For An. pseudopunctipennis, mean observed values of the duration of the gonotrophic cycle at constant temperatures in laboratory conditions are in agreement with results from An. albimanus, another Neotropical Anopheles . Egg maturation in An. pseudopunctipennis is temperature dependant and the egg-laying is light dependant: These night active mosquitoes stop laying eggs during day time. One single An. pseudopunctipennis will lay eggs once. This behaviour is not shared by all mosquito species. For example, one Ae. aegypti placed in the same experimental conditions as for An. pseudopunctipennis will lay eggs for two or three consecutive days and may even hold its eggs (, Lardeux, pers. obs.) complicating even more the computation of the duration of its gonotrophic cycle. As for a batch of An. pseudopunctipennis is concerned, several consecutive night are needed until the last mosquito has laid its eggs. The range of nights over which oviposition takes place is wider when temperature decreases, with a minimum variation of three nights at 31°C which seems to be the temperature at which egg maturation is the shortest (range 1.8 – 3.9 days). In general terms, the variance is larger with decreasing temperatures. So during the cold season, not only is the mean time for the first cohort of mosquitoes to lay eggs late, but also few mosquitoes will lay eggs each consecutive night.
A model of physiological time development should take into account this number of successive ovipositing nights. To achieve this, the present model contained several sub-models corresponding to the successive mosquito cohorts. However, another way of using the model could be to parameterize it with the overall mean estimates of the parameters of Table 2 and simply weight it by the proportion of mosquitoes that laid eggs in the different cohorts. Four cohorts were (sub-) modelled, representing the egg development history of ≈80–100% of mosquitoes when temperatures are > 20°C. When temperatures are low (< 20°C), An. pseudopunctipennis is basically inactive and transmission greatly reduced, even disappearing. As a consequence, the cohorts observed in the laboratory at low temperature are almost virtual in nature. Therefore, the four cohorts which are part of the model are sufficient to describe the gonotrophic cycle duration in the temperature range where An. pseudopunctipennis usually lives, and they may account for almost all mosquitoes laying eggs.
For simplicity of the analysis, only results from the first cohort of An. pseudopunctipennis were presented, giving predicted minimum values for the gonotrophic length. However, it is easy to complete the analysis for that mosquito as each following cohort appears 24 h later.
The minimum number of cohorts was three and was observed at optimal (high) temperatures, and is therefore a minimum number to correctly describe the dynamics of the gonotrophic cycle of An. pseudopunctipennis. As such, the gonotrophic cycle duration cannot be summarized by only one single value (i.e., an overall mean of all cycle lengths of all mosquitoes from all the cohorts) as it is usually done. The suggested presentation of the gonotrophic cycle duration by means of a mathematical vector of n triplets (d
), representing each of the n cohorts laying eggs with their relative proportion P
and the mean value (and variance) of the cohort cycle duration d
)) may be an alternative. However, such a vector should be computed for each period of varying temperature, at least on a season basis or less (for example, on a monthly basis) if temperature variations are on a shorter scale. These findings are important in precise modelling of transmission and should be taken into account whatever the mosquito species under study. Some attempts have been made to incorporate the influence of temperature via the gonotrophic cycle in transmission dynamics modelling . These kinds of models could be improved using a physiological time approach and, for the gonotrophic cycle duration, the use of the suggested mathematical vector.
In the field, the situation may be even more complicated as a significant proportion of An. pseudopunctipennis (≈5%) has tendency to take several blood meals to complete the maturation of its eggs, thus increasing the overall vectorial capacity . If so, the risk of transmission is not only directly linked to the gonotrophic cycle duration. At least some mosquitoes may transmit more frequently than predicted. Transmission may thus occur and this may partly explain the (low) levels of transmission by An. pseudopunctipennis despite apparently weak components of its vectorial capacity .
The time spent to search for a host (phase 1 of Belekmishev) may also be significant for An. pseudopunctipennis as indicated by the significant proportion of mosquitoes with "advanced" ovary development at the time of (re)feeding. If so, predictions from the physiological time model are minimum values of the cycle duration for An. pseudopunctipennis and they should be slightly adjusted upwards to give more accurate estimations. This is particularly true during winter conditions when temperatures are lower. The model also gives a value of ≈36°C for the upper temperature (i.e., temperature at which rates are the fastest). This value is biologically realistic and in accordance with the temperature of 35°C of the experiments where apparently the development rate was the fastest for at least 70% of the tested mosquitoes. As such, the computed value indicates that the model may correctly describe the phenomenon.
Indeed, other factors than the gonotrophic cycle length have an impact on the vectorial capacity, such as mosquito densities, mosquito longevity, and the duration of the extrinsic cycle of the parasite. All of them are more or less influenced by temperatures [36–38]. The definition of vectorial capacity assumes that the length of the gonotrophic cycle and survival are independent parameters. It is not always the case and present results on An. pseudopunctipennis, although in laboratory conditions, indicate that they are not: as temperature decreased, the length of the gonotrophic cycle and the mosquito survival increased. If An. pseudopunctipennis longevity is higher when temperatures are low, it may then live long enough to transmit, even if it takes longer to complete its gonotrophic cycle. The extension in survival at low temperatures could in theory nullify the decreasing effect of a long gonotrophic cycle on transmission. As vectorial capacity (and R
0) is more influenced by survival than by the gonotrophic cycle length, it is probable that effects of low temperatures on the gonotrophic cycle will be compensated (and even overwhelmed) by increased survival, generating transmission. At higher temperatures, higher vector mortality may limit the transmission although the gonotrophic cycle is shorter. The question is then if the mosquitoes have enough time to transmit before dying. In nature, other ecological factors than temperature may interfere with mortality, complicating such analysis. Therefore, transmission variations cannot be simply interpreted by only variations in the gonotrophic cycle length. However, for An. pseudopucntipennis, model predictions of the gonotrophic cycle duration are qualitatively correlated with malaria transmission patterns observed in the four sites studied. Therefore, the model can in a rough and cautiously first approach be used to better understand transmission variations in the distribution range of the vector in Bolivia. However, more research is needed to completely model the influence of temperature on An. pseudopunctipennis survival and to include the results in a temperature-dependant model of vectorial capacity embodying not only survival, but also the parasite extrinsic cycle and the gonotrophic cycle as others temperature-dependent phenomenon. It is likely that temperature will be revealed to be an important factor that will explain, along with a poor human biting index , why An. pseudopunctipennis is a poor malaria vector as compared to other Anopheles species (An. darlingi in the Amazon region of Bolivia for example, or other African species).
