Dan Cohen

Maximizing final yield when growth is limited by time or by limiting resources

A mathematical model is developed of growth and seed production in plants when the growing period is limited. The time course of the partition coefficient of photosynthetic products between vegetative and reproductive growth which maximizes final seed yield, i.e. the optimal strategy, has been worked out. For a given growing period ts, the optimal strategy is to switch over from 100% vegetative growth to 100% reproductive growth at a time trM = ts + rR − 1RL, where R is the net photosynthetic production per unit leaf weight, L is the weight ratio of the leaves in the whole vegetative body of the plant, and r is the fraction of the leaf weight which is re-utilized for making seeds at the end of the growing period. When ts is a random variable, the optimal transition from vegetative to reproductive growth is gradual, its spread increasing with the variance of ts. The implications of the model are discussed with respect to the expected difference between wild and crop plants, and when the growing period is terminated by lack of water in the soil.

Dispersal in patchy environments: The effects of temporal and spatial structure

A model for the evolution of dispersal in fluctuating environments is extended to environments that are temporally correlated and spatially heterogeneous. The effects of dormancy also are examined. In some cases, evolutionarily stable strategies result, and are estimated through simulations and through analytical approximations. However, in other cases, e.g., in spatially heterogeneous environments, or in the homogeneous case with negative temporal correlation, there is no intermediate evolutionarily stable strategy; rather, in some situations the “best” type, termed an evolutionarily compatible strategy (ECS), is one that can invade any other single type, but also is open to invasion by any type. For these cases, it is conjectured that there is a stable coexisting band of types, not necessarily including the ECS. In general, positive (Markovian) temporal correlations decrease the optimal dispersal fraction by increasing the average yield of non-dispersing seeds; dormancy has a similar effect. Spatial heterogeneity has some features in common with positive temporal correlations, but the structure of the autocorrelation function is more complicated. Optimal dispersal is decreased; but as mentioned above, there is no ESS in general. Diffuse competitive effects may not be understood entirely in terms of pairwise interactions, and a variety of open problems exist in characterizing interactions among multiple types.

On the Founder Effect and the Evolution of Altruistic Traits

The possible mechanisms for the establishment of altruistic traits in a popula- tion have been discussed by several workers (e.g., Haldane, 1932; Fisher, 1958; Hamilton, 1963, 1964a,b, 1973). In agreement with the terminology of previous authors, we adopt here the term altruist in its biological meaning for any inherited trait which reduces the fitness of its individual carrier but which is beneficial to the neighboring population of this carrier. In this sense, altruistic traits may be either behavioral, physiological, or biochemical. Altruistic traits can be spread and maintained in a population only if the benefit endowed by the altruistic action of an individual altruist benefits other altruistic individuals more than it benefits selfish individuals in the same population (Hamilton, 1963; Maynard- Smith, 1964). Without a kinship structure which is recognizable by the indivi- dual, this usually means that the average frequency of altruists in the area near an average altruistic individual must be greater than the frequency of altruists in the population as a whole. In general, this would be the case in any population in which mobility and mixing are not high enough to overcome the local random fluctuations in gene frequency (Wright, 1945). More specifically, whenever a population is naturally divided into (not necessarily isolated) subpopulations or demes, one may measure the demographic mobility of such a population by the probability that an arbitrary individual of an arbitrary deme has been born to parents of other demes. In this case it has been shown (Eshel, 1972) that for any altruistic trait there is a critical level of demographic mobility under which selection would always operate for the establishment of the altruist. If, on the other hand, demographical mobility surpasses another critical value, selection will favor the selfish. Moreover, these two critical values depend on the average

How portulaca seedlings avoid their neighbours

SummaryPortulaca oleracea L. seedlings do not develop in the direction of neighbours, even when these neighbours are small and distant. Neighbouring plants could be simulated by small rectangles of a plastic that resembled leaves in its spectral characteristics. Unlike seedlings, mature plants did not respond to objects that do not influence photosynthetic light. When light of equal intensity was received from all directions, Portulaca seedlings avoided the direction with higher far-red light. Portulaca is thus able to use spectral composition and direction of light as clues for the probability of the direction of future shade.

The Evolution of Flower Display and Reward

The evolution of the allocation of resources for display and reward in flowers is critically analyzed. We construct models which take into account the foraging behavior and preferences of pollinators and their effects on the pollination success of the plants. The resulting equilibrium ESS (evolutionary stable strategy) of the flowers—pollinators community is analyzed at both the short-term ecological level and the long-term coevolutionary level.

