Infective prey leads to a partial role reversal in a predator-prey interaction

An infective prey has the potential to infect, kill and consume its predator. Such a prey-predator relationship fundamentally differs from the predator-prey interaction because the prey can directly profit from the predator as a growth resource. Here we present a population dynamics model of partial role reversal in the predator-prey interaction of two species, the bottom dwelling marine deposit feeder sea cucumber Apostichopus japonicus and an important food source for the sea cucumber but potentially infective bacterium Vibrio splendidus. We analyse the effects of different parameters, e.g. infectivity and grazing rate, on the population sizes. We show that relative population sizes of the sea cucumber and V. Splendidus may switch with increasing infectivity. We also show that in the partial role reversal interaction the infective prey may benefit from the presence of the predator such that the population size may exceed the value of the carrying capacity of the prey in the absence of the predator. We also analysed the conditions for species extinction. The extinction of the prey, V. splendidus, may occur when its growth rate is low, or in the absence of infectivity. The extinction of the predator, A. japonicus, may follow if either the infectivity of the prey is high or a moderately infective prey is abundant. We conclude that partial role reversal is an undervalued subject in predator-prey studies.


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The predator (S) and the prey (C) interact according to a conventional predator-prey 81 model. However, the prey is pathogenic to the predator, and a part of the predator 82 population is infected (I). An infected predator can recover, die naturally, or become 83 consumed by the pathogenic prey.
84 85 A distinctive aspect in our predator-prey interaction is that both the prey and the 86 predator are only a part of a food web. Both species have a base growth rate that is 87 independent of their mutual interaction, and they both are able to grow 88 independently according to the respective carrying capacity of the environment ((vi) 89 and (vii) in Fig 1). 102 where the increases of the prey and predator abundances are both defined as logistic 103 growth. Parameters , , and are the growth rates and carrying capacities of 104 the prey and predator, respectively. Parameter (0≤a≤1) denotes the attack rate of 105 the predator S. This can be interpreted either as a fraction of the feeding area grazed 106 during a time step, or it can equally be interpreted as the prey selectivity coefficient of 107 the predator. Thus, the total number of the prey harvested by the predator is aC, and 108 the harvesting is described as Type I functional response. Parameter denotes the 109 fraction of the infective prey from the total prey population. Thus, from the predation 140 Therefore, the area of the feeding unit is set to = 1 2 0.14 = 7 2 and depth of 141 foraging to 1cm. We calculated the predator attack rate using the formula 142 = = 150 ·5.3·10 -3 -1 ℎ -1 1 -3 ⋅ 70000 2 ⋅ 1 = 1.14 ⋅ 10 -5 ℎ -1 = 2.73·10 -4 -1 . 8 144 eaten by the sea cucumber per hour per gram of sea cucumber [4], ρ is the density of 145 the sediment as given by Kennish [9], and V is the volume of the feeding unit. The 146 resulting attack rate is the nominal portion of the available prey eaten within a time 147 step. Because the actual attack rate depends also from the selectivity of the predator,  153 The symbols and parameters used in the model and are shown in Table 1.

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a) Both species coexists at a general equilibrium: , , > 0. Stability of this 190 equilibrium represent continuing coexistence of the species.

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In the absence of species interaction the environmental carrying capacity of 192 the prey is equal to K C and that of the predator is equal to ( -) / .  209 were used throughout, as well as the high mortality rates shown to be associated with 12 211 infective prey α, and the attack rate a were tested using wide parameter ranges.
212 Though the outbreaks caused by V. splendidus have been associated with high 213 mortality rates, we tested the model also with low infection mortality rates and high 214 recovery rates. Even when infection mortality μ inf and infected predator recovery β 215 were 0.3 and 0.7, respectively, the results remained qualitatively same. Initial 216 population sizes did not affect the results, and the model gives consistent results.

Results
218 For an opportunist prey with a high environmental growth rate the level of infectivity, 219 e SI, is not crucial (Fig 2). The prey population size will settle around the level of 220 carrying capacity K C . A low infectivity e SI combined with a high environmental growth 221 rate r C of the prey can be beneficial also for the predator because the predator is able 222 to sustain population levels above the environmental carrying capacity ( -) /

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. Rising the level of infectivity, however, decreases the predator population. To the 224 contrary, the population size of a prey with slow environmental growth depends on 225 the level of infectivity. Low infectivity leads to the extinction of the slowly growing 226 prey. 229 For low infectivity e SI a higher outside prey growth rate r C supports larger prey 230 population than a lower growth rate, but this is reversed if e SI increases enough. After

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243 High infectivity e SI increases the population size of a slowly growing prey because 244 increasing infectivity allows the prey to reach a higher prey population size as 245 compared to a prey with a higher growth rate r C (Fig 2). However, due to the high 246 mortality µ inf associated with the infection, a too high level of infectivity causes the 247 extinction of the predator and a decline in the prey population size. Likewise, in the 248 case of fast growing prey, very high infectivity leads the prey population size to settle 249 at the environmental carrying capacity.  286 If attack rate approaches zero both the prey and the predator population sizes tend 287 towards the environmental carrying capacity regardless of the infectivity (Fig 4).
288 Increasing attack rate may have different effects on the prey and predator sizes. When 289 the value of the infectivity remains low an increase in the attack rate benefits the 290 predator (Fig 4B). High growth rate of the prey results in larger predator population 291 than low growth rate. If the value of the infectivity is increased slightly (moderate 292 infectivity) an increment in growth rate decreases predator population sizes (Fig 4D). 297 In subfigures A and B the prey's infectivity e SI is weak. Increasing the predator attack 298 rate a decreases prey and increases predator population sizes. In contrast, e SI in 299 subfigures C and D is slightly greater, and increasing attack rate decreases the 300 population levels of the prey as well as of the predator. As the attack rate decreases, 16 302 purple and blue lines are fast (r C =50), medium (r C =5) and slow (r C =0.5) growth rates.

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The infectivity values are e SI =10 -13 in subfigures A and B, and e SI =10 -10 in subfigures C 304 and D.
305 Extinction of the species 306 We consider here the possibility of extinction of the predator or the prey. The

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The extinction of the prey depends crucially also on the attack rate of the predator 333 (Fig 5). There is a threshold value or a minimum attack rate at which the predator can 334 cause the extinction of the prey. 336 Extinction of prey is possible if the predator's attack rate is higher than the threshold 337 defined by the prey's growth rate. Fast growing prey survives higher predator attack 338 rate than slow growing. If the prey's infectivity e SI is high, only a small fraction α of the 339 prey population needs to be infective to escape the extinction. Prey growth rate 340 r C =10.

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342 If the prey is a specialist such that it consumes only the predator (r C =0), then the 18 344 low prey growth rate may keep the prey population alive, if the prey is infective 345 enough. Because infective prey can survive when its outside growth rate r C =0, a 346 positive growth rate guarantees the survival also in the case of relatively low 347 infectivity, if the infective prey forms large part of the predator's diet.