Temperature might also account for the unstable time/season pattern (in both the long and short terms) of An. pseudopunctipennis transmission in reputed malaria areas. Used with field temperature records, the model showed that the predicted gonotrophic cycle of An. pseudopunctipennis in Bolivia is variable following a seasonal pattern and that the variations of amplitudes depend also on the geographic location. The predicted variations are more pronounced at high altitudes where temperature conditions may vary greatly, and also in some lowland places where climatic phenomenon such as the "surazo" prevails (i.e., in the foothills of the Andes, from the south of Bolivia up to the latitude of Santa Cruz (≈ 17.8°W). The "surazo" events have a strong influence in the Bolivian lowlands on the distribution of biocenosis and ecosystems and are responsible for the southern limit of most Amazonian animals and plants in the lowlands . Moreover, these polar air masses and cold winds can lower the ambient temperature by more than 20°C in one day. In winter, the frequency of such events is more or less of twice per month and each lasts a mean of 2–6 days . The locality of Yacuiba is characteristic of "surazo" events. There, the gonotrophic cycle of An. pseudopunctipennis can be very long, as illustrated by the model predictions, due to these periods of cold air influence, limiting transmission strength. On the other hand, during summer, cycle duration can be very short, improving the vectorial capacity of the mosquito. As a consequence, malaria transmission is indeed more active during summer as confirmed by epidemiological data of human cases . "Surazos" are less active in the inter-Andean valleys. As such, regions where the gonotrophic cycle of An. pseudopunctipennis is more or less constant and short are the mesothermic Andean valleys for which Mataral and Aiquile could be prototype localities. Results of ecological niche modelling for An. pseudopunctipennis using MAXENT algorithm  showed that this mosquito vector is well present in these ecological regions, where temperature conditions are also optimal for a short gonotrophic cycle. Epidemiological data confirm that these valleys account for the majority of malaria cases due to An. pseudopunctipennis . With predicted short cycle durations and small variances all year long, transmission in Mataral is likely to be almost constant if parasites and mosquitoes are present in sufficient densities. In Aiquile, malaria transmission is more likely during summer but less active than in Mataral. At the edges of its distribution range, An. pseudopunctipennis encounters less favourable climatic condition for a short gonotrophic cycle and as a consequence, epidemiological data confirm that transmission is less active in these areas. In Sucre for example, the predicted gonotrophic cycle length is always > 10 days, impeding malaria transmission (even if mosquito survival may be increased by low temperatures, the extrinsic cycle of the parasite is too long to enable transmission). A brief outline of the various geographical and seasonal situations encountered in Bolivia and their impact on the predicted gonotrophic cycle duration of An. pseudopunctipennis is summarized in Table 3 which could be used as a first rough approach for cycle duration estimates throughout Bolivia.
It is known that insects avoid extreme temperatures and may respond to such stress with a kind of behavioural regulation. Mosquitoes can regulate their body temperature by moving into adequate areas . Within the normal range of temperature in which they are active, mosquitoes have a preferred range in which, given the choice, they tend to remain for relatively long periods, in particular when they digest their bloodmeals. As such, one might doubt the model predictions if inadequate temperature records are used to run it. However, with the Mataral example, the model gave similar predictions when using hourly temperatures records in a field resting site (the cave) for An. pseudopunctipennis to when using the maximum/minimum values from a close meteorological station. Consequently, meteorological station records can reasonably be used to model the gonotrophic cycle duration in many field situations in Bolivia.
The model uses a S-shaped curve for developmental rates which embodies the assumption that developmental rates adjust instantaneously to changes in temperature. This is reasonable given the gradual nature of field temperature curves. Another assumption is the lack of synergism due to fluctuating versus constant temperatures. This second assumption is more tenuous  but has been found to be approximately true for many situations, and in particular for An. pseudopunctipennis for which model predictions in variable temperature experiments were identical to the observed values for the cycle duration.
Long before, other attempts have been made to model the duration of the gonotrophic cycle duration of mosquitoes taking into account temperature variations with empirical functions [37, 44]. The flexibility of the present model can encompass complex situations of variable temperatures and can be adapted to a variety of bloodsucking insects. Climatic conditions and amongst them temperature variations are more and more taken into account in the light of the global warming phenomenon to predict changes in species niche occupation and also to model changes in vector transmission risks [45–48], even in Europe [49, 50]. The model presented here is a first step toward the modelling of malaria risk transmission in Bolivia that could be used in a GIS analysis to map the vectorial capacity of Anopheles pseudopunctipennis (or better, the basic reproduction index R
0 of the transmitted Plasmodium parasite that encompasses all the parameters of the vectorial capacity of the mosquito and some disease characteristics) .