Worker-queen conflict and the evolution of social insects

Abstract A general expression for the inclusive fitness of haplodiploids is developed. The optimal investment of colony resources in eusocial Hymenoptera is then derived by maximizing the inclusive fitnesses of workers and queens subject to an ergonomic constraint. Because of assymmetries in the coefficients of relatedness, there is a genotypic “conflict of interest” between the queen and her daughters. We show how the inclusive fitness formula can be used to investigate this situation and to determine who is controlling the colony investment policy. Finally, we show that the optimization of inclusive fitness is consistent with the equilibria of a detailed genetic model.

Production of Macrobrachium rosenbergii in monosex populations: Yield characteristics under intensive monoculture conditions in cages

Abstract The production of Macrobrachium rosenbergii monosex populations was examined under intensive growth conditions in cages. It was found that an all-male population yielded 473 g/m 2 within 150 days, whereas an all-female population and a mixed population produced 248 g/m 2 and 260 g/m 2 , respectively, during the same growout period. Since the performance of the mixed population in cages is comparable to that of a normal typical juvenile population in commercial earthen ponds, with an average production of 2500–3000 kg/ha, it appears possible to obtain a yield of 4700 kg/ha within 150 days from all-male populations grown under intensive monoculture conditions. A comparison of growth performance of each of the sexes when raised alone and when raised in mixed populations showed that whereas females are strongly affected by the presence of males, resulting in growth inhibition, males are hardly influenced by the presence of females. The findings of this study call for intensive efforts in research directed towards the controlled establishment of prawn monosex populations.

Effect of androgenic gland ablation on morphotypic differentiation and sexual characteristics of male freshwater prawns, Macrobrachium rosenbergii

Mature males of the freshwater prawn, Macrobrachium rosenbergii (de Man), may change from one to another morphotype, according to a set sequence. Small males may develop into orange-claw males and orange-claw males into dominant blue-claw males. Each of the three morphotypes demonstrates distinctive reproductive behavior and secondary sexual characteristics. The role of the androgenic gland in this morphotypic transformation was examined experimentally by bilateral androgenic gland ablation (andrectomy) of small males and orange-claw males. For andrectomy initiated in the small male morphotype, transformation to the next morphotype was permitted (orange-claw), but subsequent transformation to the blue-claw morphotype was blocked. Andrectomy of orange-claw males did not prevent transformation into the blue-claw. Andrectomy on both small and orange-claw males caused disappearance of the genital papillae and atrophy of the sperm ducts and testes. The growth rates of the andrectomized small and orange-claw males were significantly lower than those of the unoperated and sham-operated controls. We conclude that androgenic gland factors control not only the differentiation of male secondary sexual characteristics but also morphotypic differentiation. Bioassays based on the results of this study will be instrumental in the characterization of such a factor(s).

The Interaction between Dispersal and Dormancy Strategies in Varying and Heterogeneous Environments

Natural environments are heterogeneous in space and time. This heterogeneity favors the evolution of mechanisms such as dispersal of seeds or other propagules, because dispersal allows escape in space from locally unfavorable conditions and, on the average, exploitation of ones temporarily more favorable (Levin 1976, Motro 1982). Similarly, delayed germination may be advantageous because it allows seeds to avoid exposure to unfavorable conditions and, on the average, to exploit more favorable ones (Cohen 1966, Templeton and Levin 1979).

An optimal policy for the metabolism of storage materials in unicellular algae.

A theoretical model is presented for the evaluation of the optimal policy of the metabolism of storage materials in unicellular algae, with some experimental testing of the model. Optimality is defined as the maximization of the long term growth rate and/or survival of the population. The main predictions of the analysis of the optimal policy are: (1) The cells divide only during the night. (2) The energy for division is provided by storage materials produced during the day. Under most conditions, storage materials are produced in the exact amount needed to supply the energy required during the night. (3) Storage materials are produced only toward the end of the light period, while the production machinery is synthesized at the beginning of the light period. (4) The weight fraction of storage materials, S , increases when the light intensity increases. The duration of the synthesis of S decreases when light intensity increases, i.e. it starts later in the day. (5) Day length has only a small effect on S and even a smaller effect on the duration of the synthesis. Predictions (1), (3), (4) and (5) have been tested and confirmed experimentally with Chlamydomonas reinhardi . The theoretical and experimental results, and results from the literature, support the optimality hypothesis, and reject the current hypothesis that storage materials are synthesized only when there is a current excess of energy supply.