Consider a patch of favorable habitat surrounded by unfavorable habitat and assume that due to a shifting climate, the patch moves with a fixed speed in a one-dimensional universe. Let the patch be inhabited by a population of individuals that reproduce, disperse, and die. Will the population persist? How does the answer depend on the length of the patch, the speed of movement of the patch, the net population growth rate under constant conditions, and the mobility of the individuals? We will answer these questions in the context of a simple dynamic profile model that incorporates climate shift, population dynamics, and migration. The model takes the form of a growth-diffusion equation. We first consider a special case and derive an explicit condition by glueing phase portraits. Then we establish a strict qualitative dichotomy for a large class of models by way of rigorous PDE methods, in particular the maximum principle. The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate. It is also shown that range shift may be easier to detect at the expanding front, simply because it is considerably steeper than the retreating back.

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Can sex allocation be controlled by haplo-diploid organisms where both males and females arise from fertilised eggs but males become effectively haploid by paternal genome loss (pseudo-arrhenotoky)? If so, how does the control of mean and variance of sex allocation compare with haplo-diploids where males arise from unfertilised eggs (arrhenotoky)? These questions are addressed by experiments with two species of pseudo-arrhenotokous plant-inhabiting predatory mites: Typhlodromus occident&s Nesbitt and Phytoseiulus persimilis Athias-Henriot (Atari: Phytoseiidae).It is shown that females conditionally adjust offspring sex ratio in response to the presence of conspecifics or their cues. The sex ratios are precise in that their variance is less than expected from a binomial distribution. Because eggs are produced one-by-one at regular intervals, it is not possible to designate separate clutches, thus rendering conventional clutch-based estimates of precision inadequate. To remedy this a range of time scales was investigated and this showed an increase in precision with time scale (and hence "clutch" size). Markovian analysis of son-daughter sequences showed that this increase arises only if the predator "memorizes" the mean sex ratio of all eggs laid before.Control of mean and variance of sex allocation is selectively advantageous when local mating groups vary in size and are usually small, as is the case for the phytoseiid mites under study. Predictions of the optimal sex ratio from local mate competition models were in agreement for T. occident&is. However, P. persimilis, * Author for correspondence 649 650 Nagelkerke and Sabelis exhibited a stronger female bias than predicted. We suggest that this may be due to selection levels operating at a larger spatial scale than the local mating group. Control of sex allocation seems as good as in arrhenotokous arthropods, suggesting that -in this respect -pseudo-arrhenotoky is not at a disadvantage compared to arrhenotoky.

Evolution of pseudo-arrhenotokySabelis, M.W.; Nagelkerke, C.J. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. In arrhenotokous arthropods, males arise from unfertilized eggs. Hence, by controlling the fertilization process mothers can adjust the sex ratio in their offspring. In pseudo-arrhenotokous phytoseiid mites, however, males are haploid, but arise from fertilized eggs. The haploid state is achieved through elimination of the paternal chromosome set during embryonic development. It is shown in this paper that phytoseiid females can control the sex ratio in their offspring and that this control seems as flexible as in arrhenotokous arthropods. As predicted by current evolutionary theory of sex allocation, sex ratios approached half males/half females under random mating, whereas a female bias was observed under sib-mating. The importance of these results for understanding the adaptive significance of pseudo-arrhenotoky is discussed. It is suggested that arrhenotoky is selected for when there is a substantial risk to the females of remaining unmated. When this risk of becoming a 'wall-flower' is low, pseudo-arrhenotoky may evolve because it retains the possibility to reinstal lost genetic information in the maternally derived chromosome by using the paternal chromosome as a template for DNA-repair. The retention of the diploid state in males during embryonic development may thus have certain advantages. It is argued that pseudo-arrhenotoky may be an adaptive genetic system under certain conditions, and not an unstable system that readily reverts to diploidy or evolves towards arrhenotoky or thelytoky.

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Spatial distribution in the two collembolan species Tomocerus minor and Orchesella cincta is greatly influenced by the distribution of the environmental factors water and food. T. minor is totally restricted in distribution to water-saturated places, where it forms spaced-out aggregations. O. cincta assembles in water-saturated places during ecdysis and subsequent reproduction. This leads to dense contact-aggregations. 'Dispersal' follows during the feeding period, probably caused by food shortage, presence of other species and/or saturated conditions in the aggregation site. After feeding, orientation toward water-saturated places occurs by means of orthokinetic reactions and the aggregations are reestablished. The effect of this 'periodical aggregation" for the population is discussed.