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1. Social trematode parasites increase standing army size in areas of greater invasion threat

   https://doi.org/10.1098/rsbl.2019.0765  

   Resetarits, Emlyn J.; Torchin, Mark E.; Hechinger, Ryan F. (February 2020, Biology Letters)

   Organisms or societies are resource limited, causing important trade-offs between reproduction and defence. Given such trade-offs, optimal allocation theory predicts that, for animal societies with a soldier caste, allocation to soldiers should reflect local external threats. Although both threat intensity and soldier allocation can vary widely in nature, we currently lack strong evidence that spatial variation in threat can drive the corresponding variation in soldier allocation. The diverse guild of trematode parasites of the California horn snail provides a useful system to address this problem. Several of these species form colonies in their hosts with a reproductive division of labour including a soldier caste. Soldiers are non-reproductive and specialized in defence, attacking and killing invading parasites. We quantified invasion threat and soldier allocation for 168 trematode colonies belonging to six species at 26 sites spread among 10 estuaries in temperate and tropical regions. Spatial variation in invasion threat was matched as predicted by the relative number of soldiers for multiple parasite species. Soldier allocation correlated with invasion threat at fine spatial scales, suggesting that allocation is at least partly inducible. These results may represent the first clear documentation of a spatial correlation between allocation to any type of caste and a biotic selective agent. 

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2. Sources of variation in maternal allocation in a long‐lived mammal

   https://doi.org/10.1111/1365-2656.13243  

   Macdonald, Kaitlin R.; Rotella, Jay J.; Garrott, Robert A.; Link, William A. (October 2020, Journal of Animal Ecology)

   1. Life history theory predicts allocation of energy to reproduction varies with maternal age, but additional maternal features may be important to the allocation of energy to reproduction. 2. We aimed to characterize age-specific variation in maternal allocation and assess the relationship between maternal allocation and other static and dynamic maternal features. 3. Mass measurements of 531 mothers and pups were used with Bayesian hierarchical models to explain the relationship between diverse maternal attributes and both the proportion of mass allocated by Weddell seal mothers, and the efficiency of mass transfer from mother to pup during lactation as well as the weaning mass of pups. 4. Our results demonstrated that maternal mass was strongly and positively associated with the relative reserves allocated by a mother and a pup's weaning mass but that the efficiency of mass transfer declines with maternal parturition mass. Birthdate was positively associated with proportion mass allocation and pup weaning mass, but mass transfer efficiency was predicted to be highest at the mean birthdate. The relative allocation of maternal reserves declined with maternal age but the efficiency of mass transfer to pups increases, suggestive of selective disappearance of poor-quality mothers. 5. These findings highlight the importance of considering multiple maternal features when assessing variation in maternal allocation. 

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3. Computing Pareto-Optimal and Almost Envy-Free Allocations of Indivisible Goods

   https://doi.org/10.1613/JAIR.1.15414  

   Garg, Jugal; Murhekar, Aniket (May 2024, Journal of Artificial Intelligence Research)

   We study the problem of fair and efficient allocation of a set of indivisible goods to agents with additive valuations using the popular fairness notions of envy-freeness up to one good (EF1) and equitability up to one good (EQ1) in conjunction with Pareto-optimality (PO). There exists a pseudo-polynomial time algorithm to compute an EF1+PO allocation and a non-constructive proof of the existence of allocations that are both EF1 and fractionally Pareto-optimal (fPO), which is a stronger notion than PO. We present a pseudopolynomial time algorithm to compute an EF1+fPO allocation, thereby improving the earlier results. Our techniques also enable us to show that an EQ1+fPO allocation always exists when the values are positive and that it can be computed in pseudo-polynomial time.We also consider the class of k-ary instances where k is a constant, i.e., each agent has at most k different values for the goods. For such instances, we show that an EF1+fPO allocation can be computed in strongly polynomial time. When all values are positive, we show that an EQ1+fPO allocation for such instances can be computed in strongly polynomial time. Next, we consider instances where the number of agents is constant and show that an EF1+PO (likewise, an EQ1+PO) allocation can be computed in polynomial time. These results significantly extend the polynomial-time computability beyond the known cases of binary or identical valuations.We also design a polynomial-time algorithm that computes a Nash welfare maximizing allocation when there are constantly many agents with constant many different values for the goods. Finally, on the complexity side, we show that the problem of computing an EF1+fPO allocation lies in the complexity class PLS. 

