $et\:al.$, 2017), an population approach have been implemented using a set of two partial differential equation, one per sex, for modeling the growth (in terms of weight) of $P.\:maculata$. For the females population density is: $u_t(x,t)-(g(x)u(x,t))_{x}=-\mu u(x,t)$ where $u(t,x)$ represents the density of female snails of size $x$ (represented by the weight) at time $t$, $g(x)$ is the per capita growth rate of female apple snails of weight $x$ and death rate $\mu$, which is assumed as constant over the median lifespan of a female apple. An analogous equation is used for modeling the male snails density. As a preliminary of a work that has as objective the developing of populations models for some species of ampullarids of Argentina, here we present an optimal design for the time sampling of the growth of the snail $Pomacea\:canaliculata$ based in both first hand and literature data. The underlying model consist of only one equation that, taking into account empirical data on the species growth, incorporates sexual differential growth as a delay in a first growth phase in the female. The optimal schema derived will be used for prospective studies in the population growth dynamics of the species both in laboratory and natural conditions.

Joint work with Diana Rubio (Universidad de San Martín, Argentina).