Parker G A, Ball M A, Chubb J C
Division of Population and Evolutionary Biology, School of Biological Sciences, University of Liverpool, Liverpool L69 7ZB, UK.
J Theor Biol. 2009 May 7;258(1):135-47. doi: 10.1016/j.jtbi.2009.01.016. Epub 2009 Jan 25.
Larval helminths in intermediate hosts often stop growing long before their growth is limited by host resources, and do not grow at all in paratenic hosts. We develop our model [Ball, M.A., Parker, G.A., Chubb, J.C., 2008. The evolution of complex life cycles when parasite mortality is size- or time-dependent. J. Theor. Biol. 253, 202-214] for optimal growth arrest at larval maturity (GALM) in trophically transmitted helminths. This model assumes that on entering an intermediate host, larval death rate initially has both time- (or size-) dependent and time-constant components, the former increasing as the larva grows. At GALM, mortality changes to a new and constant rate in which the size-dependent component is proportional to that immediately before GALM. Mortality then remains constant until death or transmission to the definitive host. We analyse linear increasing and accelerating forms for time-dependent mortality to deduce why there is sometimes growth (intermediate hosts) and sometimes no growth (paratenic hosts). Calling i the intermediate or paratenic host, and j the definitive host, conditions favouring paratenicity are: (i) high values in host i for size at establishment, size-related mortality, expected intensity, (ii) low values in host i for size-independent mortality rate, potential growth rate, transmission rate to j, and ratio of death rate in j/growth rate in j. Opposite conditions favour growth in the (intermediate) host, either to GALM or until death without GALM. We offer circumstantial evidence from the literature supporting some of these predictions. In certain conditions, two of the three possible growth strategies (no growth; growth to an optimal size then growth arrest (GALM); unlimited growth until larval death) can exist as local optima. The effect of the discontinuity in death rate after GALM is complex and depends on mortality and growth parameters in the two hosts, and on the mortality functions before and after GALM.
中间宿主体内的幼虫期蠕虫往往早在其生长受到宿主资源限制之前就停止生长，而在转续宿主体内则根本不生长。我们基于营养传播蠕虫幼虫成熟时的最佳生长停滞（GALM）构建了我们的模型[Ball, M.A., Parker, G.A., Chubb, J.C., 2008. 当寄生虫死亡率与大小或时间相关时复杂生命周期的演化。《理论生物学杂志》253, 202 - 214]。该模型假设，幼虫进入中间宿主后，其死亡率最初既有与时间（或大小）相关的成分，也有与时间无关的恒定成分，前者会随着幼虫的生长而增加。在GALM时，死亡率转变为一个新的恒定速率，其中与大小相关的成分与GALM之前的比例成正比。然后死亡率保持恒定，直至死亡或传播到终末宿主。我们分析了与时间相关的死亡率的线性增加和加速形式，以推断为何有时会生长（中间宿主），而有时不会生长（转续宿主）。将i称为中间宿主或转续宿主，j称为终末宿主，有利于转续现象的条件是：（i）宿主i中建立时的大小、与大小相关的死亡率、预期感染强度较高；（ii）宿主i中与大小无关的死亡率、潜在生长速率、向j的传播速率以及j中的死亡率/j中的生长速率的比值较低。相反的条件则有利于（中间）宿主体内的生长，要么生长到GALM，要么在没有GALM的情况下直至死亡。我们从文献中提供了一些间接证据来支持其中一些预测。在某些条件下，三种可能的生长策略中的两种（不生长；生长到最佳大小然后生长停滞（GALM）；无限生长直至幼虫死亡）可以作为局部最优解存在。GALM后死亡率的不连续性的影响很复杂，取决于两个宿主中的死亡率和生长参数，以及GALM前后的死亡率函数。