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4. Trade‐offs in above‐ and below‐ground biomass allocation influencing seedling growth in a tropical forest

   https://doi.org/10.1111/1365-2745.13543  

   Umaña, María Natalia; Cao, Min; Lin, Luxiang; Swenson, Nathan G.; Zhang, Caicai; Liu, ed., Xiaojuan (November 2020, Journal of Ecology)

   Abstract Plants allocate biomass to different organs in response to resource variation for maximizing performance, yet we lack a framework that adequately integrates plant responses to the simultaneous variation in above‐ and below‐ground resources. Although traditionally, the optimal partition theory (OPT) has explained patterns of biomass allocation in response to a single limiting resource, it is well‐known that in natural communities multiple resources limit growth. We study trade‐offs involved in plant biomass allocation patterns and their effects on plant growth under variable below‐ and above‐ground resources—light, soil N and P—for seedling communities.We collected information on leaf, stem and root mass fractions for more than 1,900 seedlings of 97 species paired with growth data and local‐scale variation in abiotic resources from a tropical forest in China.We identified two trade‐off axes that define the mass allocation strategies for seedlings—allocation to photosynthetic versus non‐photosynthetic tissues and allocation to roots over stems—that responded to the variation in soil P and N and light. Yet, the allocation patterns did not always follow predictions of OPT in which plants should allocate biomass to the organ that acquires the most limiting resource. Limited soil N resulted in high allocation to leaves at the expense of non‐photosynthetic tissues, while the opposite trend was found in response to limited soil P. Also, co‐limitation in above‐ and below‐ground resources (light and soil P) led to mass allocation to stems at the expense of roots. Finally, we found that growth increased under high‐light availability and soil P for seedlings that invested more in photosynthetic over non‐photosynthetic tissues or/and that allocated mass to roots at the expense of stem.Synthesis. Biomass allocation patterns to above‐ and below‐ground tissues are described by two independent trade‐offs that allow plants to have divergent allocation strategies (e.g. high root allocation at the expense of stem or high leaf allocation at the expense of allocation to non‐photosynthetic tissues) and enhance growth under different limiting resources. Identifying the trade‐offs driving biomass allocation is important to disentangle plant responses to the simultaneous variation in resources in diverse forest communities. 

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5. Fair and Efficient Allocations of Chores under Bivalued Preferences

   https://doi.org/10.1609/aaai.v36i5.20436  

   Garg, Jugal; Murhekar, Aniket; Qin, John (June 2022, Proceedings of the AAAI Conference on Artificial Intelligence)

   We study the problem of fair and efficient allocation of a set of indivisible chores to agents with additive cost functions. We consider the popular fairness notion of envy-freeness up to one good (EF1) with the efficiency notion of Pareto-optimality (PO). While it is known that EF1+PO allocations exists and can be computed in pseudo-polynomial time in the case of goods, the same problem is open for chores. Our first result is a strongly polynomial-time algorithm for computing an EF1+PO allocation for bivalued instances, where agents have (at most) two disutility values for the chores. To the best of our knowledge, this is the first non-trivial class of chores to admit an EF1+PO allocation and an efficient algorithm for its computation. We also study the problem of computing an envy-free (EF) and PO allocation for the case of divisible chores. While the existence of EF+PO allocation is known via competitive equilibrium with equal incomes, its efficient computation is open. Our second result shows that for bivalued instances, an EF+PO allocation can be computed in strongly polynomial-time. 

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